@@ -1,7273 +1,7273 @@
-%                          REDUCE BIBLIOGRAPHY
-
-%                              Part 1:  A-E
-
-% Copyright (c) 1995 RAND.  All Rights Reserved.
-
-% Additions and corrections are solicited.  Please send them, in the
-% same format as these entries if possible, to reduce at rand.org.
-
-
-@ARTICLE{Abbott:85,
- AUTHOR = "J. A. Abbott and R. J. Bradford and J. H. Davenport",
- TITLE = "A Remark on Factorisation",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1985, VOLUME = 19, NUMBER = 2, PAGES = "31-33", MONTH = "May"}
-
-@INPROCEEDINGS{Abbott:86,
- AUTHOR = "J. A. Abbott and R. J. Bradford and J. H. Davenport",
- TITLE = "The {Bath} Algebraic Number Package",
- BOOKTITLE = "Proc. of {SYMSAC} '86",
- YEAR = 1986, PAGES = "250-253"}
-
-@INPROCEEDINGS{Abbott:87,
- AUTHOR = "J. A. Abbott and J. H. Davenport",
- TITLE = "Polynomial Factorization: An Exploration of {Lenstra's}
-Algorithm",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes in Computer Science",
- YEAR = 1987, VOLUME = 378, PAGES = "391-402",
- PUBLISHER = "Springer-Verlag"}
-
-@INPROCEEDINGS{Abbott:87a,
- AUTHOR = "J. A. Abbott",
- TITLE = "Integration: Solving the {Risch} Differential Equation",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "465-467",
- PUBLISHER = "Springer-Verlag"}
-
-@PHDTHESIS{Abbott:88,
- AUTHOR = "J. A. Abbott",
- TITLE = "Factorisation of Polynomials over Algebraic Number Fields",
- SCHOOL = "Univ. of Bath, England",
- YEAR = 1988}
-
-@ARTICLE{Abbott:88a,
- AUTHOR = "J. A. Abbott and J. H. Davenport",
- TITLE = "A Remark on a Paper by {Wang}: Another Surprising Property of 42",
- JOURNAL = "Math. Comp.",
- YEAR = 1988, VOLUME = 51, PAGES = "837-839"}
-
-@INPROCEEDINGS{Abbott:89,
- AUTHOR = "J. A. Abbott",
- TITLE = "Recovery of Algebraic Numbers from their p-Adic Approximations",
- BOOKTITLE = "Proc. of {ISSAC} '89", PUBLISHER = "{ACM} Press, New York",
- YEAR = 1989, PAGES = "112-120"}
-
-@TECHREPORT{Abbott:89a,
- AUTHOR = "J. A. Abbott and R. J. Bradford and J. H. Davenport",
- TITLE = "A Remark on the Multiplication of Sparse Polynomials",
- NUMBER = "TR 89-21", YEAR = 1989,
- INSTITUTION = "School of Mathematical Sciences, University of Bath"}
-
-@INPROCEEDINGS{Abdali:88,
- AUTHOR = "S. K. Abdali and D. S. Wise",
- TITLE = "Experiments with Quadtree Representation of Matrices",
- BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
- YEAR = 1988, VOLUME = 358, PAGES = "96-108"}
-
-@ARTICLE{Abiezzi:83,
- AUTHOR = "Salim S. {Abi-Ezzi}",
- TITLE = "Clarification to the Symbolic Mode in {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1983, VOLUME = 17, NUMBER = "3 and 4", PAGES = "43-47",
- MONTH = "August and November"}
-
-@INPROCEEDINGS{Abramov:91,
- AUTHOR = "S. A. Abramov and K. Yu. Kvansenko",
- TITLE = "Fast Algorithms to Search for the Rational Solutions of Linear
-Differential Equations with Polynomial Coefficients",
- EDITOR = "Stephen M. Watt",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- PUBLISHER = "ACM Press", ADDRESS = "Maryland", YEAR = 1991,
- PAGES = "267-270"}
-
-@TECHREPORT{Abramov:91a,
- AUTHOR = "S. A. Abramov and K. Yu. Kvashenko",
- TITLE = "Fast search of a certain type solutions of linear ordinary
-differential equations with polynomial coefficients",
- INSTITUTION = "Computer Center of the USSR, Academy of Science, Moscow",
- YEAR = 1991}
-
-@InProceedings{Adamchik90,
-  author =      "V. S. Adamchik and O. I. Marichev",
-  title =       "The Algorithm for calculating Integrals of
-                 Hypergeometric type functions and its realization in
-                 {REDUCE} System",
-  booktitle =   "Proceedings of the 1990 International Symposium on
-                 Symbolic and Algebraic Computation",
-  year =        "1990",
-  editor =      "S. Watanabe and Morio Nagata",
-  pages =       "212-224",
-  organization =        "ACM",
-  publisher =   "Addison-Wesley"
-}
-
-@ARTICLE{Adams:83,
- AUTHOR = "K. J. Adams",
- TITLE = "Analytic Estimates for the Dynamic Aperture of Nonlinear Lattices",
- JOURNAL = "IEEE Trans. Nucl. Sci.",
- YEAR = 1983, VOLUME = "NS-30", PAGES = "2436-2438",
- COMMENT = {"For an accelerator lattice{\ldots}" {REDUCE} was used to obtain low
-order coefficients in the calculation of the amplitude.}}
-
-@ARTICLE{Adkins:83,
- AUTHOR = "G. S. Adkins",
- TITLE = "Analytic Evaluation of an {O}($\alpha$) Vertex Correction to the
-Rate of Orthopositronium",
- JOURNAL = "Phys. Rev. A",
- YEAR = 1983, VOLUME = 27,  PAGES = "530-532",
- ABSTRACT = {The order-$\alpha$ correction to the lowest order
-orthopositronium decay rate due to the two outer-vertex graphs obtained in
-analytic form.}}
-
-@ARTICLE{Adkins:83a,
- AUTHOR = "G. S. Adkins and  F. R. Brown",
- TITLE = "Rate for Positronium Decay to Five Photons",
- JOURNAL = "Phys. Rev. A",
- YEAR = 1983, VOLUME = 28, PAGES = "1164-1165",
- COMMENT = {{REDUCE} used to calculate trace of $\gamma$ matrices.  Large
-calculation.}}
-
-@ARTICLE{Adkins:85,
- AUTHOR = "G. S. Adkins",
- TITLE = "Inner-Vertex Contributions to the Decay Rate of Orthopositronium",
- JOURNAL = "Phys. Rev. A",
- YEAR = 1985, VOLUME = 31, PAGES = "1250-1252",
- COMMENT = {{REDUCE} trace calculations.  "In this paper the order-$\alpha$
-contribution to the inner-vertex graphs to the decay rate of
-orthopositronium is obtained in analytic form."}}
-
-@ARTICLE{Aguilera-Navarro:87,
- AUTHOR = "V. C. Aguilera-Navarro and  R. Guardiola and C. Keller and
-M. de Llano and M. Popovic and M. Fortes",
- TITLE = "Van der {Waals} Perturbation Theory for Fermion and Boson
-Ground-State Matter",
- JOURNAL = "Phys. Rev. A",
- YEAR = 1987, VOLUME = 35, PAGES = "3901-3910",
- COMMENT = {Uses computer algebra to rearrange ideal-gas-based low-density
-expansions; to them {REDUCE} or {MACSYMA} provide just the expertise they
-require to substitute forms into equations, and so makes their
-formulation possible.}}
-
-@TECHREPORT{Akselrod:90,
- AUTHOR = "I.R. Akselrod and V.P. Gerdt and V.E. Kovtun and V.N. Robuk",
- TITLE = "Construction of a {Lie} algebra by a subset of generators and
-commutation relations",
- INSTITUTION = "J.I.N.R.", YEAR = 1990, TYPE = "Preprint",
- NUMBER = "E5-90-508",
- ABSTRACT = {The problem of constructing the quotient algebra for a free
-{Lie} algebra over an ideal given by a subset of generators and commutation
-relations is investigated.  The method proposed to solve this problem can be
-applied in particular for constructing a {L-A} pair for nonlinear evolution
-equations.  The algorithm is based on the concept of {Hall} basis for a
-free {Lie} algebra and is implemented in the computer algebra system
-{REDUCE}.}}
-
-@ARTICLE{Aldins:69,
- AUTHOR = "J. Aldins and S. J. Brodsky and A. J. Dufner and
-T. Kinoshita",
- TITLE = "Photon-Photon Scattering Contribution to the Sixth
-Order Magnetic Moments of the Muon and Electron",
- JOURNAL = "Phys. Rev. Lett.",
- YEAR = 1969, VOLUME = 23, PAGES = "441-443"}
-
-@TECHREPORT{Alekseev:86,
- AUTHOR = "A. I. Alekseev and V. F. Edneral",
- TITLE = "Tensor Structure of Axial Gauge Polarization Operator in the
-Infrared Region",
- INSTITUTION = "IHEP", YEAR = 1986, TYPE = "Preprint",
- NUMBER = "86-46"}
-
-@ARTICLE{Alekseev:87,
- AUTHOR = "A. I. Alekseev and V. F. Edneral",
- TITLE = "Tensor Structure of Gluon Polarization Operator in the
-Axial Gauge for Infra-Red Region",
- JOURNAL = "Journal of Nuclear Physics",
- YEAR = 1987, PAGES = "1105-1114"}
-
-@TECHREPORT{Alekseev:87a,
- AUTHOR = "A. I. Alekseev and V. F. Edneral",
- TITLE = "On Evaluation of {Feynman} Integrals in Axial Gauge",
- INSTITUTION = "IHEP", YEAR = 1987, TYPE = "Preprint",
- NUMBER = "87-118",
- ABSTRACT = {The recurrent algorithm for axial gauge calculations of
-one-loop massless {Feynman} integrals in the n-dimensional
-momentum space is described.  The algorithm we suggest is
-realized on the basis of {REDUCE} system and presented as
-a procedure.  It is rather effective for cumbersome
-combinations of those integrals.}}
-
-@ARTICLE{Alfeld:82,
- AUTHOR = "P. Alfeld",
- TITLE = "Fixed Point Iteration with Inexact Function Values",
- JOURNAL = "Math. Comp.",
- YEAR = 1982, VOLUME = 38, PAGES = "87-98",
- COMMENT = {Numerical analysis generating an improved iterative scheme.
-"The technical manipulations in this paper were carried out using the
-symbol manipulation language {REDUCE}."}}
-
-@TECHREPORT{Amirkhanov:87,
- AUTHOR = "I. V. Amirkhanov and E. P. Zhidkov and I. E. Zhidkova",
- TITLE = "The Conditions of Bounding of the Oscillation Amplitudes of
-Charge Particle within the Resonance Vicinity Investigations",
- INSTITUTION = "J.I.N.R., Dubna", YEAR = 1987, NUMBER = "P11-87-452"}
-
-@INPROCEEDINGS{Amirkhanov:91,
- AUTHOR = "I.V. Amirkhanov and E.P. Zhidkov and I.E. Zhidkova",
- TITLE = "The Betatron Oscillations in the Vicinity of Nonlinear Resonance
-in Cyclic Accelerator Investigation",
- EDITOR = "Stephen M. Watt",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- PUBLISHER = "ACM Press", ADDRESS = "Maryland", YEAR = 1991,
- PAGES = "452-453"}
-
-@ARTICLE{Antweiler:89,
- AUTHOR = "Werner Antweiler and Andreas Strotmann and Volker Winkelmann",
- TITLE = "A {\TeX}-{REDUCE}-Interface",
- JOURNAL = "SIGSAM Bulletin",
- YEAR = 1989, VOLUME = 23,
- MONTH = "February", PAGES = "26-33"}
-
-@ARTICLE{Appelquist:70,
- AUTHOR = "T. W. Appelquist and S. J. Brodsky",
- TITLE = "The Order $\alpha^{2}$ Electrodynamic Corrections to
-the {Lamb} Shift",
- JOURNAL = "Phys. Rev. Letters",
- YEAR = 1970, VOLUME = 24, PAGES = "562-565"}
-
-@TECHREPORT{Arbuzov:86,
- AUTHOR = "B. A. Arbuzov and E. E. Boos and A. I. Davydychev",
- TITLE = "Infrared Asymptotics of Gluonic {Green} Functions
-in Covariant Gauge",
- INSTITUTION = "IHEP", YEAR = 1986, TYPE = "Preprint",
- NUMBER = "86-123"}
-
-@TECHREPORT{Kendall:93,
- AUTHOR = "Gerard Ben Arous and Michael Cranston and Wilfrid S. Kendall",
- TITLE = "Coupling constructions for hypoelliptic diffusions:  Two
-examples",
- INSTITUTION = "University of Warwick, Dept. of Statistics", YEAR = 1993,
- MONTH = "October", TYPE = "Research Report", NUMBER = 261,
- ABSTRACT = {Coupling constructions are given for two examples of
-hypoelliptic diffusions with smooth coefficients:  the two-dimensional
-diffusion formed by scalar Brownian motion and its time integral; and the
-three-dimensional diffusion formed by planar Brownian motion and its
-stochastic area.  In both cases it is shown that one can construct
-co-adapted copies of Brownian motion such that the corresponding copies of
-the diffusion will couple in finite time.  The first case uses stopping
-time arguments; the second is computationally more involved and the
-solution was found using a computer algebra implementation of stochastic
-calculus (though the final proof has been checked completely by hand).
-Questions are formulated about coupling problems for more general
-hypoelliptic diffusions with smooth coefficients.}}
-
-@ARTICLE{Aso:81,
- AUTHOR = "T. Aso and T. Nonoyama and S. Kato",
- TITLE = "Numerical Simulation of Semidiurnal Atmospheric Tides",
- JOURNAL = "J. Geophysical R.",
- YEAR = 1981, VOLUME = 86, NUMBER = 11, PAGES = "388-400",
- COMMENT = {"Numerical modeling of the solar and lunar semidiurnal
-atmospheric tides has been performed by invoking a comprehensive approach that
-includes both algebraic manipulation and numerical solution of the
-primitive equation system."  Used {REDUCE} to overcome difficulties of
-complication and error.}}
-
-@ARTICLE{Atherton:73,
- AUTHOR = "R. W. Atherton and G. M. Homsey",
- TITLE = "Use of Symbolic Computation to Generate Evolution
-Equations and Asymptotic Solutions to Elliptic Equations",
- JOURNAL = "Journ. Comp. Phys.",
- YEAR = 1973, VOLUME = 1, PAGES = "45-59"}
-
-@ARTICLE{Aurenche:84,
- AUTHOR = "P. Aurenche and A. Douir and R. Baier and M. Fontannaz and
-D. Schiff",
- TITLE = "Photoproduction of Hadrons at Large Transverse Momentum in
-Second Order {QCD}",
- JOURNAL = "Phys. Lett.",
- YEAR = 1984, VOLUME = "135B", PAGES = "164-168",
- COMMENT = {Uses {REDUCE} and {SCHOONSCHIP} in the extension of calculations
-to a higher order to keep pace with experimental results.}}
-
-@ARTICLE{Aurenche:84a,
- AUTHOR = "P. Aurenche and A. Douir and R. Baier and M. Fontannaz and
-D. Schiff",
- TITLE = "Prompt Photon Production at Large $p_{\tau}$ in {GCD} Beyond the
-Leading Order",
- JOURNAL = "Phys. Lett.",
- YEAR = 1984, VOLUME = "140B", PAGES = "87-92",
- COMMENT = {Uses {REDUCE} and {SCHOONSCHIP}.}}
-
-@ARTICLE{Autin:89,
- AUTHOR = "B. Autin and J. Bengtsson",
- TITLE = "Symbolic Evaluation of Integrals Occurring in Accelerator
-Orbit Theory",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1989, VOLUME = 7, NUMBER = 2, PAGES = "183-187", MONTH = "February"}
-
-@ARTICLE{Baekler:84,
- AUTHOR = "P. Baekler and F. W. Hehl",
- TITLE = "A Charged {Taub-NUT} Metric with Torsion:  A New Axially
-Symmetric Solution of the {Poincar\'{e}} Gauge Field Theory",
- JOURNAL = "Phys. Lett.",
- YEAR = 1984, VOLUME = "100A", PAGES = "277-316"}
-
-@TECHREPORT{Baekler:84a,
- AUTHOR = "Peter Baekler and Friedrich W. Hehl",
- TITLE = "On the Dynamics of the Torsion of Spacetime:
-Exact Solutions in a Gauge Theoretical Model of Gravity",
- INSTITUTION = "Department of Physics, University of California,
-Los Angeles", YEAR = 1984,
- NUMBER = "UCLA/84/TEP/19", PAGE = "18", MONTH = "December"}
-
-@INPROCEEDINGS{Baekler:86,
- AUTHOR = "P. Baekler and F. W. Hehl and E. W. Mielke",
- TITLE = "Nonmetricity and Torsion:  Facts and Fancies in Gauge
-Approaches to Gravity",
- EDITOR = "R. Ruffini",
- BOOKTITLE = "Proc. 4th Marcel Grossmann Meeting on
-General Relativity", PUBLISHER = "North-Holland, Amsterdam",
- YEAR = 1986, PAGES = "277-316"}
-
-@ARTICLE{Baekler:87,
- AUTHOR = "P. Baekler and R. Hecht and F. W. Hehl and T. Shirafuji",
- TITLE = "Mass and Spin of Exact Solutions of the {Poincar{\'e}} Gauge
-Theory",
- JOURNAL = "Prog. Theor. Phys.",
- YEAR = 1987, VOLUME = 78, PAGES = "16-21"}
-
-@ARTICLE{Baekler:87a,
- AUTHOR = "P. Baekler and M. Guerses",
- TITLE = "Exact Solutions of the {Poincar{\'e}} Gauge Theory from Its
-Linearized Field Equations",
- JOURNAL = "Lett. Math. Phys.",
- YEAR = 1987, VOLUME = 14, PAGES = "185-191"}
-
-@ARTICLE{Baekler:87b,
- AUTHOR = "P. Baekler and E. W. Mielke and F. W. Hehl",
- TITLE = "Kinky Torsion in a {Poincar{\'e}} Gauge Model of Gravity Coupled
-to a Massless Scalar Field",
- JOURNAL = "Nuclear Phys.",
- YEAR = 1987, VOLUME = "B288", PAGES = "800-812"}
-
-@ARTICLE{Baekler:88,
- AUTHOR = "P. Baekler and M. Seitz and V. Winkelmann",
- TITLE = "Cylindrically Symmetric Solutions of Self-Consistently
-Coupled {Dirac} Fields in Gauge Theories of Gravity",
- JOURNAL = "Class. Quantum Grav.",
- YEAR = 1988, VOLUME = 5, PAGES = "479-490"}
-
-@ARTICLE{Baekler:88a,
- AUTHOR = "P. Baekler and M. Guerses and F. W. Hehl and J. D. McCrea",
- TITLE = "The Exterior Gravitational Field of a Charged Spinning
-Source in the {Poincar{\'e}} Gauge Theory:  A {Kerr-Newman} Metric with
-Dynamic Torsion",
- JOURNAL = "Phys. Lett.",
- YEAR = 1988, VOLUME = "A128", PAGES = "245-250"}
-
-@ARTICLE{Baekler:88b,
- AUTHOR = "P. Baekler and M. Guerses and F. W. Hehl",
- TITLE = "A New Method to Solve the Field Equations of {Poincar{\'e}}
-Gauge Theories",
- JOURNAL = "Class. Quantum Grav.",
- YEAR = 1988}
-
-@TECHREPORT{Bahrdt:90,
- AUTHOR = "J. Bahrdt and G. W{\"u}stefeld",
- TITLE = "A New Tracking Routine for Particles in Undulator and
-Wiggler Fields",
- INSTITUTION = "Technischer Bericht",
- YEAR = 1990, TYPE = "Report", NUMBER = "BESSY TB Nr. 158",
- MONTH = "October",
- ABSTRACT = {In this report we present an approximated solution of the
-particle motion in wiggler and undulator fields by an algebraic mapping
-routine.  The solution is based on a series expansion up to the third
-order in the two transversal angle coordinates and, as a third variable,
-the bending radius of the particle orbit.  The wiggler and undulator fields
-are represented by an expansion as suggested by K. Halbach.
-
-The report consists of two parts.  In the first part we solve the
-equations of motion by an iteration procedure, which originally was also
-the first approach.  In the second part the solution is based on a Taylor
-series expansion.  Both approaches are equivalent.},
-ABSTRACT2 = {Beside the presentation of the solution, the main topics
-discussed in the two parts are the calculation speed and accuracy of the
-algebraic method in comparison to integration methods along undulator
-fields, as they are typically applied in lattice design codes.
-
-As a further result of the discussion we obtain a proper canonical mapping
-routine at least as accurate but faster than typical integration routines.}}
-
-@ARTICLE{Baier:81,
- AUTHOR = {V. N. Baier and A. G. Grozin},
- TITLE = {Inclusive quarkonium production in {$e^+ e^-$} annihilation},
- JOURNAL = {Yad. Fiz. (Sov. J. Nucl. Phys.)},
- YEAR = 1981, VOLUME = 33, NUMBER = 2, PAGES = {491-500}}
-
-@ARTICLE{Baier:85,
- AUTHOR = {V. N. Baier and A. G. Grozin},
- TITLE = {Gluonic contributions to the exclusive amplitudes},
- JOURNAL = {Zeit. f\"ur Phys. C},
- YEAR = 1985, VOLUME = 29, PAGES = {161-165}}
-
-@ARTICLE{Baier:90,
- AUTHOR = {V. N. Baier and A. G. Grozin},
- TITLE = {Decay {$B \to D l \bar\nu$} from {QCD} sum rules},
- JOURNAL = {Zeit. f\"ur Phys. C},
- YEAR = 1990, VOLUME = 47, PAGES = {669-675}}
-
-@TECHREPORT{Bajla:78,
- AUTHOR = "I. Bajla and G. A. Ososkov and A. C. Hearn",
- TITLE = "The Orthogonalization Program of Polynomials
-in Two Variables in {REDUCE}-2 Language",
- INSTITUTION = "J.I.N.R., Dubna",
- YEAR = 1978, TYPE = "Report", NUMBER = "P10-11944",
- ABSTRACT = {The analytical algorithm for constructing orthogonal
-polynomials in two variables, based on the {Gram-Schmidt}
-orthogonalization method, is proposed.}}
-
-@INPROCEEDINGS{Balian:78,
- AUTHOR = "R. Balian and G. Parisi and A. Voros",
- TITLE = "Quartic Oscillator",
- YEAR = 1978, MONTH = "May",
- BOOKTITLE = "Proc. of the Colloq. on Mathematical Problems in {Feynman}
-Path Integrals, Marseille",
- ABSTRACT = {On the example of the semi-classical expansion for the levels
-of the quartic oscillator -(d**2/dq**2)+q**4, we show how the complex WKB
-method provides information about the singularities of the Borel transform
-of the semi-classical series.}}
-
-@ARTICLE{Baker:81,
- AUTHOR = "G. A. Baker and L. P. Benofy and M. Fortes and M. de Llano and
-S. M. Peltier and A. Plastino",
- TITLE = "Hard-Core Square-Well Fermion",
- JOURNAL = "Phys. Rev. A",
- YEAR = 1982, VOLUME = 26, PAGES = "3575-3588",
- COMMENT = {The mixed use of {FORTRAN} and {REDUCE}, various derivative were
-calculated algebraically, but the double series was evaluated numerically.}}
-
-@ARTICLE{Barbier:92,
- AUTHOR = "Christine Barbier and Peter Bettess and Jacqueline A. Bettess",
- TITLE = "Automatic Generation of Mapping Functions for Infinite Elements
-using {REDUCE}",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1992, VOLUME = 14, NUMBER = 5, PAGES = "523-534", MONTH = "November",
- ABSTRACT = {Co continuous basis functions for use in the finite element
-method when the elements extend to infinity in one or more directions can be
-derived simply following the method of Zienkiewicz.  The numerical code
-for these functions can be generated automatically using computer algebra
-languages such as {REDUCE}.  This paper describes the method and explains
-how {REDUCE} is used to easily produce numerical code.}}
-
-@ARTICLE{Barfoot:86,
- AUTHOR = "D. T. Barfoot and D. J. Broadhurst",
- TITLE = "Investigation of a bound on the anomalous dimensions of four-quark
-operators",
- JOURNAL = "Phys. Lett. B",
- YEAR = 1986, VOLUME = 166, PAGES = "347-350"}
-
-@ARTICLE{Barfoot:87,
- AUTHOR = "D. T. Barfoot and D. J. Broadhurst",
- TITLE = "Finite field theories in three dimensions with and without
-supersymmetry",
- JOURNAL = "Zeitschrift {f\"{u}r} Physik C",
- YEAR = 1987, VOLUME = 33, PAGES = "391-395"}
-
-@ARTICLE{Barfoot:88,
- AUTHOR = "D. T. Barfoot and D. J. Broadhurst",
- TITLE = {$\mbox{Z}_2\times\mbox{S}_6$ symmetry of the two-loop diagram},
- JOURNAL = "Zeitschrift {f\"{u}r} Physik C",
- YEAR = 1988, VOLUME = 41, PAGES = "81-85"}
-
-@ARTICLE{Bark:78,
- AUTHOR = "Fritz H. Bark and Herman Tinoco",
- TITLE = "Stability of Plane {Poiseuille} Flow of a Dilute
-Suspension of Slender Fibres",
- JOURNAL = "J. Fluid Mech.",
- YEAR = 1978, VOLUME = 87, PAGES = "321-333",
- ABSTRACT = {The linear hydrodynamic stability problem for plane {Poiseuille}
-flow of a dilute suspension of rigid fibers is solved
-numerically.  The constitutive equation given by {Batchelor}
-is used to model the rheological properties of the suspension.
-The resulting eigenvalue problem is shown to be singular.}}
-
-@ARTICLE{Barthes-Biesel:73,
- AUTHOR = "D. Barthes-Biesel and A. Acrivos",
- TITLE = "On Computer Generated Analytic Solutions to the
-Equations of Fluid Mechanics, The Case of Creeping Flows",
- JOURNAL = "Journ. Comp. Phys.",
- YEAR = 1973, VOLUME = 3, PAGES = "403-411"}
-
-@ARTICLE{Barton:72,
- AUTHOR = "David Barton and Anthony C. Hearn",
- TITLE = "Comment on Problem \#2 - The {Y(2n)} Functions",
- JOURNAL = "SIGSAM Bulletin",
- YEAR = 1972, VOLUME = 15,
- ABSTRACT = {A compact program for the solution of {SIGSAM} Problem \#2
-is presented.}}
-
-@ARTICLE{Bateman:86,
- AUTHOR = "G. Bateman and R. G. Storer",
- TITLE = "Direct Determination of Axisymmetric Magnetohydrodynamic
-Equilibrium in {Hamada} Coordinates",
- JOURNAL = "Journ. Comp. Phys.",
- YEAR = 1986, VOLUME = 64, PAGES = "161-176",
- COMMENT = {Plasma.  {"REDUCE} was used to analyse the general set of
-equations for large numbers of {Fourier} harmonics {\ldots}"}}
-
-@INPROCEEDINGS{Belkov:91,
- AUTHOR = "Alexander A. Bel'Kov and Alexander V. Lanyov",
- TITLE = "{REDUCE} Usage for Calculation of Low-Energy Process Amplitudes in
-Chiral {QCD} Model",
- EDITOR = "Stephen M. Watt",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- PUBLISHER = "ACM Press", ADDRESS = "Maryland", YEAR = 1991,
- PAGES = "454-455",
- ABSTRACT = {We describe the extension of {REDUCE} capabilities for the
-calculations of strong and weak meson processes within the chiral
-Lagrangians with higher derivatives.  The main non-trivial difficulty is to
-obtain the process amplitude from the Lagrangian, describing these
-interactions.  Another one is to overcome some {REDUCE} deficiencies such
-as the lack of arguments in the matrix data type as well as of some
-physical operations with the particle operators.  This package of procedures
-allows one to claculate the amplitudes of the strong and weak processes by
-simple specifying the particles involved and their momenta.}}
-
-@TECHREPORT{Bennett:88,
- AUTHOR = "J. P. Bennett and J. H. Davenport and H. M. Sauro",
- TITLE = "Solution of Some Equations in Biochemistry",
- INSTITUTION = "School of Mathematical Sciences, University of
-Bath, England", NUMBER = "88-12", YEAR = 1988}
-
-@ARTICLE{Bennett:93,
- AUTHOR = "J. P. Bennett and M. Grinfeld and J. Hubble",
- TITLE = "Computer Algebra Techniques in Affinity Binding Equations:
-the Dimer Case",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1993, VOLUME = 15, NUMBER = 1, PAGES = "79-83", MONTH = "January",
- COMMENT = {In this note we apply computer algebra techniques to affinity
-binding equations.  We treat the situation in which the protein is
-dimeric and shows cooperative binding.  Special attention is paid to the
-case where more than one molecule of the immobilized ligand can be
-bound by the macromolecule.}}
-
-@ARTICLE{Berends:81,
- AUTHOR = "A. Berends and R. Kleiss and P. de Causmaecher and T. T. Wu",
- TITLE = "Single Bremsstrahlung Process in Gauge Theories",
- JOURNAL = "Phys. Lett.",
- YEAR = 1981, VOLUME = "103B", PAGES = "124-128",
- COMMENT = {Used {REDUCE} to calculate 25 {Feynman} diagrams to produce
-theoretical results which could be checked against experiment.}}
-
-@TECHREPORT{Berkovich:89,
- AUTHOR = "L.M. Berkovich and V.P. Gerdt and Z.T. Kostova and
-M.L. Nechaevsky",
- TITLE = "Second Order Reducible Linear Differential Equations",
- INSTITUTION = "J.I.N.R., Dubna", YEAR = 1989, TYPE = "Preprint",
- NUMBER = "E5-89-141"}
-
-@TECHREPORT{Berkovich:90,
- AUTHOR = "L.M. Berkovich and V.P. Gerdt and Z.T. Kostova and
-M.L. Nechaevsky",
- TITLE = "Computer algebra generating related {2nd} order linear differential
-equation",
- INSTITUTION = "J.I.N.R., Dubna", YEAR = 1990, TYPE = "Preprint",
- NUMBER = "E5-90-509",
- ABSTRACT = {An algorithm with its mathematical foundation concerning {2nd}
-order ordinary linear differential equations {(OLDE)} is described.  It
-allows one to generate related {four-parametric} families of {OLDE} with
-coefficients of preassigned (in the scope of the procedure) structures
-integrable in terms of a given (generating) equation.  The number of those
-families in each next generation grows according to geometric progression
-with ratio eight.  Several examples of both mathematical and physical
-significance illustrate the efficiency of the algorithm implemented in the
-{REDUCE} compute algebra system.}}
-
-@ARTICLE{Berman:63,
- AUTHOR = "S. M. Berman and Y. S. Tsai",
- TITLE = "Intermediate Boson Pair Production as a Means for
-Determining its Magnetic Moment",
- JOURNAL = "Phys. Rev. Lett.",
- YEAR = 1963, VOLUME = 11, PAGES = "483-487"}
-
-@INPROCEEDINGS{Berndt:91,
- AUTHOR = "R. Berndt and A. Lock and G. Witte and Ch. W{\"o}ll",
- TITLE = "Application of Computer Algebra to Surface Lattice Dynamics",
- EDITOR = "Stephen M. Watt",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- PUBLISHER = "ACM Press", ADDRESS = "Maryland", YEAR = 1991,
- PAGES = "433-438",
- ABSTRACT = {Lattice dynamical calculations for surfaces and in particular
-for stepped and adsorbed covered surfaces are commonly hampered by the
-complexity of the dynamical matrix for these systems.  We propose the use
-of computer algebra programs to set up the dynamical matrix.  In the
-present implementation the dynamical matrix is calculated fully analytically
-within the framework of a force constant-model and partially analytically
-for other interaction models such as the shell model or the bond charge
-model.}}
-
-@ARTICLE{Bessis:85,
- AUTHOR = "N. Bessis and G. Bessis and D. Roux",
- TITLE = "Closed-Form Expressions for the {Dirac-Coulomb} Radial $r^{t}$
-Integrals",
- JOURNAL = "Phys. Rev. A",
- YEAR = 1985, VOLUME = 32, PAGES = "2044-2050",
- COMMENT = {No direct algebraic manipluation, but the formula is stated to be
-well suited to evaluation by {REDUCE} or {MACSYMA}, and this is an
-advantage of their formula.}}
-
-@ARTICLE{Bilge:92,
- AUTHOR = "Ay{\c{s}}e H{\"{u}}meyra Bilge",
- TITLE = "A {REDUCE} program for the integration of differential
-polynomials",
- JOURNAL = "Comp. Phys. Commun.",
- YEAR = 1992, VOLUME = 71, NUMBER = 3, PAGES = "263-268",
- MONTH = "September",
- COMMENT = {A differential polynomial F[u] is a polynomial expression of the
-derivatives of the function u(x).  A {REDUCE} program for the integration
-of differential polynomials is given.  The program is tested on the
-computation of the conserved densities of polynomial evolution equations.
-Input and output from the test runs are included in the library files.}}
-
-@TECHREPORT{Billoire:78,
- AUTHOR = "A. Billoire and R. Lacaze and A. Morel and H. Navelet",
- TITLE = "The {OZI} Rule Violating Radiative Decays of the Heavy
-Pseudoscalars",
- INSTITUTION = "{CEN}-Saclay", YEAR = 1978, TYPE = "Report",
- NUMBER = "DpH-T 43/78",
- COMMENT = {Submitted to Phys. Letters B.
-In lowest order {QCD} the rates for radiative transitions violating the {OZI}
-rule of heavy pseudoscalars are found to be extremely small.}}
-
-@ARTICLE{Biro:86,
- AUTHOR = "T. S. Biro and J. Zimanyi and M. Zimanyi",
- TITLE = "Hadrochemistry in Relativistic Mean Fields",
- JOURNAL = "Physics Letters",
- YEAR = 1986, VOLUME = "167B", NUMBER = 3, PAGES = "271-276",
- MONTH = "February"}
-
-@ARTICLE{Biro:87,
- AUTHOR = "T. S. Biro and K. Niita and A. L. de Paoli and W. Bauer
-and W. Cassing and U. Mosel",
- TITLE = "Microscopic Theory of Photon Production in Proton-Nucleus
-and Nucleus-Nucleus Collisions",
- JOURNAL = "Nuclear Physics",
- YEAR = 1987, VOLUME = "475A", PAGES = "579-597", MONTH = "December"}
-
-@TECHREPORT{Birrell:77,
- AUTHOR = "N. D. Birrell",
- TITLE = "The Application of Adiabatic Regularization
-to Calculations of Cosmological Interest",
- INSTITUTION = "Dept. Math, King's College, London",
- YEAR = 1977}
-
-@ARTICLE{Biswas:75,
- AUTHOR = "S. N. Biswas and S. R. Chaudhuri and K. S. Taank
-and J. A. Campbell",
- TITLE = "Neutrino Production in Stellar Matter by Photons
-in a Renormalizable Scalar-Boson-Exchange Model of Weak
-Interactions",
- JOURNAL = "Phys. Rev. D",
- YEAR = 1975, VOLUME = 8, PAGES = "2523-2525"}
-
-@TECHREPORT{Bittencourt:90,
- AUTHOR = "Guilherme Bittencourt and Jacques Calmet",
- TITLE = "Integrating Computer Algebra and Knowledge Representation",
- INSTITUTION = "Universit{\"a}t Karlsruhe Institut f{\"u}r
-Algorithmen und Kognitive Systeme", YEAR = 1990, TYPE = "Preprint"}
-
-@InProceedings{Blum:93,
-  author =      "W. Blum and V. Ganzha and W. Strampp",
-  title =       "An Introduction to ODE's by CAS",
-  booktitle =   "Proceedings of the 1993 International IMACS Symposium on
-                 Symbolic Computation",
-  year =        "1993",
-  editor =      "G. Jacob and N. E. Oussous and S. Steinberg",
-  pages =       "110-119",
-  organization ="IMACS",
-  publisher =   "Laboratoire d'Informatique Fondamentale de Lille, France",
-  comment =     {Use of {REDUCE} and MATHEMATICA for math education.}
-}
-
-@ARTICLE{Bocko:92,
- AUTHOR = "J. Bocko",
- TITLE = "{EQSHELL} - a {REDUCE-based} program for generation of equations
-of equilibrium for shell",
- JOURNAL = "Comp. Phys. Commun.",
- YEAR = 1992, VOLUME = 69, NUMBER = 1, PAGES = "215-222", MONTH = "February",
- COMMENT = {EQSHELL is a REDUCE-based program which generates the equations
-of equilibrium for various shapes of shells.  This program also produces
-other important characteristics of the shell.}}
-
-@ARTICLE{Boege:86,
- AUTHOR = "W. Boege and R. Gebauer and H. Kredel",
- TITLE = "Some Examples for Solving Systems of Algebraic Equations
-by Calculating {Groebner} Bases",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1986, VOLUME = 2, NUMBER = 1, PAGES = "83-98", MONTH = "March"}
-
-@ARTICLE{Bogdanova:88,
- AUTHOR = "N. Bogdanova and H. Hogreve",
- TITLE = "A {REDUCE} Package for Exact {Coulomb} Interaction Matrix
-Elements",
- JOURNAL = "Comp. Phys. Commun.",
- YEAR = 1988, VOLUME = 48, NUMBER = 2, PAGES = "319-326", MONTH = "February"}
-
-@ARTICLE{Bordoni:81,
- AUTHOR = "Luciana Bordoni and Attilio Colagrossi",
- TITLE = "An Application of {REDUCE} to Industrial Mechanics",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1981, VOLUME = 15, NUMBER = 2, PAGES = "8-12", MONTH = "May"}
-
-@InProceedings{Borst:94,
-  author =       "W. N. Borst and V. V. Goldman and J. A. van Hulzen",
-  title =        {{GENTRAN} 90: a {REDUCE} package for the generation of
-		  {Fortran} 90 code},
-  booktitle =    {Symbolic and Algebraic Computation},
-  editor =       {},
-  series =       {ISSAC},
-  year =         {1994},
-  organization = {SIGSAM},
-  publisher =    {ACM},
-  pages =        {45--51},
- ABSTRACT = {GENTRAN is a code GENerator and TRANslator running under REDUCE
-and MACSYMA.  It is a tool for generating Fortran 77, RATFOR or C programs
-from program specifications and symbolic expressions.  Its facilities
-include template processing, automatic segmentation of large expressions
-and a file handling mechanism.  GENTRAN can be used in combination with
-SCOPE 1.5, a Source Code Optimization PackagE for REDUCE.  We present an
-extension of the REDUCE version of GENTRAN, called GENTRAN 90.  It makes
-generation of Fortran 90 code possible.}}
-
-@INPROCEEDINGS{Bowyer:87,
- AUTHOR = "A. Bowyer and J. H. Davenport and P. S. Milne and J. A. Padget
-and A. F. Wallis",
- TITLE = "Applications of Computer Algebra in Solid Modelling",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "244-245",
- PUBLISHER = "Springer-Verlag"}
-
-@TECHREPORT{Boyd:78,
- AUTHOR = "John P. Boyd",
- TITLE = "The Effects of Latitudinal Shear on Equatorial
-Waves, Part {I}:  Theory and Methods",
- INSTITUTION = "Dept. of Atmos. and Oceanic Science, Univ.
-of Michigan",
- YEAR = 1978, TYPE = "Preprint", MONTH = "January",
- COMMENT = {To be published in Journal of The Atmospheric Sciences.
-By using the method of multiple scales in height and a
-variety of methods in latitude, analytic solutions for
-equatorial waves in combined vertical and horizontal shear
-are derived.}}
-
-@ARTICLE{Boyd:93,
- AUTHOR = "John P. Boyd",
- TITLE = "Chebyshev and {Legendre} Spectral Methods in Algebraic Manipulation
-Languages",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1993, MONTH = "October", VOLUME = 16, NUMBER = 4, PAGES = "377-399",
- COMMENT = {In this tutorial, we show how to combine Galerkin and collocation
-methods with algebraic manipulation languages.  Because polynomial and
-trigonometric manipulations are a special strength of {REDUCE}, Maple, and
-other symbolic languages, it is easy to use Chebyshev and Legendre
-polynomials and Fourier series as the basis sets.  However, because the
-truncation is small and calculations are performed symbolically in rational
-arithmetic, many of the standard precepets for numerical use of spectral
-methods must be modified or reversed.  We offer many guidelines and
-suggestions.  Six examples programmed in {REDUCE}, and
-Maple---eigenproblems, bifurcations, and nonlinear diffusion--illustrate
-the possibilities.}}
-
-@INPROCEEDINGS{Brackx:87,
- AUTHOR = "F. Brackx and H. Serras",
- TITLE = "Boundary Value Problems for the {Laplacian} in {Euclidean} Space
-Solved by Symbolic Computation",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "208-215",
- PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{Brackx:87a,
- AUTHOR = "F. Brackx and D. Constales and R. Delanghe and H. Serras",
- TITLE = "{Clifford} Algebra with {REDUCE}",
- JOURNAL = "Rend. Circ. Mat. Palermo, Ser. II",
- YEAR = 1987, VOLUME = 16, PAGES = "11-19"}
-
-@ARTICLE{Brackx:89,
- AUTHOR = "F. Brackx and D. Constales and A. Ronveaux and H. Serras",
- TITLE = "On the Harmonic and Monogenic Decomposition of Polynomials",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1989, VOLUME = 8, NUMBER = 3, PAGES = "297-304", MONTH = "September"}
-
-@BOOK{Brackx:92,
- AUTHOR = "F. Brackx and D. Constales",
- TITLE = "Computer Algebra with LISP and REDUCE",
- PUBLISHER = "Kluwer Academic Publishers",
- YEAR = 1992,
- PREFACE = {This text is based upon a series of lectures on LISP and REDUCE
-  held at the Universities of Averio and Coimbra (Portugal), as part of the
-  European Community's ERASMUS Project, and at the University of Gent
-  (Belgium).  It has been adapted to the newest release of REDUCE, version
-  3.4}}
-
-@INPROCEEDINGS{Bradford:86,
- AUTHOR = "R. J. Bradford and A. C. Hearn and J. A. Padget
-and E. Schr{\"u}fer",
- TITLE = "Enlarging the {REDUCE} Domain of Computation",
- BOOKTITLE = "Proc. of {SYMSAC} '86",
- YEAR = 1986, PAGES = "100-106"}
-
-@INPROCEEDINGS{Bradford:88,
- AUTHOR = "R. J. Bradford and J. H. Davenport",
- TITLE = "Effective Tests for Cyclotomic Polynomials",
- BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
- YEAR = 1988, VOLUME = 358, PAGES = "244-251"}
-
-@InProceedings{Bradford90,
-  author =      "Russell Bradford",
-  title =       "A parallelization of the {Buchberger} Algorithm",
-  booktitle =   "Proceedings of the International Symposium on
-                 Symbolic and Algebraic Computation",
-  year =        "1990",
-  editor =      "S. Watanabe and Morio Nagata",
-  pages =       "296",
-  organization =        "ACM",
-  publisher =   "Addison-Wesley"
-}
-
-@ARTICLE{Broadhurst:83,
- AUTHOR = "D. J. Broadhurst",
- TITLE = "{Non-relativistic sum rules for $\mbox{QCD}_2$, {QED} and
-$\mbox{QCD}_4$}",
- JOURNAL = "Phys. Lett. B",
- YEAR = 1983, VOLUME = 123, PAGES = "251-254"}
-
-@ARTICLE{Broadhurst:84,
- AUTHOR = "D. J. Broadhurst and S. C. Generalis",
- TITLE = "Can mass singularities be minimally subtracted?",
- JOURNAL = "Phys. Lett. B",
- YEAR = 1984, VOLUME = 142, PAGES = "75-79"}
-
-@ARTICLE{Broadhurst:85,
- AUTHOR = "D. J. Broadhurst and S. C. Generalis",
- TITLE = "Dimension-8 contributions to light-quark {QCD} sum rules",
- JOURNAL = "Phys. Lett. B",
- YEAR = 1985, VOLUME = 165, PAGES = "175-180"}
-
-@ARTICLE{Broadhurst:85a,
- AUTHOR = "D. J. Broadhurst",
- TITLE = "Evaluation of a Class of {Feynman} Diagrams for all Numbers of
-Loops and Dimensions",
- JOURNAL = "Phys. Lett. B",
- YEAR = 1985, VOLUME = 164, PAGES = "356-360",
- COMMENT = {Uses {REDUCE} to calculate explicitly the l-loop member of a
-class of massless, dimensionally regularized {Feynman} diagrams, in order to
-verify an explicit formula.}}
-
-@ARTICLE{Broadhurst:86,
- AUTHOR = "D. J. Broadhurst and A. G. Grozin",
- TITLE = "Exploiting the 1,440-fold symmetry of the master two-loop diagram",
- JOURNAL = "Zeitschrift {f\"{u}r} Physik c",
- YEAR = 1986, VOLUME = 32, PAGES = "249-253"}
-
-@ARTICLE{Broadhurst:87,
- AUTHOR = "D. J. Broadhurst",
- TITLE = "Two-loop negative-dimensional integration",
- JOURNAL = "Phys. Lett. B",
- YEAR = 1987, VOLUME = 197, PAGES = "179-182"}
-
-@ARTICLE{Broadhurst:90,
-  AUTHOR = "D. J. Broadhurst",
- TITLE = "The master two-loop diagram with masses",
- JOURNAL = "Zeitschrift {f\"{u}r} Physik C",
- YEAR = 1990, VOLUME = 47, PAGES = "115-124"}
-
-@ARTICLE{Broadhurst:91,
- AUTHOR = {D. J. Broadhurst and A. G. Grozin},
- TITLE = {Two-loop renormalization of the effective field theory
-of a static quark},
- JOURNAL = {Phys. Lett. B},
- YEAR = 1991, VOLUME = 267, PAGES = {105-110}}
-
-@TECHREPORT{Broadhurst:91a,
- AUTHOR = {D. J. Broadhurst and A. G. Grozin},
- TITLE = {Operator product expansion in static-quark effective theory:
-large perturbative corrections},
- INSTITUTION = {Open University, Milton Keynes MK7 6AA, England},
- YEAR = 1991, NUMBER = {OUT-4102-31}}
-
-@ARTICLE{Broadhurst:91b,
- AUTHOR = "D. J. Broadhurst and N. Gray and K. Schilcher",
- TITLE = {Gauge-invariant on-shell ${Z}_2$ in {QED}, {QCD} and the effective
-field theory of a static quark},
- JOURNAL = "Zeitschrift {f\"{u}r} Physik C",
- YEAR = 1991, VOLUME = 52, PAGES = "111-122"}
-
-@ARTICLE{Broadhurst:92,
- AUTHOR = {D. J. Broadhurst and A. G. Grozin},
- TITLE = "Operator product expansion in static-quark effective field theory:
-Large perturbative correction",
- JOURNAL = {Phys. Lett. B},
- YEAR = 1992, VOLUME = 274, PAGES = {421- }}
-
-@ARTICLE{Broadhurst:92a,
- AUTHOR = {D. J. Broadhurst},
- TITLE = {Three-loop on-shell charge renormalization without integration:
-$\Lambda^{\overline{\rm MS}}_{\rm QED}$ to four loops},
- JOURNAL = "Zeitschrift {f\"{u}r} Physik C",
- YEAR = 1992, VOLUME = 54, PAGES = {599- }}
-
-@ARTICLE{Broadhurst:93,
- AUTHOR = "D. J. Broadhurst",
- TITLE = "Large {N} expansion of {QED}: asymptotic photon propagator and
-contributions to the muon anomaly, for any number of loops",
- JOURNAL = "Zeitschrift {f\"{u}r} Physik C",
- YEAR = 1993, VOLUME = 58, PAGES = {339-345}}
-
-@ARTICLE{Broadhurst:93a,
- AUTHOR = "D. J. Broadhurst and J. Fleischer and O. V. Tarasov",
- TITLE = "Two-loop two-point functions with masses:  asymptotic expansions
-and {Taylor} series, in any dimension",
- JOURNAL = "Physics Letters", VOLUME = "B329", PAGES = {103-110}, YEAR = 1994,
- ABSTRACT = {In all mass cases needed for quark and gluon self-energies,
-the two-loop master diagram is expanded at large and small $q^{2}$, in
-$d$ dimensions, using identities derived from integration by parts.
-Expansions are given, in terms of hypergeometric series, for all gluon
-diagrams and for all but one of the quark diagrams; expansions of the
-latter are obtained from differential equations.  Pad\'{e} approximants
-to truncations of the expansions are shown to be of great utility.  As an
-application, we obtain the two-loop photon self-energy, for all $d$, and
-achieve highly accelerated convergence of its expansions in powers of
-$q^{2}/m^{2}/q^{2}$, for $d=4$.}}
-
-@TECHREPORT{Broadhurst:94,
- AUTHOR = {D. J. Broadhurst and P. A. Baikov and J. Fleischer and V. A.
-Smirnov},
- TITLE = {Two-loop gluon-condensate contributions to heavy-quark
-current correlators: exact results and approximations},
- INSTITUTION = {Open University, Milton Keynes MK7 6AA, England},
- YEAR = 1994, NUMBER = {OUT-4102-49},
- ABSTRACT = {The coefficient functions of the gluon condensate $\langle
-G^2\rangle$, in the correlators of heavy-quark vector, axial, scalar and
-pseudoscalar currents, are obtained analytically, to two loops, for all values
-of $z=q^2/4m^2$.  In the limiting cases $z\to0$, $z\to1$, and $z\to-\infty$,
-comparisons are made with previous partial results.  Approximation methods,
-based on these limiting cases, are critically assessed, with a view to
-three-loop work.  High accuracy is achieved using a few moments as input.
-A {\em single\/} moment, combined with only the {\em leading\/} threshold and
-asymptotic behaviours, gives the two-loop corrections to better than 1\% in
-the next 10 moments.  A two-loop fit to vector data yields
-$\langle\frac{\alpha_{\rm s}}{\pi}G^2\rangle\approx0.021$~GeV$^4$}}
-
-@ARTICLE{Brodsky:62,
- AUTHOR = "S. J. Brodsky and A. C. Hearn and R. G. Parsons",
- TITLE = "Determination of the Real Part of the {Compton} Amplitude
-at a Nucleon Resonance",
- JOURNAL = "Phys. Rev.",
- YEAR = 1962, VOLUME = 187, PAGES = "1899-1904"}
-
-@ARTICLE{Brodsky:67,
- AUTHOR = "S. J. Brodsky and J. D. Sullivan",
- TITLE = "W-Boson Contribution to the Anomalous Magnetic Moment of the
-Muon",
- JOURNAL = "Phys. Rev.",
- YEAR = 1967, VOLUME = 156, PAGES = "1644-1647"}
-
-@INPROCEEDINGS{Brodsky:69,
- AUTHOR = "S. J. Brodsky",
- TITLE = "Status of Quantum Electrodynamics",
- YEAR = 1969,
- BOOKTITLE = "Proc. International Symposium on
-Electron and Photon Interactions at High Energies, Liverpool,
-England"}
-
-@TECHREPORT{Brodsky:70,
- AUTHOR = "S. J. Brodsky",
- TITLE = "Quantum Electrodynamic Theory:  Its Relation to Precision Low
-Energy Experiments",
- INSTITUTION = "SLAC",
- YEAR = 1970, TYPE = "Report", NUMBER = "SLAC-PUB-795",
- MONTH = "August"}
-
-@INPROCEEDINGS{Brodsky:71,
- AUTHOR = "S. J. Brodsky",
- TITLE = "Algebraic Computation Techniques in Quantum Electrodynamics",
- YEAR = 1971, VOLUME = "II", PAGES = "IV-1 to IV-27",
- BOOKTITLE = "Proc. {2nd} Computing Methods in Theoretical Physics,
-Marseilles"}
-
-@TECHREPORT{Brodsky:72,
- AUTHOR = "S. J. Brodsky",
- TITLE = "Atomic Physics and Quantum Electrodynamics in the Infinite
-Momentum Frame",
- INSTITUTION = "SLAC", YEAR = 1972,
- TYPE = "Report",
- NUMBER = "SLAC-PUB-1118", MONTH = "August",
- COMMENT = {Presented at the Third International Conference on Atomic
-Physics.}}
-
-@ARTICLE{Brodsky:72a,
- AUTHOR = "S. J. Brodsky and J. F. Gunion and R. L. Jaffe",
- TITLE = "Test for Fractionally Charged Partons from
-Deep-Inelastic Bremsstrahlung in the Scaling Region",
- JOURNAL = "Phys. Rev. D",
- YEAR = 1972, VOLUME = 6, PAGES = "2487-2494"}
-
-@ARTICLE{Brodsky:72b,
- AUTHOR = "S. J. Brodsky and R. Roskies",
- TITLE = "Quantum Electrodynamics and Renormalization Theory
-in The Infinite Momentum Frame",
- JOURNAL = "Phys. Lett.",
- YEAR = 1972, VOLUME = "41B", PAGES = "517-520"}
-
-@ARTICLE{Brodsky:73,
- AUTHOR = "S. J. Brodsky and R. Roskies and R. Suaya",
- TITLE = "Quantum Electrodynamics and Renormalization Theory in the
-Infinite-Momentum Frame",
- JOURNAL = "Phys. Rev. D",
- YEAR = 1973, VOLUME = 8, PAGES = "4574-4594"}
-
-@ARTICLE{Broughan:82,
- AUTHOR = "K. A. Broughan",
- TITLE = "{Grad-Fokker-Planck} Plasma Equations.  Part 1. {Collision}
-Moments",
- JOURNAL = "J. Plasma Phys.",
- YEAR = 1982, VOLUME = 27, PAGES = "437-452",
- COMMENT = {{REDUCE} used in collaboration with hand calculation.  {REDUCE}
-did the substitutions, with hand integrations.  "Thirteen moments are taken
-of the collision term in Boltzmann-Fokker-Planck
-equation{\ldots}plasma{\ldots}"}}
-
-@ARTICLE{Broughan:91,
- AUTHOR = "K. A. Broughan and G. Keady and T. D. Robb and M. G. Richardson
-and M. C. Dewar",
- TITLE = "Some Symbolic Computing Links to the {NAG} Numeric Library",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1991, VOLUME = 25, NUMBER = 3, PAGES = "28-37", MONTH = "July"}
-
-@ARTICLE{Brown:79,
- AUTHOR = "W. S. Brown and A. C. Hearn",
- TITLE = "Applications of Symbolic Algebraic Computation",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1979, VOLUME = 17, PAGES = "207-215",
- COMMENT = {This paper is a survey of applications of systems for symbolic
-algebraic computation.}}
-
-@ARTICLE{Bryan-Jones:87,
- AUTHOR = "Jane Bryan-Jones",
- TITLE = "A Tutorial in Computer Algebra for Statisticians",
- JOURNAL = "The Professional Statistician",
- YEAR = 1987, VOLUME = 6, NUMBER = 6, MONTH = "December",PAGES = "TBD"}
-
-@TECHREPORT{Burnel,
- AUTHOR = "A. Burnel and H. Caprasse",
- TITLE = "Locality in Class III Noncovariant Gauges",
- INSTITUTION = "Physique Th{\'e}orique et Math{\'e}matique,
-Universit{\'e} de Li{\`e}ge",
- ABSTRACT = {It is shown within a perturbative calculation of the gluon
-self-energy that, in the framework of a general formulation of linear gauges,
-axial gauges do not exhibit nonlocal counterterms.}}
-
-@TECHREPORT{Burnel:94,
- AUTHOR = "A. Burnel and H. Caprasse and A. Dresse",
- TITLE = "Computing the {BRST} operator",
- INSTITUTION = "D{\'e}partement d'Astronomie et d'Astrophysique,
-Universit{\'e} de Li{\`e}ge", YEAR = 1994,
- ABSTRACT = {It is shown that for a large class of non-holonomic quantum
-mechanical systems one can make the computation of {BRST} charge fully
-algorithmic.  Two computer algebra programs written in the language of
-{REDUCE} are described.  They are able to realize the complex calculations
-needed to determine the charge for general nonlinear algebras.  Some
-interesting specific solutions are discussed.}}
-
-@ARTICLE{Burnel:94a,
- AUTHOR = "A. Burnel and H. Caprasse",
- TITLE = "Computing the {BRST} Operator Used in Quantization of Gauge
-Theories",
- JOURNAL = "International Journal of Modern Physics C",
- YEAR = 1994, VOLUME = 5, NUMBER = 6, PAGES = "1035-1047",
- COMMENTS = {It is shown that for a large class of non-holonomic quantum
-mechanical systems one can make the computation of BRST charge fully
-algorithmic.  Two computer algebra programs written in the language of REDUCE
-are described.  They are able to realize the complex calculations needed
-to determine the charge for general nonlinear algebras.  Some interesting
-specific solutions are discussed.}}
-
-@TECHREPORT{Calmet:72,
- AUTHOR = "Jacques Calmet",
- TITLE = "Further Evaluation of the Sixth Order Corrections to the
-Anomalous Magnetic Moment of the Electron",
- INSTITUTION = "Department of Physics, University of Utah",
- YEAR = 1972,
- ABSTRACT = {We report on the contributions to the $\alpha^{3}$
-part of the anomalous magnetic moment of the electron from the
-seven so-called cross and ladder diagrams.}}
-
-@ARTICLE{Calmet:72a,
- AUTHOR = "Jacques Calmet",
- TITLE = "A {REDUCE} Approach to the Calculation of {Feynman} Diagrams",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1972, VOLUME = 4, PAGES = "199-204",
- ABSTRACT = {A brief survey of two existing {REDUCE} programs (by
-Campbell-Hearn and by Calmet) dealing with algebraic computation of
-{Feynman} diagrams is given.  Work in progress on a more general approach
-to this problem is discussed.}}
-
-@ARTICLE{Calmet:74,
- AUTHOR = "Jacques Calmet",
- TITLE = "Computer Recognition of Divergences in {Feynman} Graphs",
- JOURNAL = "SIGSAM Bulletin",
- YEAR = 1974, VOLUME = 8, NUMBER = 3, PAGES = "74-75", MONTH = "August",
- ABSTRACT = {A description of a program for the recognition of divergences
-in {Feynman} graphs is given.}}
-
-@INCOLLECTION{Calmet:83,
- AUTHOR = "J. Calmet and J. A. van Hulzen",
- TITLE = "Computer Algebra Applications",
- EDITOR = "B. Buchberger and G. E. Collins and R. Loos and R. Albrecht",
- BOOKTITLE = "Computer Algebra Symbolic and Algebraic Computation",
- EDITION = "2nd", PUBLISHER = "Springer-Verlag", YEAR = 1983}
-
-@ARTICLE{Campbell:67,
- AUTHOR = "J. A. Campbell",
- TITLE = "Algebraic Computation of Radiative Corrections for
-Electron-Positron Scattering",
- JOURNAL = "Nucl. Phys.",
- YEAR = 1967, VOLUME = "B1", PAGES = "283-300"}
-
-@ARTICLE{Campbell:68,
- AUTHOR = "J. A. Campbell",
- TITLE = "Astrophysical Consequences of the Existence of Charged
-Intermediate Vector Bosons",
- JOURNAL = "Aust. Journ. of Phys.",
- YEAR = 1968, VOLUME = 21, PAGES = "139-148"}
-
-@ARTICLE{Campbell:70,
- AUTHOR = "J. A. Campbell and A. C. Hearn",
- TITLE = "Symbolic Analysis of {Feynman} Diagrams by Computer",
- JOURNAL = "Journ. of Comp. Phys.",
- YEAR = 1970, VOLUME = 5, PAGES = "280-327"}
-
-@ARTICLE{Campbell:70a,
- AUTHOR = "J. A. Campbell and R. B. Clark and D. Horn",
- TITLE = "Low-T Theorems for Charged-Pion Photoproduction",
- JOURNAL = "Phys. Rev. D",
- YEAR = 1970, VOLUME = 2, PAGES = "217-224"}
-
-@ARTICLE{Campbell:74,
- AUTHOR = "J. A. Campbell",
- TITLE = "Symbolic Computing and Its Relationship to Particle Physics",
- JOURNAL = "Acta Physica Austriaca",
- YEAR = 1974, VOLUME = "Suppl. XIII", PAGES = "595-647"}
-
-@ARTICLE{Campbell:87,
- AUTHOR = "J. A. Campbell and P. O. Fr{\"o}man and E. Walles",
- TITLE = "Explicit series formulae for the evaluation of integrals by the
-method of steepest descents",
- JOURNAL = "Studies in Applied Mathematics",
- YEAR = 1987, VOLUME = 77, PAGES = "151-172"}
-
-@TECHREPORT{Caprasse:84,
- AUTHOR = "H. Caprasse",
- TITLE = "Description et Utilisation d'Une Extension du Programme {REDUCE}",
- INSTITUTION = "Physique Th{\'e}orique et Math{\'e}matique,
-Universit{\'e} de Li{\`e}ge", YEAR = 1984, MONTH = "October"}
-
-@ARTICLE{Caprasse:85,
- AUTHOR = "H. Caprasse and M. Hans",
- TITLE = "A New Use of Operators in the Algebraic Mode of {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1985, VOLUME = 19, NUMBER = 3, PAGES = "46-52", MONTH = "August"}
-
-@ARTICLE{Caprasse:86,
- AUTHOR = "H. Caprasse",
- TITLE = "Description of an Extension of the Matrix Package of {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1986, VOLUME = 20, NUMBER = 4, PAGES = "7-10", MONTH = "December"}
-
-@ARTICLE{Caprasse:86a,
- AUTHOR = "H. Caprasse",
- TITLE = "A Complete Simplification Package for the Absolute Value
-Function in {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1986, VOLUME = 20, NUMBER = "1 and 2", PAGES = "18-21",
- MONTH = "February and May",
- COMMENT = {Implementation for {REDUCE} 3.2 of the function {"ABS"}.}}
-
-@INPROCEEDINGS{Caprasse:88,
- AUTHOR = "H. Caprasse and J. Demaret and E. Schruefer",
- TITLE = "Can {EXCALC} be Used to Investigate {High-dimensional}
-Cosmological Models with {Non-Linear Lagrangians}?",
- BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
- YEAR = 1988, PAGES = "116-124"}
-
-@ARTICLE{Caprasse:89a,
- AUTHOR = "H. Caprasse",
- TITLE = "Les Th{\'e}ories des {Champs} dans le monde de {REDUCE}
-(in {French})",
- JOURNAL = "{CALSYF} (to appear)",
- YEAR = 1989}
-
-@ARTICLE{Caprasse:90,
- AUTHOR = "H. Caprasse",
- TITLE = "Renormalization Group, Function Iterations and Computer
-Algebra",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1990, VOLUME = 9, NUMBER = 1, PAGES = "61-72", MONTH = "January",
- COMMENT = {Based on a renormalization group equation met in Quantum Field
-Theory, Continuous Iterations of a large class of functions are computed
-using {REDUCE}.}}
-
-@ARTICLE{Caprasse:91,
- AUTHOR = "H. Caprasse and J. Demaret and K. Gatermann and H. Melenk",
- TITLE = "Power-law type solutions of fourth-order gravity for
-multidimensional {Bianchi I} Universes",
- JOURNAL = "International Journal of Modern Physics C",
- YEAR = 1991, VOLUME = 2, NUMBER = 2, PAGES = "601-611",
- COMMENT = {This paper is devoted to the application of computer algebra to
-the study of solutions of the field equations derived from a non-linear
-Lagrangian, as suggested by recently proposed unified theories.  More
-precisely, we restrict ourselves to the most general quadratic Lagrangian,
-i.e. containing quadratic contributions in the different curvature tensors
-exclusively.  The corresponding field equations are then fourth-order in the
-metric tensor components.  The cosmological models studied are the simplest
-ones in the class of spatially homogeneous but anisotropic models,
-i.e. Bianchi I models.  For these models, we consider only power-law
-type solutions of the field equations.  All the solutions of the associated
-system of algebraic equations are found, using computer algebra, from a
-search of its Groebner bases.  While, in space dimension d=3, the
-Einsteinian-Kasner metric is still the most general power-law type solution,
-for d>3, no solution, other than the Minkowski space-time, is common to the
-three systems of equations corresponding to the three contributions to the
-Lagrangian density.  In the case of a pure Riemann-squared contribution to the
-Lagrangian (suggested by a recent calculation of the effective action for
-the heterotic string), the possibility exists to realize a splitting of the
-d-dimensional space into a (d-3)-dimensional internal space and a physical
-3-dimensional space, the latter expanding in time as a power bigger than
-2 (about 4.5 when d=9).}}
-
-@ARTICLE{Carlson:80,
- AUTHOR = "P. Carlson",
- TITLE = "Coordinate Free Relativity",
- JOURNAL = "J. Math. Phys.",
- YEAR = 1980, VOLUME = 21, PAGES = "1149-1154",
- COMMENT = {{REDUCE} programs for tetrad formulation of GR.}}
-
-@PHDTHESIS{Carroll:73,
- AUTHOR = "R. Carroll",
- TITLE = "The Anomalous Magnetic Moment of the Electron in the
-Mass Operator Formalism",
- SCHOOL = "University of Michigan",
- YEAR = 1973}
-
-@ARTICLE{Carroll:75,
- AUTHOR = "R. Carroll",
- TITLE = "Mass-Operator Calculation of the Electron g-Factor",
- JOURNAL = "Phys. Rev. D",
- YEAR = 1975, VOLUME = 8, PAGES = "2344-2354"}
-
-@TECHREPORT{Cejchan,
- AUTHOR = "A. Cejchan and J. Nadrchal",
- TITLE = "Application of {REDUCE}-2 and Analytic Integration
-Program in the Theoretical Solid State Physics",
- INSTITUTION = "Institute of Physics, CSAV, Prague"}
-
-@INPROCEEDINGS{Chaffy:88,
- AUTHOR = "C. Chaffy-Camus",
- TITLE = "An Application of {REDUCE} to the Approximation of $f(x,y)$",
- BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
- YEAR = 1988, VOLUME = 358, PAGES = "73-84"}
-
-@ARTICLE{Chinnick:86,
- AUTHOR = "K. Chinnick and C. Gibson and J. F. Griffiths and W. Kordylewski",
- TITLE = "Isothermal Interpretations of Oscillatory Ignition During
-Hydrogen Oxidation in an Open System.  {I}.  {Analytical} Predictions and
-Experimental Measurements of Periodicity",
- JOURNAL = "Proc. Royal Soc. Lond.",
- YEAR =  1986, VOLUME = "A405", PAGES = "117-128",
- COMMENT = {Used {REDUCE} to solve Jacobian, but answer too complicated to
-be of any use.}}
-
-@ARTICLE{Cline:90,
- AUTHOR = "Terry Cline and Harold Abelson and Warren Harris",
- TITLE = "Symbolic Computing in Engineering Design",
- JOURNAL = "AI EDAM", YEAR = 1990, MONTH = "February"}
-
-@TECHREPORT{Cohen:76,
- AUTHOR = "H. I. Cohen and O. Leringe and Y. Sundblad",
- TITLE = "The Use of Algebraic Computing in General Relativity",
- INSTITUTION = "The Royal Institute of Technology Department of Mechanics",
- YEAR = 1976, NUMBER = "TRITA-MEK-76-02"}
-
-@TECHREPORT{Cohen:76a,
- AUTHOR = "I. Cohen and F. Bark",
- TITLE = "Perturbation Calculations for the Spin Up Problem Using {REDUCE}",
- INSTITUTION = "The Royal Institute of Technology, Department
-of Mechanics",
- YEAR = 1976, NUMBER = "TRITA-MEK-76-03"}
-
-@TECHREPORT{Cohen:77,
- AUTHOR = "I. Cohen and S. Yu. Slavyanov",
- TITLE = "Smooth Perturbations of the {Schr{\"o}dinger} Equation with a
-Linear Potential Related to the Charmonium Models",
- INSTITUTION = "University of Stockholm Institute of Physics",
- YEAR = 1977, TYPE = "USIP Report", NUMBER = "77-17"}
-
-@ARTICLE{Cohen:79,
- AUTHOR = "J. P. Fitch and H. I. Cohen",
- TITLE = "Using {CAMAL} for Algebraic Calculations in General Relativity",
- JOURNAL = "General Relativity and Gravitation", VOLUME = 11, YEAR = 1979,
- PAGES = "411-418"}
-
-@ARTICLE{Cohen:84,
- AUTHOR = "H. I. Cohen and I. B. Frick and J. E. {\AA}man",
- TITLE = "Algebraic Computing in General Relativity",
- JOURNAL = "General Relativity and Gravitation, ed.",
- YEAR = 1984, PAGES = "139-162",
- COMMENT = {General relativity review.}}
-
-@INPROCEEDINGS{Cohen:89,
- AUTHOR = "Joel S. Cohen",
- TITLE = "The Effective Use of Computer Algebra Systems",
- YEAR = 1989, PAGES = "677-698",
- BOOKTITLE = "Transactions of the Sixth Army Conference on Applied
-Mathematics and Computing",
- COMMENT = {Review of author's experience with four computer algebra
-systems.}}
-
-@ARTICLE{Connor:84,
- AUTHOR = "J. N. L. Connor and P. R. Curtis and D. Farrelly",
- TITLE = "The Uniform Asymptotic Swallowtail Approximation:  Practical
-Methods for Oscillating Integrals with Four Coalescing Saddle Points",
- JOURNAL = "J. Phys. A",
- YEAR = 1984, VOLUME = 17, PAGES = "283-310",
- COMMENT = {Used {REDUCE} and {SCHOONSCHIP} for some algebraic
-manipulations, and then checked the results with {MACSYMA}; this is the most
-distrustful reference we have found.}}
-
-@ARTICLE{Connor:84a,
- AUTHOR = "J. N. L. Connor and P. R. Curtis and C. J. Edge and A. Lagan{`a}",
- TITLE = "The Uniform Asymptotic Swallowtail Approximation:  Application
-to the Collinear $H+F_{2}$",
- JOURNAL = "J. Chem. Phys.", YEAR = 1984, VOLUME = 80, NUMBER = 3,
- PAGES = "1362-1363", MONTH = "February"}
-
-@ARTICLE{Conwell:84,
- AUTHOR = "P. R. Conwell and P. W. Barber and C. K. Rushworth",
- TITLE = "Resonant Spectra of Dielectric Sphere",
- JOURNAL = "J. Opt. Soc. Am. A",
- YEAR = 1984, VOLUME = 1, PAGES = "62-67",
- COMMENT = {{REDUCE} used to confirm independently convergence and accuracy
-of {Numerical Bessel} function routine, expanding series by {REDUCE} and
-using bigfloats.  Described as slow but worthwhile.}}
-
-@INPROCEEDINGS{Cowan:79,
- AUTHOR = "Richard M. Cowan and Martin L. Griss",
- TITLE = "Hashing -- The Key to Rapid Pattern Matching",
- BOOKTITLE = "Proc. {EUROSAM} 1979, Lecture Notes
-in Computer Science", YEAR = 1979, VOLUME = 72, PAGES = "266-278",
- PUBLISHER = "Springer-Verlag"}
-
-@BOOK{Cox:92,
- AUTHOR = "D. Cox and J. Little and D. O'Shea",
- TITLE = "deals, Varieties and Algorithms:
-   An Introduction of Computational Algebraic Geometry 
-   and Commutative Algebra",
- PUBLISHER = "Springer-Verlag",
- YEAR = 1992,
- COMMENTS = {The appendix contains a discussion of the Groebner basis
-     package for REDUCE},
- ABSTRACT = {This book is an introduction to algebraic geometry and 
-commutative algebra aimed primarily at undergraduates. It emphasizes 
-applications and the computational and algorithmic aspects of the 
-subject.  Less abstract than other texts, and with prerequisites 
-(a course in linear algebra and any course discussing how to do 
-simple proofs), the text is also ideal for computer scientists as
-well as mathematicians interested in the subject.  The exposition
-assumes that students have access to a computer algebra system such 
-as Maple, REDUCE or Mathematica, but assumes no prior experience 
-with a computer.
-
-Table of Contents: Geometry, Algebra and Algorithms; Groebner Bases;
-Elimination Theory; The Algebra-Geometry Dictionary; Polynomial and 
-Rational Functions on a Variety; Robotics and Automatic Geometric 
-Theorem Proving; Invariant Theory of Finite Groups; Projective 
-Algebraic Geometry; The Dimension of a Variety; Appendices on Some 
-Concepts From Algebra, Pseudocode, Computer Algebra Systems, and 
-Independent Projects.}}
-
-@ARTICLE{Cung:75,
- AUTHOR = "V. K. Cung",
- TITLE = "Differential Cross Section of e+ + e- to e+ + $\mu-$ +
-$\bar{\nu}_\mu$ + $\bar{\nu}_e$",
- JOURNAL = "Phys. Lett.",
- YEAR = 1975, VOLUME = "55B", PAGES = "67-70"}
-
-@TECHREPORT{Darbaidze:86,
- AUTHOR = "Ya. Z. Darbaidze",
- TITLE = "A Gluon Bremsstrahlung in Supersymmetry {QCD}",
- INSTITUTION = "JINR", YEAR = 1986, TYPE = "Preprint",
- NUMBER = "P2-86-825"}
-
-@ARTICLE{Darbaidze:86a,
- AUTHOR = "J. Z. Darbaidze and V. A. Matveev and
-Z. V. Merebashvili and L. A. Slepchenko",
- TITLE = "Gluon Bremsstrahlung in Supersymmetric {QCD}",
- JOURNAL = "Phys. Lett.",
- YEAR = 1986, VOLUME = "B177", PAGE = "188"}
-
-@TECHREPORT{Darbaidze:88,
- AUTHOR = "Ya. Z. Darbaidze and Z.V. Merebashvili and V.A. Rostovtsev",
- TITLE = "Some Computer Realizations of the {REDUCE-3} Calculations for
-Exclusive Processes",
- INSTITUTION = "JINR", YEAR = 1988, TYPE = "Preprint",
- NUMBER = "P2-88-769"}
-
-@TECHREPORT{Darbaidze:89,
- AUTHOR = "Ya. Z. Darbaidze and V.A. Rostovtsev",
- TITLE = "Analysis of the Differential Equations for the Exclusive Processes
-and Explanation for the {``Mystery''} of the {Gamma-Distribution}",
- INSTITUTION = "JINR", YEAR = 1989, TYPE = "Preprint",
- NUMBER = "E2-89-286"}
-
-@INPROCEEDINGS{Dautcourt:79,
- AUTHOR = "G. Dautcourt",
- TITLE = "Application of {REDUCE} to Algebraic Computations in General
-Relativity and Astrophysics",
- YEAR = 1979, MONTH = "September",
- BOOKTITLE = "Proc. of the Workshop in Symbolic Computation, Dubna,
-{U.S.S.R.}",
- COMMENT = {Reports the use of the system {REDUCE} 2 for general relativistic
-calculations.}}
-
-@TECHREPORT{Dautcourt:80,
- AUTHOR = "G. Dautcourt and K. P. Jann",
- TITLE = "A Program Package in {REDUCE} 2 for Algebraic Computations in
-General Relativity",
- YEAR = 1980,
- INSTITUTION = "Zentralinstitut fuer Astrophysik der
-Akademie der Wissenschaften"}
-
-@ARTICLE{Dautcourt:81,
- AUTHOR = "G. Dautcourt and K. P. Jann and E. Riemer and M. Riemer",
- TITLE = "User's Guide to {REDUCE} Subroutines For Algebraic
-Computations in General Relativity",
- JOURNAL = "Astron. Nachr.",
- YEAR = 1981, VOLUME = 302, PAGES = "1-13"}
-
-@ARTICLE{Dautcourt:83,
- AUTHOR = "G. Dautcourt",
- TITLE = "The Cosmological Problem as an Initial Value Problem on the
-Observer's Past Light Cone:  Geometry",
- JOURNAL = "J. Phys. A",
- YEAR = 1983, VOLUME = 16, PAGES = "3507-3528",
- COMMENT = {Checked calculations with {REDUCE}, mainly {Riemann} tensor in
-null coordinates.}}
-
-@ARTICLE{Davenport:81,
- AUTHOR = "James Harold Davenport",
- TITLE = "On the Integration of Algebraic Functions",
- JOURNAL = "Lecture Notes in Computer Science",
- PUBLISHER = "Springer-Verlag",
- YEAR = 1981, VOLUME = 102, PAGES = "1-197"}
-
-@ARTICLE{Davenport:82,
- AUTHOR = "James H. Davenport",
- TITLE = "Fast {REDUCE:}  The {trade-off} between efficiency and
-generality",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1982, VOLUME = 16, NUMBER = 1, PAGES = "8-11", MONTH = "February"}
-
-@ARTICLE{Davenport:82a,
- AUTHOR = "James H. Davenport",
- TITLE = "What do we want from a {high-level} language?",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1982, VOLUME = 16, NUMBER = 4, PAGES = "6-9", MONTH = "November"}
-
-@INPROCEEDINGS{Davenport:85,
- AUTHOR = "James Davenport and Julian Padget",
- TITLE = "{HEUGCD:}  How Elementary Upperbounds Generate Cheaper Data",
- BOOKTITLE = "Proc. {EUROCAL} 1985, Lecture Notes
-in Computer Science", YEAR = 1985, VOLUME = 204, PAGES = "18-28",
- PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{Davenport:88,
- AUTHOR = "J. H. Davenport",
- TITLE = "The World of Computer Algebra",
- JOURNAL = "New Scientist",
- YEAR = 1988, MONTH = "September", VOLUME = 1629, PAGES = "71-72"}
-
-@BOOK{Davenport:88a,
- AUTHOR = "J. H. Davenport and Y. Siret and E. Tournier",
- TITLE = "Computer Algebra, Systems and Algorithms for Algebraic Computation",
- PUBLISHER = "Academic Press", EDITION = "2nd", YEAR = 1993}
-
-@BOOK{Davenport:88b,
- AUTHOR = "J. H. Davenport and Y. Siret and E. Tournier",
- TITLE = "Calcul Formel (in French)",
- PUBLISHER = "Masson", EDITION = "2nd", YEAR = 1993}
-
-@BOOK{Davenport:88c,
- AUTHOR = "J. H. Davenport and Y. Siret and E. Tournier",
- TITLE = "Kompyuter Algebra (in Russian)",
- PUBLISHER = "MIR", EDITION = "1st", YEAR = 1991}
-
-@TECHREPORT{Della-Dora:81,
- AUTHOR = "J. Della Dora and E. Tournier",
- TITLE = "Solutions Formelles D'Equations Differentielles au Voisinage de
-Points Singuliers Reguliers",
- INSTITUTION = "Centre National de la Recherche Scientifique",
- YEAR = 1981, TYPE = "Report", NUMBER = 239}
-
-@INPROCEEDINGS{Della-Dora:84,
- AUTHOR = "J. Della Dora and E. Tournier",
- TITLE = "Homogeneous Linear Difference Equation {(Frobenius-Boole Method)}",
- BOOKTITLE = "Proc. {EUROSAM} 1984, Lecture Notes
-in Computer Science", YEAR = 1984, VOLUME = 174, PAGES = "2-12",
- PUBLISHER = "Springer-Verlag"}
-
-@TECHREPORT{Della-Dora:85,
- AUTHOR = "Jean Della-Dora and Claire Dicrescenzo and Dominique Duval",
- TITLE = "About a New Method for Computing in Algebraic Number Fields",
- INSTITUTION = "Universit{\'e} de Grenoble, Institut Fourier,
-France", YEAR = 1985, MONTH = "November"}
-
-@ARTICLE{Demaret:89,
- AUTHOR = "J. Demaret and H. Caprasse and A. Moussiaux and Ph. Tombal and
-D. Papadopoulos",
- TITLE = "{Ten-dimensional Lovelock-type Space-Times}",
- JOURNAL = "{To appear} Phys. Rev. D",
- YEAR = 1989, MONTH = "July"}
-
-@ARTICLE{DeMenna:87,
- AUTHOR = "L. De Menna and G. Miano and G. Rubinacci",
- TITLE = "Volterra's Series Solutions of Free Boundary Plasma Equilibria",
- JOURNAL = "Phys. Fluids",
- YEAR = 1987, VOLUME = 30, PAGES = "409-416",
- COMMENT = {Magnetohydrodynamics.  "We have carried out the computations up
-to the fourth order, (the fourth order has been obtained by means of the
-symbolic program {REDUCE}").}}
-
-@ARTICLE{Demichev:85,
- AUTHOR = "A. P. Demichev and A. Ya. Rodionov",
- TITLE = "A {REDUCE} Program for the Calculation of Geometrical
-Characteristics of Compactified Multidimensional {Riemannian} Space",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1985, VOLUME = 38, PAGES = "441-448",
- COMMENT = {Covariant theories in N dimensional ($N \geq 4$) space-time.
-{REDUCE} programs to calculate {Ricci, Einstein and Yang-Mills} curvature
-and energy-momentum tensor.}}
-
-@TECHREPORT{Demichev:86,
- AUTHOR = "A. P. Demichev and A. Ya. Rodionov",
- TITLE = "Freund-{Rubin} Type Solutions for Different Compactifications of
-the Eleven-Dimensional Space",
- INSTITUTION = "Institute for High Energy Physics", YEAR = 1986,
- TYPE = "Preprint", NUMBER = "86-85",
- ABSTRACT = {The results of calculating geometrical characteristics of
-seven-dimensional quotient spaces are represented.  These
-quantities are necessary for the construction of compactifying
-solutions of the eleven-dimensional supergravity.}}
-
-@ARTICLE{deRop:88,
- AUTHOR = "Y. de Rop and J. Demaret",
- TITLE = "Using {EXCALC} to Study Nondiagonal Multidimensional
-Spatially Homogeneous Cosmologies",
- JOURNAL = "Gen. Rel. Grav.",
- YEAR = 1988, VOLUME = 20, PAGES = "1127-1139"}
-
-@TECHREPORT{DeVos:89,
- AUTHOR = "Alexis De Vos",
- TITLE = "The use of {Reduce} in solar energy conversion theory",
- INSTITUTION = "State University of Gent, {CAGe} Computer Algebra
-Group", YEAR = 1989, TYPE = "Reports of the {CAGe} Project",
-NUMBER = 4, MONTH = "August"}
-
-@TECHREPORT{DeVos:93,
- AUTHOR = "Alexis De Vos",
- TITLE = "Carnot engines, {Gr{\"o}bner} bases and all the winds on the Earth",
- INSTITUTION = "University of Gent, {CAGe} Computer Algebra Group",
- YEAR = 1993, TYPE = "The {CAGe} Reports", NUMBER = 9, MONTH = "March",
- ABSTRACT = {In the present paper, we determine which part of the solar
-energy incident on a planet can be converted into mechanical work.  The
-planet is assumed to be spherical and not rotating around an axis.  From
-numerical calculations, we find that at the most 9.64% of the absorbed
-solar energy can be converted into work.  But can we find an analytical
-expression for this fundamental number?  We try this challenge with the
-REDUCE procedures for manipulation of polynomials.}}
-
-@INPROCEEDINGS{Dewar:89,
- AUTHOR = "M. C. Dewar",
- TITLE = "{IRENA --} An Integrated Symbolic and Numerical Computation
-Environment",
- BOOKTITLE = "Proc. of {ISSAC} '89", PUBLISHER = "{ACM} Press, New York",
- YEAR = 1989, PAGES = "171-179"}
-
-@ARTICLE{Dhar:85,
- AUTHOR = "D. Dhar and J-M. Maillard",
- TITLE = "Susceptibility of the Checkerboard {Ising} Model",
- JOURNAL = "J. Phys. A",
- YEAR = 1985, VOLUME = 18, PAGES = "L383-L388",
- COMMENT = {Used {REDUCE} for tedious algebra, and got a simple answer.
-statistical mechanics(?). "At the disorder variety, the n-point correlation
-functions of the checkerboard Potts model has a simple causal
-structure.  An exact expression for the susceptibility in the Ising
-case is obtained."}}
-
-@TECHREPORT{Dicrescenzo:85,
- AUTHOR = "Claire Dicrescenzo",
- TITLE = "Algebraic Computation on Algebraic Numbers",
- INSTITUTION = "Institut Fourier, Laboratoire de
-Math{\'e}matiques, France", YEAR = 1985, MONTH = "December",
- COMMENT = {Examples are given of a new method, implemented on {REDUCE},
-for computing algebraically on algebraic numbers.}}
-
-@TECHREPORT{Diver,
- AUTHOR = "D. A. Diver and E. Q. Laing and C. C. Sellar",
- TITLE = "Waves in a Cold Plasma with a Spatially Rotating Magnetic Field",
- YEAR = 1988,
- INSTITUTION = "Department of Physics and Astronomy, University of
-Glasgow, Plasma Physics Group", TYPE = "Report", NUMBER = "GU TPA 88/12-1",
- COMMENT = {"{\ldots}The algebraic manipulation system {REDUCE} was used in
-constructing the following tensor definitions which allows us to make fewer
-approximations than other authors."}}
-
-@INPROCEEDINGS{Diver:86,
- AUTHOR = "D. A. Diver and E. W. Laing",
- TITLE = "Proc. 8th {Europhysics} Conference on
-Computational Physics",
- YEAR = 1986,
- BOOKTITLE = "Computing in Plasma Physics"}
-
-@INPROCEEDINGS{Diver:88,
- AUTHOR = "D. A. Diver and E. W. Laing",
- BOOKTITLE = "Proc. {XV} {European} Conference on Controlled
-Fusion and Plasma Heating",
- YEAR = 1988}
-
-@TECHREPORT{Diver:88a,
- AUTHOR = "D. A. Diver and E. W. Laing",
- TITLE = "Alfven Resonance Absorption in a Magnetofluid",
- YEAR = 1988, TYPE = "Report",
- INSTITUTION = "Department of Physics and Astronomy, University of
-Glasgow, Plasma Physics Group",
- NUMBER = "GUTPA 88/04-01", MONTH = "July",
- COMMENT = {Presented at 15th {UK} Plasma Physics Conference, {UMIST}.}}
-
-@ARTICLE{Diver:91,
- AUTHOR = "D. A. Diver",
- TITLE = "Modelling Waves with Computer Algebra",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1991, VOLUME = 11, NUMBER = 3, PAGES = "275-289", MONTH = "March",
- ABSTRACT = {A sophisticated model for linear waves in an inhomogeneous
-plasma is tackled completely using the computer algebra system {REDUCE}.
-The algebra code mirrors the mathematics, and is structured in a simple
-and straightforward manner.  In so doing, the solution technique is made
-obvious, and the overall philosophy of the approach is intuitive to the
-{non-specialist} computer algebra user.}}
-
-@TECHREPORT{Dorfi:85,
- AUTHOR = "E. A. Dorfi and L. O'C. Drury",
- TITLE = "Simple Adaptive Grids for {1D} Initial Value Problems",
- INSTITUTION = "Max-Plack-Institut fuer Kernphysik, Heidelberg,
-West Germany", YEAR = 1985,
- NUMBER = "MPI H-1985-V21"}
-
-@ARTICLE{Dorizzi:86,
- AUTHOR = "B. Dorizzi and B. Grammaticos and J. Hietarinta and A. Ramani
-and F. Schwarz",
- TITLE = "New integrable three dimensional quartic potentials",
- JOURNAL = "Phys. Lett.",
- YEAR = 1986, VOLUME = "116A", PAGES = "432-436",
- COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
-
-@TECHREPORT{dosSantos:85,
- AUTHOR = "R. P. dos Santos and P. P. Srivastava",
- TITLE = "Two-loop Effective Potential for {Wess-Zumino} Model using
-Superfields",
- INSTITUTION = "International Centre for Theoretical Physics",
- YEAR = 1985, NUMBER = "IC/85/205", MONTH = "October",
- ABSTRACT = {For the case of several interacting chiral superfields the
-propagators for the unconstrained superfield potentials in the 'shifted'
-theory, where the supersymmetry is explicitly broken, are derived in a
-compact form.  They are used to compute one-loop effective potential in
-the general case, while a superfield calculation of renormalized effective
-potential to two loops for the Wess-Zumino model is performed.}}
-
-@ARTICLE{dosSantos:87,
- AUTHOR = "Renato P. dos Santos",
- TITLE = "Using {REDUCE} in Supersymmetry",
- JOURNAL = "J. Symb. Comp.",
- YEAR = 1989, VOLUME = 7, PAGES = "523-525"}
-
-@PHDTHESIS{dosSantos:87a,
- AUTHOR = "R. P. dos Santos",
- TITLE = "O M{\'e}todo de Supercampos para o C{\'a}lculo de Potencial
-Efetivo em Modelos com Supercampos Quirais: Os Modelos de Wess e
-Zumino e de O'Raifeartaigh",
- SCHOOL = "Centro Brasileiro de Pesquisas F{\'i}sicas",
- YEAR = 1987,
- COMMENT = {{(In Portuguese)} Using the method of {Superfields}, the
-effective potential for supersymmetric models of {Wess-Zumino} and of
-{O'Raifeartaigh} is evaluated up to two-loop order. The spontaneous
-supersymmetry breaking is discussed.  {REDUCE} plays very important
-role in evaluation of the {Feynman} superdiagrams and in
-renormalization.}}
-
-@TECHREPORT{dosSantos:88a,
- AUTHOR = "Renato P. dos Santos",
- TITLE = "Introdu\c{c}\~{a}o ao Sistema {REDUCE} de C\'{a}lculo
-Alg\'{e}brico",
- INSTITUTION = "CBPF, Rio de Janeiro, Brazil",
- YEAR = 1988, NUMBER = "CBPF-NT-001/88",
- COMMENT = {{(In Portuguese)} Lecture notes of a course on {REDUCE}.}}
-
-@ARTICLE{dosSantos:90,
- AUTHOR = "R. P. dos Santos and W. L. Roque",
- TITLE = "On the Design of an Expert Help System for Computer Algebra
-Systems",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1990, VOLUME = 24, NUMBER = 4, PAGES = "22-25", MONTH = "October"}
-
-@InProceedings{Dresse:93,
-  author =      "A. Dresse",
-  title =       "Treatment of Dummy Variables and {BRST} Theory in Computer
-		 Algebra",
-  booktitle =   "Proceedings of the 1993 International IMACS Symposium on
-                 Symbolic Computation",
-  year =        "1993",
-  editor =      "G. Jacob and N. E. Oussous and S. Steinberg",
-  pages =       "110-119",
-  organization ="IMACS",
-  publisher =   "Laboratoire d'Informatique Fondamentale de Lille, France",
-  comment =     {A canonical form algorithm for quantities with locally scoped
-                 variables (e.g. Summation convention, tensor products) is
-                 developed in a {REDUCE} package.}
-}
-
-@ARTICLE{Drska:90,
- AUTHOR = "Ladislav Drska and Richard Liska and Milan Sinor",
- TITLE = "Two practical packages for computational physics{-GCPM, RLFI}",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1990, VOLUME = 61, NUMBER = "1-2", MONTH = "November",
- PAGES = "225-230",
- ABSTRACT = {Two handy computer-program packages for technical support of
-the work in two different branches of the computational physics are reported:
-(1) A general package for the symbolic and numerical transformation of
-expressions from one system of units to another.  (2) A package allowing
-high-quality two-dimensional output of mathematical formulas from the
-computer-algebra system {REDUCE}.}}
-
-@ARTICLE{Dubowsky:75,
- AUTHOR = "S. Dubowsky and J. L. Grant",
- TITLE = "Application of Symbolic Manipulation to Time
-Domain Analysis of Nonlinear Dynamic Systems",
- JOURNAL = "Journ. of Dynamic Systems, Measurement, and Control",
- YEAR = 1975, VOLUME = "75-Aut-J"}
-
-@ARTICLE{Dudley:89,
- AUTHOR = "M. L. Dudley and R. W. James",
- TITLE = "{Computer-aided} Derivation of Spherical Harmonic Spectral Equations
-in Astrogeophyics",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1989, VOLUME = 8, NUMBER = 4, PAGES = "423-427", MONTH = "October"}
-
-@ARTICLE{Dufner:69,
- AUTHOR = "A. M. Dufner and Y. S. Tsai",
- TITLE = "Phenomenological Analysis of the $\gamma$NN* Form Factors",
- JOURNAL = "Phys. Rev.",
- YEAR = 1969, VOLUME = 168, PAGES = "1801-1809"}
-
-@INPROCEEDINGS{Dulyan:87,
- AUTHOR = "L. S. Dulyan",
- TITLE = "The Calculation of {QCD} Triangular {Feynman} Graphs in the
-External Gluonic Field Using {REDUCE}-2 System",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "172-173",
- PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{Duncan:86,
- AUTHOR = "Anthony Duncan and Ralph Roskies",
- TITLE = "Representations of Unusual Mathematical Structures in Scientific
-Applications of Symbolic Computation",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1986, VOLUME = 2, NUMBER = 2, PAGES = "201-206", MONTH = "June",
- ABSTRACT = {We present examples of techniques we have used to apply {REDUCE}
-to problems in particle physics which have mathematical structures unknown to
-{REDUCE}.}}
-
-@PHDTHESIS{Duval:87,
- AUTHOR = "Dominique Duval",
- TITLE = "Diverses questions relatives au Calcul Formel
-Avec des Nombres Alg{\'e}briques",
- SCHOOL = "L'Universit{\'e} Scientifique, Technologique
-et M{\'e}dicale de Grenoble", YEAR = 1987}
-
-@InProceedings{Dyer:94,
-  author =       {Charles C. Dyer},
-  title =        {An Application of Symbolic Computation in the
-		  Physical Sciences},
-  booktitle =    {Symbolic and Algebraic Computation},
-  editor =       {},
-  series =       {ISSAC},
-  year =         {1994},
-  organization = {SIGSAM},
-  publisher =    {ACM},
-  pages =        {181--186}
-}
-
-@ARTICLE{Earles:70,
- AUTHOR = "D. Earles",
- TITLE = "A Measurement of the Electron-Production of Muon Pairs",
- JOURNAL = "Phys. Rev. Lett.",
- YEAR = 1970, VOLUME = 25, PAGES = "129-133"}
-
-@ARTICLE{Eastwood:87,
- AUTHOR = "James W. Eastwood",
- TITLE = "Orthovec:  A {REDUCE} Program for {3-D} Vector Analysis
-in Orthogonal Curvilinear Coordinates",
- JOURNAL = "Comp. Phys. Commun.",
- YEAR = 1987, VOLUME = 47, NUMBER = 1, PAGES = "139-147", MONTH = "October"}
-
-@TECHREPORT{Eastwood:87a,
- AUTHOR = "James W. Eastwood and Christopher J. H. Watson",
- TITLE = "An Analytic Theory of {Wave-Current} Interactions",
- INSTITUTION = "Culham Laboratory, Theory and Optics Division",
- YEAR = 1987, NUMBER = "Plasma Physics Note 87/7", MONTH = "February",
- ABSTRACT = {This report presents results of the Department of Energy
-contract to obtain high order analytic solutions to nonlinear hydrodynamic
-equation describing steady periodic waves propagating in sheared currents.
-The purpose of this work is to provide working formulae for computing
-combined wave and current loadings in the design of offshore structures.
-Using the {REDUCE} algebra package, we have identified minor typographical
-errors in the published fifth coefficients for uniform currents given by
-{Fenton [2]} and by Skjelbreia and {Hendrickson [5]}.  We have demonstrated
-the equivalence of corrected forms of these expressions to fifth order, and
-extended Fenton's expansion to seventh order.  We present a new fifth order
-theory for bilinear current profiles. {FORTRAN} software for the seven order
-uniform current and fifth order bilinear current theories are given.}}
-
-@ARTICLE{Eastwood:91,
- AUTHOR = "James W. Eastwood",
- TITLE = "{ORTHOVEC:} version 2 of the {REDUCE} program for {3-D} vector
-analysis in orthogonal curvilinear coordinates",
- JOURNAL = "Comp. Phys. Commun.",
- YEAR = 1991, VOLUME = 64, NUMBER = 1, PAGES = "121-122", MONTH = "April"}
-
-@TECHREPORT{Edelen:81,
- AUTHOR = "Dominic G. B. Edelen",
- TITLE = "Programs for Calculation of Isovector Fields in the
-{REDUCE}-2 Environment",
- INSTITUTION = "Center for the Application of Mathematics,
-Lehigh University", YEAR = 1981, NUMBER = "TBD", MONTH = "August"}
-
-@ARTICLE{Edelen:82,
- AUTHOR = "D. G. B. Edelen",
- TITLE = "Isovector Fields for Problems in the Mechanics of Solids and
-Fluids",
- JOURNAL = "Int. Journ. Eng. Sci.",
- YEAR = 1982, VOLUME = 20, PAGES = "803-815",
- COMMENT = {Prolongation methods as a {REDUCE} package for this, available
-from Center for Applications of Mathematics, Lehigh Univ., Bethlehem, PA
-18015.  Applications to mechanics of solids and fluids.}}
-
-@BOOK{Edneral:89,
- AUTHOR = "Viktor F. Edneral and Aleksandr P. Kryukov and
-Anatolii Ia. Rodionov",
- TITLE = "The language of the analytic computer program {REDUCE}",
- PUBLISHER = "Moscow, {Izd-vo}, Moskovskogo {un-ta}", YEAR = 1989,
- COMMENT = {This monograph -- first in The Soviet Union with a systematic
-treatment of the analytical computer (program) {REDUCE}.}}
-
-@ARTICLE{Eisenberger:90,
- AUTHOR = "Moshe Eisenberger",
- TITLE = "Application of Symbolic Algebra to the Analysis of Plates
-on Variable Elastic Foundation",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1990, VOLUME = 9, NUMBER = 2, PAGES = "207-213", MONTH = "February"}
-
-@TECHREPORT{Eissfeller:86,
- AUTHOR = "Bernd Ei{\ss}feller and G{\"u}nter W. Hein",
- TITLE = "A Contribution to {3D-Operational} Geodesy",
- INSTITUTION = "Universit{\"a}rer Studiengang Vermessungswesen
-and Universit{\"a}t der Bundeswehr M{\"u}nchen",
- YEAR = 1986, NUMBER = "Heft 17", MONTH = "December"}
-
-@PHDTHESIS{Eitelbach:73,
- AUTHOR = "D. L. Eitelbach",
- TITLE = "Automatic Analysis of Problems in Elementary Mechanics",
- SCHOOL = "University of Illinois",
- YEAR = 1973}
-
-@ARTICLE{Eleuterio:82,
- AUTHOR = "S. M. Eleut{\'e}rio and R. V. Mendes",
- TITLE = "Note on Equivalence and Singularities:  An Application of
-Computer Algebra",
- JOURNAL = "Journ. Comp. Phys.",
- YEAR = 1982, VOLUME = 48, PAGES = "150-156",
- COMMENT = {{GR} equivalence, commenting on \AAman & Karlhede.}}
-
-@ARTICLE{Eliseev:85,
- AUTHOR = "V. P. Eliseev and R. N. Fedorova and V. V. Kornyak",
- TITLE = "A {REDUCE} Program for Determining Point and Contact {Lie}
-Symmetries of Differential Equations",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1985, VOLUME = 36, PAGES = "383-389",
- ABSTRACT = {A universal {REDUCE} program for obtaining the systems of
-determining equations of the Lie algebra of point and contact
-symmetries is proposed.}}
-
-@ARTICLE{Elishakoff:87,
- AUTHOR = "Isaac Elishakoff and Joseph Hollkamp",
- TITLE = "Computerized Symbolic Solution for a Nonconservative
-System in Which Instability Occurs by Flutter in One Range
-of a Parameter and by Divergence in Another",
- JOURNAL = "Comp. Methods in Applied Mechanics and Engineering",
- YEAR = 1987, VOLUME = 62, PAGES = "27-46",
- COMMENT = {"{\ldots}the problem is solved by the {Galerkin} method in
-conjunction with computerized symbolic algebra".  The system used is {REDUCE}.
-"It carries out algebraic operations irrespective of their complexity".
-Includes snatches of code and algebraic answers.  Mainly
-differentiation and substitution, plus a little integration.  The
-coefficients get rather large (18 digits or so).}}
-
-@ARTICLE{Elishakoff:87a,
- AUTHOR = "Isaac Elishakoff and Brian Couch",
- TITLE = "Application of Symbolic Algebra to the Instability of a
-Nonconservative System",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1987, VOLUME = 4, NUMBER = 3, PAGES = "391-396", MONTH = "December"}
-
-@ARTICLE{Esteban:90,
- AUTHOR = "E.P. Esteban and E. Ramos",
- TITLE = "Algebraic computing and the {Newman-Penrose} formalism",
- JOURNAL = "Computers in Physics",
- YEAR = 1990, PAGES = "285-290", MONTH = "May/June"}
-
-%                          REDUCE BIBLIOGRAPHY
-
-%                              Part 2:  F-H
-
-% Copyright (c) 1995 RAND.  All Rights Reserved.
-
-% Additions and corrections are solicited.  Please send them, in the
-% same format as these entries if possible, to reduce at rand.org.
-
-
-@ARTICLE{Falck:89,
- AUTHOR = "N. K. Falck and D. Graudenz and G. Kramer",
- TITLE = "Cross section for {five-parton} production in $e^{+} e^{-}$
-annihilation",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1989, VOLUME = 56, PAGES = "181-198", NUMBER = 2, MONTH = "December"}
-
-@ARTICLE{Fazio:84,
- AUTHOR = "P. M. Fazio and G. E. Copeland",
- TITLE = "Cooper-Type Minima in Multipole Cross Sections of Atomic Hydrogen",
- JOURNAL = "Phys. Rev. Lett.",
- YEAR = 1984, VOLUME = 53, NUMBER = "2", MONTH = "July"}
-
-@INPROCEEDINGS{Fedorova:87,
- AUTHOR = "R. N. Fedorova and V. P. Gerdt and N. N. Govorun
-and V. P. Shirikov",
- TITLE = "Computer Algebra in Physical Research of {Joint Institute}
-for {Nuclear Research}",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "1-10",
- PUBLISHER = "Springer-Verlag"}
-
-@INPROCEEDINGS{Fedorova:87a,
- AUTHOR = "R. N. Fedorova and V. V. Kornyak",
- TITLE = "Computer Algebra Application for Determining Local Symmetries
-of Differential Equations",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "174-175",
- PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{Feldmar:86,
- AUTHOR = "E. Feldmar and K. S. K{\"o}lbig",
- TITLE = "{REDUCE} Procedures for the Manipulation of Generalized
-Power Series",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1986, VOLUME = 39, PAGES = "267-284"}
-
-@ARTICLE{Feuillebois:84,
- AUTHOR = "F. Feuillebois",
- TITLE = "Sedimentation in a Dispersion with Vertical Inhomogenieties",
- JOURNAL = "Journ. Fluid Mech.",
- YEAR = 1984, VOLUME = 139, PAGES = "145-171",
- COMMENT = {Uses {REDUCE} and {INT} to evaluate some integrals in the
-expansion of 1/s, a small quantity.}}
-
-@ARTICLE{Fitch:73,
- AUTHOR = "John Fitch",
- TITLE = "Problems \#3 and \#4 in {REDUCE} and {MACSYMA}",
- JOURNAL = "SIGSAM Bulletin",
- YEAR = 1973, PAGES = "10-11",
- ABSTRACT = {The algebra systems {REDUCE} and {MACSYMA} are used to solve
-{SIGSAM} Problem \#3, the Reversion of a Double Series, and {SIGSAM}
-Problem \#4, the Lie Transform Solution of the Harmonic Oscillator.}}
-
-@INPROCEEDINGS{Fitch:81,
- AUTHOR = "J. P. Fitch",
- TITLE = "User-based Integration Software",
- BOOKTITLE = "Proc. 1981 {ACM} Symposium on Symbolic
-and Algebraic Computation",
- YEAR = 1981, PAGES = "245-248"}
-
-@INPROCEEDINGS{Fitch:83,
- AUTHOR = "J. P. Fitch",
- TITLE = "Implementing {REDUCE} on a Microprocessor",
- BOOKTITLE = "Proc. {EUROCAL} 1983, Lecture Notes
-in Computer Science", YEAR = 1983, VOLUME = 162, PAGES = "128-136",
- PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{Fitch:85,
- AUTHOR = "J. P. Fitch",
- TITLE = "Solving Algebraic Problems with {REDUCE}",
- JOURNAL = "J. of Symbolic Computation",
- YEAR = 1985, VOLUME = 1, NUMBER = 2, PAGES = "211-227", MONTH = "June"}
-
-@INPROCEEDINGS{Fitch:85a,
- AUTHOR = "J. P. Fitch",
- TITLE = "Applying Computer Algebra",
- BOOKTITLE = "International Conference on Computer Algebra and its
-Application in Theory",
- YEAR = 1985, PAGES = "262-275"}
-
-@INPROCEEDINGS{Fitch:87,
- AUTHOR = "J. P. Fitch",
- TITLE = "Utilisation du Calcul Formel",
- BOOKTITLE = "Calcul Formel et Automatique",
- EDITOR = "P. Chenin", PUBLISHER = "Editions du {CNRS}",
- YEAR = 1987, PAGES = "119-136"}
-
-@INPROCEEDINGS{Fitch:87a,
- AUTHOR = "J. P. Fitch and R. G. Hall",
- TITLE = "Symbolic Computation and the Finite Element Method",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "95-96",
- PUBLISHER = "Springer-Verlag"}
-
-@INPROCEEDINGS{Fitch:89,
- AUTHOR = "J. P. Fitch",
- TITLE = "Can {REDUCE} be run in parallel?",
- BOOKTITLE = "Proc. of {ISSAC} '89", PUBLISHER = "{ACM} Press, New York",
- YEAR = 1989, PAGES = "155-162"}
-
-@ARTICLE{Fitch:89a,
- AUTHOR = "J. Fitch",
- TITLE = "Compiling for Parallelism",
- JOURNAL = "Computer Algebra and Parallelism", EDITOR = "J. Della Dora
-and J. Fitch",
- YEAR = 1989, PAGES = "19-31", PUBLISHER = "Academic Press, London"}
-
-@InProceedings{Fitch90,
-  author =      "J. P. Fitch",
-  title =       "A delivery system for {REDUCE}",
-  booktitle =   "Proceedings of the International Symposium on
-                 Symbolic and Algebraic Computation",
-  year =        "1990",
-  editor =      "S. Watanabe and Morio Nagata",
-  pages =       "76-81",
-  organization =        "ACM",
-  publisher =   "Addison-Wesley"
-}
-
-@ARTICLE{Fitch:90a,
- AUTHOR = "John Fitch",
- TITLE = "The symbolic-numeric interface",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1990, VOLUME = 61, NUMBER = "1-2", MONTH = "November",
- PAGES = "22-33",
- ABSTRACT = {Algebraic computation can be of great assistance in the
-preparation of numerical programs.  The paper considers some of these,
-from simple to complex, and describes work currently in progress to produce
-a true integrated symbolic-numeric computing system.}}
-
-@ARTICLE{Fitch:93,
- AUTHOR = "John Fitch",
- TITLE = "Mathematics goes automatic",
- JOURNAL = "Physics world",
- YEAR = 1993, VOLUME = 6, NUMBER = 6, MONTH = "June", PAGES = "48-52",
- COMMENT = {Computer algebra enhances the productivity of any scientist or
-engineer by increasing efficiency and doing away with tedious operations}}
-
-@TECHREPORT{Flatau:86,
- AUTHOR = "Piotr J. Flatau and John P. Boyd and William R. Cotton",
- TITLE = "Symbolic Algebra in Applied Mathematics and Geophysical
-Fluid Dynamics - {REDUCE} Examples",
- INSTITUTION = "Dept. of Atmospheric and Oceanic Science, University
-of Michigan, and Dept. of Atmospheric Science, Colorado State
-University", YEAR = 1986}
-
-@TECHREPORT{Flath:86,
- AUTHOR = "Dan Flath",
- TITLE = "Remarks on Tensor Operators",
- INSTITUTION = "National University of Singapore, Department
-of Mathematics", TYPE = "Research Report",
- YEAR = 1986, NUMBER = 266, MONTH = "July"}
-
-@ARTICLE{Fleischer:71,
- AUTHOR = "J. Fleischer",
- TITLE = "Partial Wave Analysis of Nucleon-Nucleon {Bethe}-{Salpeter}
-Equation on the Computer",
- JOURNAL = "Journ. of Comp. Phys.",
- YEAR = 1971, VOLUME = 12, PAGES = "112-123"}
-
-@ARTICLE{Fleischer:73,
- AUTHOR = "J. Fleischer and J. L. Gammel and M. T. Menzel",
- TITLE = "Matrix {Pad\'e} Approximants for the {1SO}- and
-{3PO}- Partial Waves in Nucleon-Nucleon Scattering",
- JOURNAL = "Phys. Rev. D",
- YEAR = 1973, VOLUME = 8, PAGES = "1545-1552"}
-
-@ARTICLE{Fleischer:75,
- AUTHOR = "J. Fleischer and J. A. Tjon",
- TITLE = "Bethe-{Salpeter} Equation for {J}=0 Nucleon-Nucleon
-Scattering with One-Boson Exchange",
- JOURNAL = "Nuclear Physics",
- YEAR = 1975, VOLUME = "B84", PAGES = "375-396"}
-
-@ARTICLE{Fogelholm:82,
- AUTHOR = "Rabbe Fogelholm and Inge B. Frick",
- TITLE = "Standard {LISP} for the {VAX:}  A Provisional Implementation",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1982, VOLUME = 16, NUMBER = 4, PAGES = "10-12", MONTH = "November"}
-
-@ARTICLE{Foster:89,
- AUTHOR = "Kenneth R. Foster and Haim H. Bau",
- TITLE = "Symbolic Manipulation Programs for the Personal Computer",
- JOURNAL = "Science",
- YEAR = 1989, VOLUME = 243, PAGES = "679-243", MONTH = "February",
- COMMENT = {Reviews several algebra programs that run on small machines.
-doesn't rate the {PC} version of {REDUCE} very highly because of the small
-workspace.}}
-
-@ARTICLE{Fox:71,
- AUTHOR = "J. A. Fox",
- TITLE = "Recalculation of the Crossed Graph Contribution
-to the 4th Order {Lamb} Shift",
- JOURNAL = "Phys. Rev. D",
- YEAR = 1971, VOLUME = 3, PAGES = "3228-3230"}
-
-@ARTICLE{Fox:74,
- AUTHOR = "John A. Fox and Anthony C. Hearn",
- TITLE = "Analytic Computation of Some Integrals in Fourth Order
-Quantum Electrodynamics",
- JOURNAL = "Journ. Comp. Phys.",
- YEAR = 1974, VOLUME = 14, PAGES = "301-317",
- ABSTRACT = {A program for the analytic evaluation of some parametric
-integrals which occur in fourth order {QED} calculations is described.}}
-
-@ARTICLE{Franceschetti:85,
- AUTHOR = "G. Franceschetti and I. Pinto",
- TITLE = "Nonlinear Propagation and Scattering:  Analytical Solution and
-Symbolic Code Implementation",
- JOURNAL = "J. Opt. Soc. Am. A",
- YEAR = 1985, VOLUME = 2, PAGES = "997-1006",
- COMMENT = {Volterra series using {REDUCE}.  Perturbation expansions.}}
-
-@INPROCEEDINGS{Freire:88,
- AUTHOR = "E. Freire and E. Gamero and E. Ponce and L. G. Franquelo",
- TITLE = "An Algorithm for Symbolic Computation of Center Manifolds",
- BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
- YEAR = 1988, VOLUME = 358, PAGES = "218-230"}
-
-@INPROCEEDINGS{Freire:89,
- AUTHOR = "E. Freire and E. Gamero and E. Ponce",
- TITLE = "An Algorithm for Symbolic Computation of {Hopf} Bifurcation",
- BOOKTITLE = "Proc. Computers and Mathematics '89",
- EDITOR = "E. Kaltofen and S. M. Watt",
- YEAR = 1989, PAGES = "109-118", PUBLISHER = "Springer-Verlag, New York"}
-
-@TECHREPORT{Frick:82,
- AUTHOR = "I. G. Frick and R. Fogelholm",
- TITLE = "An Implementation of {Standard} {Lisp} Built on Top of {Franz Lisp}",
- INSTITUTION = "University of Stockholm, Institute of
-Physics", YEAR = 1982, TYPE = "Report", MONTH = "April",
- COMMENT = {A Standard {LISP} system has been built for the {VAX-11}
-large-address-space computer by embedding the required function
-definitions in the available Franz Lisp system for {VAX/UNIX}.}}
-
-@ARTICLE{Fujimoto:84,
- AUTHOR = "Y. Fujimoto and T. Garavaglia",
- TITLE = "Phase Diagrams in {Scalar QED}",
- JOURNAL = "Physics Letters",
- YEAR = 1984, VOLUME = "148B", NUMBER = "1,2,3", PAGES = "220-224",
- MONTH = "November"}
-
-@ARTICLE{Fuzio:85,
- AUTHOR = "P. M. Fuzio and G. E. Copeland",
- TITLE = "Partial Radiative-Recombination Cross Sections for Excited
-States of Hydrogen",
- JOURNAL = "Phys. Rev. A",
- YEAR = 1985, VOLUME = 31, NUMBER = 1, PAGES = "187-195",
- ABSTRACT = {The squares of the dipole and quadrupole matrix elements for the
-free-to-bond transitions of hydrogen uptp high bound states are
-derived in closed analytic form using a method suitable for computer
-algebra.}}
-
-@TECHREPORT{Gaemers,
- AUTHOR = "K. J. F. Gaemers and R. Gastmans and F. M. Renard",
- TITLE = "Neutrino Counting in e+ e- Collisions",
- INSTITUTION = "NIKHEF-H, Amsterdam", TYPE = "Preprint",
- ABSTRACT = {The possibility of counting the number of neutrino types
-in e+ e- $\rightarrow$ gamma nu nubar is re-examined by taking into
-account effects of the Z-pole.}}
-
-@TECHREPORT{Gaemers:78,
- AUTHOR = "K. J. F. Gaemers and G. J. Gounaris",
- TITLE = "Polarization Amplitudes For e+e- $\rightarrow$ W+W-
-$\rightarrow$ ZZ",
- INSTITUTION = "CERN", YEAR = 1978, TYPE = "Preprint",
- NUMBER = "TH.2548-CERN", MONTH = "August",
- ABSTRACT = {The main purpose of this work is to study the three weak boson
-vertex.  We give explicit formulae for all polarization amplitudes of
-the processes e+e- $\rightarrow$ W+W- and e+e- $\rightarrow$ ZZ, with
-arbitrary couplings between the various intermediate vector bosons.}}
-
-@INPROCEEDINGS{Ganzha:89,
- AUTHOR = "V. Ganzha and R. Liska",
- TITLE = "Application of the {REDUCE} Computer Algebra System to Stability
-Analysis of Difference Schemes",
- BOOKTITLE = "Proc. Computers and Mathematics '89",
- EDITOR = "E. Kaltofen and S. M. Watt",
- YEAR = 1989, PAGES = "119-129", PUBLISHER = "Springer-Verlag, New York"}
-
-@InProceedings{Ganzha90,
-  author =      "Victor G. Ganzha and Michail Yu. Shaskov",
-  title =       "Local Approximation Study of Difference Operators by
-                 means of {REDUCE} System",
-  booktitle =   "Proceedings of the International Symposium on
-                 Symbolic and Algebraic Computation",
-  year =        "1990",
-  editor =      "S. Watanabe and Morio Nagata",
-  pages =       "185-192",
-  organization =        "ACM",
-  publisher =   "Addison-Wesley"
-}
-
-@InProceedings{Ganzha90a,
-  author =      "V. G. Ganzha and S. V. Meleshko and V. P. Shelest",
-  title =       "Application of {REDUCE} System for Analyzing
-                 Consistency of Systems of {P.D.E.'s}",
-  booktitle =   "Proceedings of the International Symposium on
-                 Symbolic and Algebraic Computation",
-  year =        "1990",
-  editor =      "S. Watanabe and Morio Nagata",
-  pages =       "301",
-  organization =        "ACM",
-  publisher =   "Addison-Wesley"
-}
-
-@INPROCEEDINGS{Ganzha:91,
- AUTHOR = "V.G. Ganzha and B. Yu. Scobelev and E.V. Vorozhtsov",
- TITLE = "Stability Analysis of Difference Schemes by the Catastrophe
-Theory Methods and by Means of Computer Algebra",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- EDITOR = "Stephen M. Watt",
- PUBLISHER = "ACM Press", ADDRESS = "Maryland", PAGES = "427-428",
- YEAR = 1991}
-
-@InProceedings{Ganzha:94,
-  author =       "V. G. Ganzha and E. V. Vorozhtsov and J. Boers and
-		  J. A. van Hulzen",
-  title =        {Symbolic-Numeric Stability Investigations of {Jameson's}
-		  Schemes for Thin-layer {Navier-Stokes} Equations},
-  booktitle =    {Symbolic and Algebraic Computation},
-  editor =       {},
-  series =       {ISSAC},
-  year =         {1994},
-  organization = {SIGSAM},
-  publisher =    {ACM},
-  pages =        {234--241}
-}
-
-@TECHREPORT{Garavaglia,
- AUTHOR = "Theodore Garavaglia",
- TITLE = "Polarized Electron Scattering on Spin Zero and Polarized Spin
-$\frac{1}{2}$ Targets:  Deep Inelastic Scattering, Elastic Electron-muon
-Scattering, and Elastic Electron-Nucleon Scattering",
- INSTITUTION = "Inst. Teich. Bhaile Atha Cliath, Eire", TYPE = "Preprint",
- ABSTRACT = {A covariant formulation is developed and used to derive
-cross-sections for the analysis of experiments in which
-polarized electrons(muons) are scattered from spin zero and
-from polarized spin 1/2 targets.}}
-
-@ARTICLE{Garavaglia:80,
- AUTHOR = "T. Garavaglia",
- TITLE = "A Covariant Formulation for Polarized Electron (Muon)
-Scattering on Spin-Zero and Polarized Spin-$\frac{1}{2}$ Targets",
- JOURNAL = "Il Nuovo Cimento",
- YEAR = 1980, VOLUME = "56A", PAGES = "121-128",
- COMMENT = {{REDUCE} used in quantum mechanics.}}
-
-@ARTICLE{Garavaglia:84,
- AUTHOR = "Theodore Garavaglia",
- TITLE = "{Dirac-} and {Majorana-neutrino-mass} effects in
-{neutrino-electron} elastic scattering",
- JOURNAL = "Physical Review {D}",
- YEAR = 1984, VOLUME = 29, NUMBER = 3, PAGES = "387-392", MONTH = "February"}
-
-@ARTICLE{Garcia:86,
- AUTHOR = "Arnaldo Garcia and Paulo Viana",
- TITLE = "Weierstrass Points on Certain Non-Classical Curves",
- JOURNAL = "Arch. Math.",
- YEAR = 1986, VOLUME = 46, PAGES = "315-322"}
-
-@ARTICLE{Garrad:86,
- AUTHOR = "A. D. Garrad and D. C. Quarton",
- TITLE = "Symbolic Computing as a Tool in Wind Turbine Dynamics",
- JOURNAL = "Journ. of Sound and Vibration",
- YEAR = 1986, VOLUME = 109, NUMBER = 1, PAGES = "65-78",
- COMMENT = {{REDUCE} as a tool in turbine design, in particular present a
-program for part of a stability analysis for a turbine tower.}}
-
-@ARTICLE{Gastmans:79,
- AUTHOR = "R. Gastmans and A. van Proeyen and P. Verbaeten",
- TITLE = "Symbolic Evaluations of Dimensionally Regularized {Feynman}
-Diagrams",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1979, VOLUME = 18, PAGES = "201-203",
- ABSTRACT = {A modification of the symbolic and algebraic manipulation
-program {REDUCE} is reported which allows the treatment of vector and gamma
-algebra in an arbitrary number of dimensions.}}
-
-@TECHREPORT{Gatermann:90,
- AUTHOR = "Karin Gatermann",
- TITLE = "Gruppentheoretische {Konstruktion} von symmetrischen
-{Kubaturformeln}",
- INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin",
- YEAR = 1990, TYPE = "Preprint", NUMBER = "TR 90-1", MONTH = "January"}
-
-@InProceedings{Gatermann90a,
-  author =      "Karin Gatermann",
-  title =       "Symbolic solution of polynomial equation systems with
-                 symmetry",
-  booktitle =   "Proceedings of the 1990 International Symposium on
-                 Symbolic and Algebraic Computation",
-  year =        "1990",
-  editor =      "S. Watanabe and Morio Nagata",
-  pages =       "112-119",
-  organization =        "ACM",
-  publisher =   "Addison-Wesley"
-}
-
-@ARTICLE{Gatermann:91,
- AUTHOR = "Karin Gatermann and Andreas Hohmann",
- TITLE = "Symbolic Exploitation of Symmetry in Numerical Pathfollowing",
- JOURNAL = "IMPACT of Computing in Science and Engineering",
- YEAR = 1991, MONTH = "December", VOLUME = 3, NUMBER = 4,
- PAGES = "330-365",
- ABSTRACT = {{Parameter-dependent} systems of nonlinear equations with
-symmetry are treated by a combination of symbolic and numerical computations.
-In the symbolic part of the algorithm the complete analysis of the symmetry
-occurs, and it is here where symmetrical normal forms, symmetry reduced
-systems, and block diagonal Jacobians are computed.  Given a particular
-problem, the symbolic algorithm can create and compute through the list of
-possible bifurcations thereby forming a {so-called} tree of decisions
-correlated to the different types of symmetry breaking bifurcation points.
-The remaining part of the algorithm deals with the numerical pathfollowing
-based on the implicit reparametrisation as suggested and worked out by
-{Deuflhard/Fiedler/Kunkel}.  The symmetry preserving bifurcation points are
-computed using recently developed augmented systems incorporating the use
-of symmetry.}}
-
-@INPROCEEDINGS{Gatermann:91a,
- AUTHOR = "Karin Gatermann",
- TITLE = "Mixed symbolic-numeric solution of symmetrical nonlinear systems",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- EDITOR = "Stephen M. Watt",
- ORGANIZATION =        "ACM",
- PUBLISHER = "ACM Press", ADDRESS = "Maryland", PAGES = "431-432",
- YEAR = 1991,
- ABSTRACT = {The mixed symbolic-numeric algorithm {SYMCON} for the fully
-automatical treatment of equivariant systems is presented. The global
-aspects of the theory of Vanderbauwhede for these systems are viewed with
-regard to the full bifurcation scenario containing solution paths with
-different isotropy groups and symmetry preserving and symmetry breaking
-bifurcation points.  The advanced exploitation of symmetry in the numerical
-computations causes an comprehensive symmetry analysis and complicated
-organization of numerical work which is done by the symbolic part of the
-algorithm.}}
-
-@TECHREPORT{Gatermann:91b,
- AUTHOR = "Karin Gatermann and Andreas Hohmann",
- TITLE = "Hexagonal Lattice Dome--Illustration of a Nontrivial Bifurcation
-Problem",
- INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
- YEAR = 1991, MONTH = "July", TYPE = "Preprint", NUMBER = "SC-91-8"}
- ABSTRACT = {The deformation of a hexagonal lattice dome under an external
-load is an example of a parameter dependent system which is equivariant
-under the symmetry group of a regular hexagon.  In this paper the mixed
-symbolic-numerical algorithm SYMCON is applied to analyze its steady state
-solutions automatically showing their different symmetry and stability
-properties.}}
-
-@TECHREPORT{Gatermann:92,
- AUTHOR = "Karin Gatermann",
- TITLE = "Computation of Bifurcation Graphs",
- INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
- YEAR = 1992, MONTH = "June", TYPE = "Preprint", NUMBER = "SC-92-13"}
- ABSTRACT = {The numerical treatment of equivariant parameter-dependent
-nonlinear equation systems, and even more its automation requires the
-intensive use of group theory.  This paper illustrates the group theoretic
-computations which are done in the preparation of the numerical computations.
-The bifurcation graph which gives the bifurcation subgroups is determined
-from the interrelationship of the irreducible representations of a group
-and its subgroups.  The Jacobian is transformed to block diagonal
-structure using a modification of the transformation which transforms to
-block diagonal structure with respect to a supergroup.  The principle of
-conjugacy is used everywhere to make symbolic and numerical computations
-even more efficient.  Finally, when the symmetry reduced problems and
-blocks of Jacobian matrices are evaluated numerically, the fact that the
-given representation is a quasi-permutation representation is exploited
-automatically.}}
-
-@TECHREPORT{Gatermann:93,
- AUTHOR = "Karin Gatermann and Bodo Werner",
- TITLE = "Group Theoretical Mode Interactions with Different Symmetries",
- INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
- YEAR = 1993, MONTH = "January", TYPE = "Preprint", NUMBER = "SC-93-3"}
- ABSTRACT = {In two-parameter systems two symmetry breaking bifurcation
-points of different types coalesce generically within one point.  This causes
-secondary bifurcation points to exit.  The aim of this paper is to
-understand this phenomenon with group theory and the innerconnectivity of
-irreducible representations of supergroup and subgroups.  Colored pictures
-of examples are included.}}
-
-@TECHREPORT{Gatermann:93a,
- AUTHOR = "Karin Gatermann and Bodo Werner",
- TITLE = "Secondary {Hopf} bifurcation caused by steady-state steady-state
-mode interaction",
- INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
- YEAR = 1993, MONTH = "July", TYPE = "Preprint", NUMBER = "SC-93-16",
- ABSTRACT = {In two-parameter systems with symmetry two steady state
-bifurcation points of different symmetry types coalesce generically within
-one point.  Under certain group theoretic conditions involving the action
-of the symmetry group on the kernels, we show that secondary Hopf
-bifurcation is borne by the mode interaction.  We explain this phenomenon
-by using linear representation theory.  For motivation an example with
-$D_{3}$-symmetry is investigated where the main properties causing the Hopf
-bifurcation are summarized.}}
-
-@TECHREPORT{Gatermann:94,
- AUTHOR = "Karin Gatermann",
- TITLE = "Semi-invariants, equivariants and algorithms",
- INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
- YEAR = 1994, MONTH = "May", TYPE = "Preprint", NUMBER = "SC-94-11",
- ABSTRACT = {The results from invariant theory and the results for semi-
-invariants and equivariants are summarized in a way suitable for the
-combination with G{r\"o}bner basis computation.  An algorithm for the
-determination of fundamental equivariants using projections and a
-Poinca\'{r}e series is described.  Secondly, an algorithm is given for the
-representation of an equivariant in terms  of the fundamental equivariants.
-Several ways for the exact determination of zeros of equivariant systems
-are discussed.}}
-
-@TECHREPORT{Gatermann:95,
- AUTHOR = "Karin Gatermann and Reiner Lauterbach",
- TITLE = "Automatic classification of normal forms",
- INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
- YEAR = 1995, MONTH = "February", TYPE = "Preprint", NUMBER = "SC-95-3",
- ABSTRACT = {The aim of this paper is to demonstrate a specific application
-of Computer Algebra to bifurcation theory with symmetry.  The
-classification of different bifurcation phenomena in case of several
-parameters is automated, based on a classification of G{r\"o}bner bases of
-possible tangent spaces.  The computations are performed in new coordinates
-of fundamental invariants and fundamental equivariants, with the induced
-weighted ordering.  In order to justify the approach the theory of
-intrinsic modules is applied.  Results for the groups $D_{3},Z_{2}$, and
-$Z_{2} x Z_{2}$ demonstrate that the algorithm works independent of the
-group and that new results are obtained.}}
-
-@INPROCEEDINGS{Gates:85,
- AUTHOR = "Barbara L. Gates and J. A. van Hulzen",
- TITLE = "Automatic Generation of Optimized Programs",
- BOOKTITLE = "Proc. {EUROCAL} '85", YEAR = 1985,
- MONTH = "April"}
-
-@ARTICLE{Gates:85a,
- AUTHOR = "Barbara L. Gates",
- TITLE = "Gentran:  An Automatic Code Generation Facility
-for {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1985, VOLUME = 19, NUMBER = 3, PAGES = "24-42", MONTH = "August"}
-
-@TECHREPORT{Gates:85b,
- AUTHOR = "Barbara L. Gates",
- TITLE = "Gentran User's Manual - {REDUCE} Version",
- INSTITUTION = "Twente University of Technology, Department of
-Computer Science, The Netherlands", TYPE = "Memorandum",
- YEAR = 1985, NUMBER = "INF-85-11", MONTH = "June"}
-
-@TECHREPORT{Gates:85c,
- AUTHOR = "Barbara L. Gates",
- TITLE = "Gentran Design and Implementation, {REDUCE} Version",
- INSTITUTION = "Twente University of Technology, Department of Computer
-Science, The Netherlands", YEAR = 1985, TYPE = "Memorandum",
- NUMBER = "INF-85-12", MONTH = "August"}
-
-@INPROCEEDINGS{Gates:86,
- AUTHOR = "Barbara L. Gates",
- TITLE = "A Numerical Code Generation Facility for {REDUCE}",
- BOOKTITLE = "Proc. {SYMSAC} '86",
- YEAR = 1986, PAGES = "94-99", MONTH = "July"}
-
-@TECHREPORT{Gebauer:85,
- AUTHOR = "R{\"u}diger Gebauer and H. Michael M{\"o}ller",
- TITLE = "A Fast Variant of {Buchberger's} Algorithm",
- INSTITUTION = "Universit{\"a}t Heidelberg and
-Fernuniversit{\"a}t {Hagen}", YEAR = 1985, MONTH = "October"}
-
-@ARTICLE{Gebauer:88,
- AUTHOR = "R{\"u}diger Gebauer and H. Michael M{\"o}ller",
- TITLE = "On an Installation of {Buchberger's} Algorithm",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1988, VOLUME = 6, NUMBER = "2 and 3", PAGES = "275-286"}
-
-@ARTICLE{Generalis:84,
- AUTHOR = "S. C. Generalis and D. J. Broadhurst",
- TITLE = "The heavy-quark expansion and {QCD} sum rules for light quarks",
- JOURNAL = "Physics Lett. B",
- YEAR = 1984, VOLUME = 139, PAGES = "85-89"}
-
-@ARTICLE{George:68,
- AUTHOR = "D. J. George",
- TITLE = "A Covariant Theory of the Disintegration of the
-Deuteron by Pions and Photons at High Energy",
- JOURNAL = "Phys. Rev.",
- YEAR = 1968, VOLUME = 167, PAGES = "1357-1364"}
-
-@ARTICLE{Gerdt:80,
- AUTHOR = "V. P. Gerdt",
- TITLE = "Analytical Calculations in High Energy Physics by Computer",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1980, VOLUME = 20, PAGES = "85-90",
- COMMENT = {A review, comparing {SCHOONSCHIP, ASHMEDAI and REDUCE-2}.}}
-
-@ARTICLE{Gerdt:80a,
- AUTHOR = "V. P. Gerdt and O. V. Tarasov and D. V. Shirkov",
- TITLE = "Analytical Calculations on Digital Computers for Applications
-in Physics and Mathematics",
- JOURNAL = "Sov. Phys. USP",
- YEAR = 1980, VOLUME = 23, PAGES = "59-77",
- COMMENT = {General review of applications in many languages.}}
-
-@TECHREPORT{Gerdt:80b,
- AUTHOR = "V. P. Gerdt",
- TITLE = "On Global Structure of the General Solution of the
-{Chew-Low} Equations",
- INSTITUTION = "J.I.N.R., Dubna",
- YEAR = 1980, TYPE = "Preprint", NUMBER = "P2-80-436"}
-
-@ARTICLE{Gerdt:85,
- AUTHOR = "V. P. Gerdt and A. B. Shvachka and A. Yu. Zharkov",
- TITLE = "Computer Algebra Application for Classification of
-Integrable Non-Linear Evolution Equations",
- JOURNAL = "J. Symb. Comp.",
- YEAR = 1985, VOLUME = 1, PAGES = "101-107"}
-
-@TECHREPORT{Gerdt:85a,
- AUTHOR = "V. P. Gerdt and N. A. Kostov and P. P. Raychev
-and R. P. Roussev",
- TITLE = "Calculation of the Matrix Elements of the
-{Hamiltonian} of the Interacting Vector Boson Model Using
-Computer Algebra - Basic Concepts of the Interacting Vector
-Boson Model and Matrix Elements of the {SU(3)-Quadrupole}
-Operator",
- INSTITUTION = "Institute for Nuclear Research and Nuclear
-Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria",
- YEAR = 1985, NUMBER = "E4-85-262"}
-
-@TECHREPORT{Gerdt:85b,
- AUTHOR = "V. P. Gerdt and N. A. Kostov and P. P. Raychev",
- TITLE = "Calculation of the Matrix Elements of the
-{Hamiltonian} of the Interacting Vector Boson Model Using
-Computer Algebra - Matrix Elements of the {Hamiltonian} and
-Some {U(6)-Clebsch-Gordon} Coefficients",
- INSTITUTION = "Institute for Nuclear Research and Nuclear
-Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria",
- YEAR = 1985, NUMBER = "E4-85-263"}
-
-@TECHREPORT{Gerdt:85c,
- AUTHOR = "V. P. Gerdt and N. A. Kostov and P. P. Raychev
-and R. P. Roussev",
- TITLE = "Calculation of the Matrix Elements of the
-{Hamiltonian} of the Interacting Vector Boson Model
-Using Computer Algebra - Matrix Elements of the {Hamiltonian} -
-Analytical Results",
- INSTITUTION = "Institute for Nuclear Research and Nuclear
-Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria",
- YEAR = 1985, NUMBER = "E4-85-264"}
-
-@TECHREPORT{Gerdt:86,
- AUTHOR = "V. P. Gerdt and M. G. Meshcheryakov and D. V. Shirkov",
- TITLE = "Computers in Theoretical Physics",
- INSTITUTION = "J.I.N.R., Dubna",
- YEAR = 1986, NUMBER = "P2-86-848",
- ABSTRACT = {The paper is written on the basis of the report presented by
-two authors ({M.G. Meshcheryakov} and {D.V. Shirkov}) at the 60th session
-of the JINR Scientific Council, June 5, 1986.  It reviews the usage of
-computer mathematics in theoretical and mathematical investigations
-carried out in the Joint Institute.  Recommendations are given on further
-development of the JINR Computer Center in accordance with the program of
-theoretical researches in nearest Five-Year Plan.}}
-
-@INPROCEEDINGS{Gerdt:87,
- AUTHOR = "V. P. Gerdt and A. B. Shabat and S. I. Svinolupov
-and A. Yu. Zharkov",
- TITLE = "Computer Algebra Application for Investigating
-Integrability of Nonlinear Evolution Systems",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "81-92",
- PUBLISHER = "Springer-Verlag"}
-
-@INPROCEEDINGS{Gerdt:87a,
- AUTHOR = "V. P. Gerdt and N. A. Kostov and Z. T. Kostova",
- TITLE = "Computer Algebra and Computation of {Puiseux} Expansions of
-Algebraic Functions",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "206-207",
- PUBLISHER = "Springer-Verlag"}
-
-@INPROCEEDINGS{Gerdt:89,
- AUTHOR = "V. P. Gerdt and N. A. Kostov",
- TITLE = "Computer Algebra in the theory of Ordinary Differential Equations
-of Halphen type",
- BOOKTITLE = "Proc. Computers and Mathematics '89",
- EDITOR = "E. Kaltofen and S. M. Watt",
- YEAR = 1989, PAGES = "279-288", PUBLISHER = "Springer-Verlag, New York"}
-
-@TECHREPORT{Gerdt:89a,
- AUTHOR = "V. P. Gerdt and Z. T. Kostova and N. A. Kostov and I. P. Yudin",
- TITLE = "Algebraic-Numeric Calculations of Proton Trajectories in Bending
-Magnets of Synchrotron Accelerator",
- INSTITUTION = "J.I.N.R., Dubna",
- YEAR = 1989, TYPE = "Preprint", NUMBER = "E11-89-755",
- ABSTRACT = {We study a solution of nonlinear differential equation of the
-second degree which describes the trajectories of the charged particles in
-the fully inhomogeneous field of cyclic accelerator.  We give the clear
-mathematical statement of the problem and algorithm of solving it.  We
-realize this algorithm on the Computer Algebra System {REDUCE 3.2}.  Our
-algorithm is based both on the existence of exact solution in terms of
-hyperelliptic integral and on the existence of power series solution of
-specific inversion problem.  We use the known {REDUCE} procedures of
-operation on generalized power series.  Using the {FORTRAN} code we give the
-numerical analysis of these series in the close relation to the concrete
-physical situation.  We apply our results to the beam dynamics modeling
-of the protons in the bending magnets in synchrotron accelerator.}}
-
-@TECHREPORT{Gerdt:89b,
- AUTHOR = "V. P. Gerdt and A. Yu. Zharkov",
- TITLE = "Solving the Polynomial System Arising in Classification of
-Integrable Coupled {KdV-like} Systems",
- INSTITUTION = "J.I.N.R., Dubna",
- YEAR = 1989, TYPE = "Preprint", NUMBER = "P5-89-231",
- ABSTRACT = {A system of algebraic equations which follows from the
-necessary integrability conditions for the {ten-parametric} family of
-coupled {KdV-like} nonlinear evolution systems is considered.  The method
-for solving this system based on the structure of the canonical local
-conservation laws densities is described.  Computer algebra system
-{REDUCE} was used to find all the solutions.  As a result we obtain the
-complete list of integrable coupled {KdV-like} systems.}}
-
-@InProceedings{Gerdt90,
-  author =      "V. P. Gerdt and A. Yu. Zharkov",
-  title =       "Computer Generation of Necessary Integrability
-                 Conditions for Polynomial-Nonlinear Evolution Systems",
-  booktitle =   "Proceedings of the International Symposium on
-                 Symbolic and Algebraic Computation",
-  year =        "1990",
-  editor =      "S. Watanabe and Morio Nagata",
-  pages =       "250-254",
-  organization =        "ACM",
-  publisher =   "Addison-Wesley"
-}
-
-@InProceedings{Gerdt90a,
-  author =      "Vladimar P. Gerdt and Nikolai V. Khutornoy and Alexey
-                 Yu. Zharkov",
-  title =       "Solving Algebraic Systems which arise as Necessary
-                 Integrability Conditions for Polynomial-Nonlinear
-                 evolution Equations",
-  booktitle =   "Proceedings of the International Symposium on
-                 Symbolic and Algebraic Computation",
-  year =        "1990",
-  editor =      "S. Watanabe and Morio Nagata",
-  pages =       "299",
-  organization =        "ACM",
-  publisher =   "Addison-Wesley"
-}
-
-@ARTICLE{Gerdt:90b,
- AUTHOR = "V. P. Gerdt and A. Yu. Zharkov",
- TITLE = "Computer Classification of Integrable Coupled {KdV-Like} Systems",
- JOURNAL = "J. Symb. Comp.",
- YEAR = 1990, VOLUME = 10, PAGES = "203-207",
- ABSTRACT = {The foundations of the symmetry approach to the classification
-problem of integrable {non-linear} evolution systems are briefly described.
-Within the framework of the symmetry approach the {ten-parametric} family
-of the third order {non-linear} evolution coupled {KdV-like} systems is
-investigated.  The necessary integrability conditions lead to an
-{over-determined} {non-linear} algebraic system.  To solve that system an
-effective method based on its structure has been used.  This allows us
-to obtain the complete list of integrable systems of a given type. All
-computation has been completed on the basis of computer algebra systems
-{FORMAC} and {REDUCE}.}}
-
-@INPROCEEDINGS{Gerdt:90c,
- AUTHOR = "V. P. Gerdt and N. A. Kostov and A. Yu. Zharkov",
- TITLE = "Nonlinear Evolution Equations and Solving Algebraic Systems:
-The Importance of Computer Algebra",
- YEAR = 1990,
- BOOKTITLE = "International Conference on Solitons and Its Applications",
- PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "120-128"}
- ABSTRACT = {In the present paper we study the application of computer
-algebra to solve the nonlinear polynomial systems which arise in
-investigation of nonlinear evolution equations.  We consider several
-systems which are obtained in classification of integrable nonlinear
-evolution equations with uniform rank.  Other polynomial systems are related
-with the finding of algebraic curves for finite-gap elliptic potentials of
-{Lame} type and generalizations.  All systems under consideration are
-solved using the method based on construction of the {Groebner} basis for
-corresponding polynomial ideals.  The computations have been carried out
-using computer algebra systems.}}
-
-@INPROCEEDINGS{Gerdt:91,
- AUTHOR = "V. P. Gerdt and A. Yu. Zharkov",
- TITLE = "Lie-{B{\"a}cklund} Symmetries of Coupled Nonlinear
-{Schr{\"o}dinger} Equations",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- EDITOR = "Stephen M. Watt",
- PUBLISHER = "ACM Press", ADDRESS = "Maryland", PAGES = "313-314",
- YEAR = 1991}
-
-@TECHREPORT{Gerdt:91a,
- AUTHOR = "V. P. Gerdt and P. Tiller",
- TITLE = "A {Reduce} Program for Symbolic Computation of {Puiseux}
-Expansions",
- INSTITUTION = "J.I.N.R., Dubna",
- YEAR = 1991, TYPE = "Preprint", NUMBER = "E5-91-401"}
- ABSTRACT = {The program is described for computation of Puiseux expansions
-of alebraic functions.  The Newton polygon method is used for construction
-of initial coefficients of all the Puiseux series at the given point.  The
-program is written in computer algebra language Reduce.  Some illustrative
-examples are given.}}
-
-@TECHREPORT{Gerdt:91b,
- AUTHOR = "V. P. Gerdt",
- TITLE = "Computer Algebra Tools for Higher Symmetry Analysis of Nonlinear
-Evolution Equations",
- INSTITUTION = "J.I.N.R., Dubna",
- YEAR = 1991, TYPE = "Preprint", NUMBER = "E5-91-402"}
- ABSTRACT = {This paper presents a computer-aided approach and a software
-package for symbolic algebraic computation to solve the problem of
-verifying the existence of the canonical Lie-B{\"a}cklund symmetries
-for multicomponent quasilinear evolution equations with polynomial-
-nonlinearity and computing a given order symmetry if any.  In the presence
-of arbitrary numerical parameters the problem is reduced to investigation
-and solving of nonlinear algebraic equations in those parameters.  It is
-remarkable that in all the known cases these algebraic equations are
-completely solvable by the Gr{\"o}bner basis technique implemented as a part
-of the software package.}}
-
-@InProceedings{Gerdt:93,
-  author =      "V. Gerdt",
-  title =       "Homogeneity of Integrability Conditions for Multiparametric
-                 Families of Polynomial-Nonlinear Evolution Equations",
-  booktitle =   "Proceedings of the 1993 International IMACS Symposium on
-                 Symbolic Computation",
-  year =        "1993",
-  editor =      "G. Jacob and N. E. Oussous and S. Steinberg",
-  pages =       "181-186",
-  organization ="IMACS",
-  publisher =   "Laboratoire d'Informatique Fondamentale de Lille, France",
-  comment =     {A canonical form algorithm for quantities with locally scoped
-                 variables (e.g. Summation convention, tensor products) is
-                 developed in a {REDUCE} package.}
-}
-
-@ARTICLE{Gervois:74,
- AUTHOR = "A Gervois and Y. Pomeau",
- TITLE = "Logarithmic Divergence in the Virial Expansion
-of Transport Coefficients of Hard Spheres",
- JOURNAL = "Phys. Rev. A",
- YEAR = 1974, VOLUME = 9, PAGES = "2196-2213"}
-
-@TECHREPORT{Gladd:82,
- AUTHOR = "N. T. Gladd",
- TITLE = "Computational Aspects of Research on the
-Relativistic {Whistler} Instability",
- INSTITUTION = "Jaycor", YEAR = 1982,
- NUMBER = "J530-82-020", MONTH = "June"}
-
-@INPROCEEDINGS{Gladkih:83,
- AUTHOR = "I. Gladkih and E. Lovas",
- TITLE = "On the Application of Computer Algebra Languages in the {Central
-Research Institute for Physics}",
- BOOKTITLE = "Proceedings of the International Conference on Systems and
-Techniques of Analytical Computing and Their Applications in Theoretical
-Physics, {D11-83-511, Dubna}", YEAR = 1983}
-
-@INPROCEEDINGS{Gladkih:84,
- AUTHOR = "I. Gladkih and M. Zimanyi",
- TITLE  = "Comparison of systems for Symbolic Computing in use in the
-{Central Research Institute for Physics} (in {Russian})",
- BOOKTITLE = "Proceedings of the International Conference on {Computer-Based}
-Scientific Research, Plovdiv", YEAR =  1984}
-
-@ARTICLE{Goldman:89,
- AUTHOR = "V. V. Goldman and J. A. van Hulzen",
- TITLE = "Automatic Code Vectorization of Arithmetic Expressions by
-Bottom-Up Structure Recognition",
- JOURNAL = "Computer Algebra and Parallelism", EDITOR = "J. Della Dora
-and J. Fitch",
- YEAR = 1989, PAGES = "119-132", PUBLISHER = "Academic Press, London"}
-
-@INPROCEEDINGS{Golley,
- AUTHOR = "Bruce W. Golley and Joseph Petrolito",
- TITLE = "An Alternative Finite Strip Technique for the Static Analysis of
-Single-Span, Multi-Span and Continuous Plates",
- YEAR = 1982,
- BOOKTITLE = "Proc. International Conference on
-Finite Element Methods"}
-
-@ARTICLE{Good:75,
- AUTHOR = "D. Good and R. L. London and W. W. Bledsoe",
- TITLE = "An Interactive Program Verification System",
- JOURNAL = "Sigplan Notices",
- YEAR = 1975, VOLUME = 10, NUMBER = 6, PAGES = "482-492"}
-
-@ARTICLE{Goto:77,
- AUTHOR = "E. Goto and T. Soma",
- TITLE = "{MOL} (Moving Objective Lens) Formulation of
-Deflective Aberration Free System",
- JOURNAL = "Optik",
- YEAR = 1977, VOLUME = 48, PAGES = "255-270"}
-
-@INPROCEEDINGS{Goto:78,
- AUTHOR = "E. Goto and T. Soma",
- TITLE = "Electron Beam Lithography for Advanced {LSI} Fabrication",
- YEAR = 1978, PAGES = "1223-1228",
- BOOKTITLE = "Proc. 1978 National Computer Conference,
-{AFIPS} Press, New Jersey"}
-
-@ARTICLE{Gould:84,
- AUTHOR = "H. W. Gould and M. E. Mays",
- TITLE = "Series Expansions of Means",
- JOURNAL = "Journ. of Mathematical Analysis and Applications",
- YEAR = 1984, VOLUME = 101, NUMBER = 2, PAGES = "611-621",
- MONTH = "July"}
-
-@ARTICLE{Graebe:93,
- AUTHOR = "Hans-Gert Gr{\"a}be",
- TITLE = "On Lucky Primes",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1993, VOLUME = 15, NUMBER = 2, PAGES = "199-209", MONTH = "February",
- COMMENT = {Winkler (1988) and Pauer (1992) present algorithms for a Hensel
-lifting of a modular Gr{\"o}bner basis over lucky primes to a rational
-one.  They have to solve a linear system with modular polynomial entries
-that requires another (modular) Gr{\"o}ner basis computation.
-After an extension of luckiness to arbitrary (commutative noetherian) base
-rings we show in this paper that for a homogeneous polynomial ideal I one
-lift not only only its Gr{\"o}bner basis but also a homogeneous basis of
-its syzygy module.  The same result holds for arbitrary ideals and
-liftings from Z/p to Q.  Moreover the same lifting can be obtained from a
-true Gro{\"o}bner trace by linear algebra over Q only.  Parallel modular
-techniques allow to find such a true Gro{\"o}bner and a lucky prime with
-high probability.
-All these results generalize in an obvious way to homogeneous modules
-generated by the rows of matrices with polynomial entries.  Since
-luckiness can be weakened to a condition that transfers from I to higher
-syzygy modules the lifting theorem generalizes to a lifting theorem for
-the resolution of I.}}
-
-@PHDTHESIS{Gragert:81,
- AUTHOR = "Peter Gragert",
- TITLE = "Symbolic Computations in Prolongation Theory",
- SCHOOL = "Twente University of Technology, The Netherlands",
- YEAR = 1981}
-
-@BOOK{Grammaticos,
- AUTHOR = "B. Grammaticos and A. Voros",
- TITLE = "Semi-Classical Approximations for Nuclear
-{Hamiltonians}:  {II}. {Spin-dependent} Potentials",
- ABSTRACT = {A systematic semi-classical expansion procedure for physical
-quantities in nuclei, based on the Thomas-Fermi approximation
-to the Hartree-Fock equations and constructed in a previous
-work, is extended here to the realistic case where the
-effective one-body {Hamiltonian} for nucleons contains
-spin-dependent terms.}}
-
-@TECHREPORT{Grammaticos:78,
- AUTHOR = "B. Grammaticos and A. Voros",
- TITLE = "Semi-classical Approximations for Nuclear
-{Hamiltonians} {I}. {Spin-independent} Potentials",
- INSTITUTION = "CEN, Saclay", YEAR = 1978, TYPE = "Preprint",
- NUMBER = "DPh-T/78-75", MONTH = "August",
- COMMENT = {Submitted to Annals of Physics},
- ABSTRACT = {A systematic procedure for calculating semi-classical
-expansions of physically interesting quantities is presented.}}
-
-@ARTICLE{Grammaticos:85,
- AUTHOR = "B. Grammaticos and B. Dorizzi and A. Ramani and J. Hietarinta",
- TITLE = "Extending integrable {Hamiltonian} systems from 2 to {N}
-dimensions",
- JOURNAL = "Phys. Lett.",
- YEAR = 1985, VOLUME = "109A", PAGES = "81-84",
- COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
-
-@ARTICLE{Gray:90,
- AUTHOR = "N. Gray and D. J. Broadhurst and W. Grafe and K. Schilcher",
- TITLE = {Three-loop relation of quark $\overline{\rm MS}$ and pole masses},
- JOURNAL = "Zeitschrift {f\"{u}r} Physik C",
- YEAR = 1990, VOLUME = 48, PAGES = "673-679"}}
-
-@ARTICLE{Greenland:84,
- AUTHOR = "P. T. Greenland",
- TITLE = "Comparison Between Phase Diffusion and Random Telegraph Signal
-Models of Laser Bandwidth",
- JOURNAL = "Journ. Phys. B",
- YEAR = 1984, VOLUME = 17, PAGES = "1919-1925",
- COMMENT = {{REDUCE} calculation of correlation matrix for molecular physics.
-Tedious, but simple result.}}
-
-@ARTICLE{Grimm,
- AUTHOR = "R. Grimm and H. K{\"u}hnelt",
- TITLE = "Using {REDUCE} in Problems of Supersymmetry and Supergravity",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1980, VOLUME = 20, PAGES = "77",
- COMMENT = {Describes how {REDUCE} may be used with advantage in tedious
-calculations of supersymmetry and supergravity.}}
-
-@INPROCEEDINGS{Griss:74,
- AUTHOR = "M. L. Griss",
- TITLE = "The Algebraic Solution of Large Sparse Systems of Linear
-Equations Using {REDUCE} 2",
- YEAR = 1974, PAGES = "105-111",
- BOOKTITLE = "Proc. ACM 74",
- ABSTRACT = {This paper discusses some of the problems encountered during the
-solution of a large system of sparse linear equations with algebraic
-coefficients, using {REDUCE} 2.}}
-
-@ARTICLE{Griss:74a,
- AUTHOR = "M. L. Griss",
- TITLE = "The Algebraic Solution of Sparse Linear Systems Via Minor
-Expansion",
- JOURNAL = "ACM TOMS 2",
- YEAR = 1976, PAGES = "31-49",
- ABSTRACT = {An improved algorithm for computing the determinants of a (large)
-sparse matrix of polynomials is described.}}
-
-@INPROCEEDINGS{Griss:75,
- AUTHOR = "Martin L. Griss",
- TITLE = "The {REDUCE} System for Computer Algebra",
- BOOKTITLE = "Proc. ACM 75",
- YEAR = 1975, PAGES = "4-5",
- ABSTRACT = {A brief description of {REDUCE} is presented.}}
-
-@INPROCEEDINGS{Griss:76,
- AUTHOR = "Martin L. Griss",
- TITLE = "The Definition and Use of Data-Structures in {REDUCE}",
- BOOKTITLE = "Proc. SYMSAC 76",
- YEAR = 1976, PAGES = "53-59",
- ABSTRACT = {This paper gives a brief description and motivation of the mode
-analyzing and data-structuring extensions to the algebraic language
-{REDUCE}.}}
-
-@INPROCEEDINGS{Griss:76a,
- AUTHOR = "Martin L. Griss",
- TITLE = "An Efficient Sparse Minor Expansion Algorithm",
- BOOKTITLE = "Proc. ACM 76",
- YEAR = 1976, PAGES = "429-434",
- ABSTRACT = {An improved algorithm for computing the minors of a (large)
-sparse matrix of polynomials is described, with emphasis on efficiency and
-optimal ordering.  A possible application to polynomial resultant
-computation is discussed.}}
-
-@INPROCEEDINGS{Griss:77,
- AUTHOR = "Martin L. Griss",
- TITLE = "Efficient Expression Evaluation in Sparse Minor
-Expansion, Using Hashing and Deferred Evaluation",
- YEAR = 1977, PAGES = "169-172",
- BOOKTITLE = "Proc. 10th Hawaii International Conference on
-Systems Sciences, Western Periodicals, Calif.",
- ABSTRACT = {Efficient computation of the determinant of a matrix with
-symbolic entries using minor expansion requires careful control of expression
-evaluation.  The use of hashing and deferred evaluation to avoid
-excess computation is explored.}}
-
-@ARTICLE{Griss:77a,
- AUTHOR = "M. L. Griss",
- TITLE = "Efficient Recursive Minor Expansion",
- JOURNAL = "ACM TOMS",
- YEAR = 1977,
- ABSTRACT = {The use of a "memo" facility to develop an efficient recursive
-minor expansion algorithm (RMEM) is discussed.  The method is simple and
-efficient, and can be implemented as an interesting non-trivial
-recursive procedure.  The method is particularly attractive for
-sparse symbolic matrices, and can also be used to enhance other
-minor expansion methods developed for sparse symbolic matrices.}}
-
-@ARTICLE{Griss:78,
- AUTHOR = "Martin L. Griss",
- TITLE = "Using an Efficient Sparse Minor Expansion Algorithm to Compute
-Polynomial Subresultants and the Greatest Common Denominator",
- JOURNAL = "IEEE Trans on Computers",
- YEAR = 1978, VOLUME = "C-27", NUMBER = 10, PAGES = "945-950",
- ABSTRACT = {In this paper, the use of an efficient sparse minor expansion
-method to directly compute the subresultants needed for the {GCD} of two
-polynomials is described.  The sparse minor expansion method (applied
-either to Sylvester's or Bezout's matrix) naturally computes the
-coefficients of the subresultants in the order corresponding to
-a {PRS}, avoiding wasteful recomputation as much as possible.  It is
-suggested that this is an efficient method to compute the Resultant
-and {GCD} of Sparse Polynomials.}}
-
-@INPROCEEDINGS{Griss:78a,
- AUTHOR = "Martin L. Griss and Robert R. Kessler",
- TITLE = "{REDUCE}/1700:  A Micro-coded Algebra System",
- YEAR = 1978, VOLUME = 11, PAGES = "130-138",
- BOOKTITLE = "Proc. Micro, {IEEE}",
- ABSTRACT = {In this paper, we report on the status of an ongoing project
-aimed at producing a micro-coded Algebra machine.}}
-
-@ARTICLE{Griss:79,
- AUTHOR = "Martin L. Griss and Anthony C. Hearn",
- TITLE = "Portable {LISP} Compiler",
- JOURNAL = "Software - Practice and Experience", VOLUME = 11,
- PAGES = "541-605", YEAR = 1979,
- ABSTRACT = {This paper describes the development of a portable {LISP}
-compiler in the sense that only Standard {LISP} functions are used in its
-definition and the output is a sequence of standard macro calls
-easily implementable on current computers.}}
-
-@TECHREPORT{Griss:79a,
- AUTHOR = "Martin L. Griss and Robert R. Kessler",
- TITLE = "A Micro-programmed Implementation of {Standard} {LISP} and
-{REDUCE} on the {Burroughs B1700/B1800} Computer",
- INSTITUTION = "University of Utah", YEAR = 1979, TYPE = "Report",
- MONTH = "February",
- ABSTRACT = {This paper describes the implementation of a microcoded {LISP}
-"machine" (the MTLISP) for the Burroughs B1700/B1800 computers.
-This interpreter supports a complete Standard {LISP} and {REDUCE}
-Algebra system, as well as a variety of experimental {LISP-like}
-systems.}}
-
-@INPROCEEDINGS{Grozin:83,
- AUTHOR={A. G. Grozin},
- TITLE={Calculation of one-loop diagrams of {$1 \to 2$} decays with {REDUCE}},
- BOOKTITLE={Proc. Int. Conf. on Computer Algebra in Theoretical Physics,
-Dubna},
- YEAR = 1983, PAGES = {226-231},
-  COMMENT = {To appear in Phys. Lett. B}}
-
-@TECHREPORT{Grozin:88,
- AUTHOR = "A. G. Grozin",
- TITLE = "Solving Physical Problems with {REDUCE.}  {1. REDUCE}
-Language {2. Classical} Nonlinear Oscillator",
- INSTITUTION = "Institute of Nuclear Physics 630090, Novosibirsk,
-{USSR}", YEAR = 1988, TYPE = "Preprint", NUMBER = "88-115",
- ABSTRACT = {This preprint is the first part of the problem book on using
-{REDUCE} in physics.  It contains many examples useful for the
-construction of programs for solving physical problems of very
-different nature.  This part contains examples illustrating {REDUCE}
-language (sect. 1) and the problem of classical nonlinear
-oscillator (sect. 2).  To be published (with additions) as a book with
-"Nauka" publishers, Moscow.}}
-
-@TECHREPORT{Grozin:88a,
- AUTHOR = "A. G. Grozin",
- TITLE = "Solving Physical Problems with {REDUCE.}  {3. Nonlinear}
-Water Waves {4. Calculation} of the Curvature Tensor {5. Angular}
-Momentum Addition",
- INSTITUTION = "Institute of Nuclear Physics 630090, Novosibirsk,
-{USSR}", YEAR = 1988, TYPE = "Preprint", NUMBER = "88-136",
- ABSTRACT = {This preprint is the second part of the problem book on using
-{REDUCE} in physics.  It contains many examples useful for the construction of
-programs for solving physical problems of very different nature.  This
-part contains the problem of nonlinear water waves (sect. 3), the
-calculation of the curvature tensor (sect. 4) and angular momentum
-addition (sect. 5).}}
-
-@TECHREPORT{Grozin:88b,
- AUTHOR = "A. G. Grozin",
- TITLE = "Solving Physical Problems with {REDUCE.}  {6. Quantum}
-Nonlinear Oscillator {7. Rotator} in a Weak Field {8. Radiative}
-Transitions in Charmonium",
- INSTITUTION = "Institute of Nuclear Physics 630090, Novosibirsk,
-{USSR}", YEAR = 1988, TYPE = "Preprint", NUMBER = "88-140",
- ABSTRACT = {This preprint is the last part of the problem book on using
-{REDUCE} in physics.  It contains many examples useful for the construction of
-programs for solving physical problems of very different nature.  This
-part contains the problem of quantum nonlinear oscillator (sect. 6),
-rotator in a weak field (sect. 7) and radiative transitions in
-charmonium (sect. 8).}}
-
-@TECHREPORT{Grozin:90,
- AUTHOR = {A. G. Grozin},
- TITLE = {{REDUCE} in elementary particle physics. {Introduction}},
- INSTITUTION = {Institute of Nuclear Physics, Novosibirsk},
- YEAR = 1990, NUMBER = {INP 90-42},
- COMMENT = {These 5 preprints together with the previous 3 will be published
-as a book "Solving physical problems with REDUCE"}}
-
-@TECHREPORT{Grozin:90a,
- AUTHOR = {A. G. Grozin},
- TITLE = {{REDUCE} in elementary particle physics. {Quantum electrodynamics}},
- INSTITUTION = {Institute of Nuclear Physics, Novosibirsk},
- YEAR = 1990, NUMBER = {INP 90-71}}
-
-@TECHREPORT{Grozin:90b,
- AUTHOR = {A. G. Grozin},
- TITLE = {{REDUCE} in elementary particle physics. {Quantum chromodynamics}},
- INSTITUTION = {Institute of Nuclear Physics, Novosibirsk},
- YEAR = 1990, NUMBER = {INP 90-62}}
-
-@TECHREPORT{Grozin:91,
- AUTHOR = {A. G. Grozin},
- TITLE = {{REDUCE} in elementary particle physics. {Weak interactions}},
- INSTITUTION = {Institute of Nuclear Physics, Novosibirsk},
- YEAR = 1991, NUMBER = {INP 91-56}}
-
-@TECHREPORT{Grozin:91a,
- AUTHOR = {A. G. Grozin},
- TITLE = {{REDUCE} in elementary particle physics. {Radiative corrections}},
- INSTITUTION = {Institute of Nuclear Physics, Novosibirsk},
- YEAR = 1991, NUMBER = {INP 91-46}}
-
-@ARTICLE{Gunion:72,
- AUTHOR = "J. F. Gunion and S. J. Brodsky and R. Blankenbecler",
- TITLE = "Composite Theory of Large Angle Scattering and New
-Tests of Parton Concepts",
- JOURNAL = "Phys. Lett.",
- YEAR = 1972, VOLUME = "39B", PAGES = "649-653"}
-
-@TECHREPORT{Gunion:73,
- AUTHOR = "J. F. Gunion and S. J. Brodsky and R. Blankenbecler",
- TITLE = "Large Angle Scattering and the Interchange Force",
- INSTITUTION = "SLAC",
- YEAR = 1973, TYPE = "Report", NUMBER = "SLAC-PUB-1183"}
-
-@ARTICLE{Gunion:85,
- AUTHOR = "J. F. Gunion and Z. Kunszt",
- TITLE = "Improved Analytic Techniques for Tree Graph Calculations and
-the $g g q {\bar q} l {\bar l}$ subprocess",
- JOURNAL = "Phys. Lett.",
- YEAR = 1985, VOLUME = "161B", PAGES = "333-340"}
-
-@ARTICLE{Hadinger:87,
- AUTHOR = "G. Hadinger and Y. S. Tergimen",
- TITLE = "Recurrence Relations for the {Dunham} Coefficients and Analytic
-Expressions of the Diagonal Radial Matrix Elements for an Anharmonic
-Oscillator",
- JOURNAL = "Journ. Chem. Phys.",
- YEAR = 1987, VOLUME = 87, NUMBER = 4, PAGES = "2143-2150",
- COMMENT = {"As an illustrative application, all the set of $Y_{n}$
-coefficients previously published are found again by using the
-computer algebraic manipulation language {REDUCE}.  A number of diagonal
-matrix elements of {CO, HBr and HCl} have been symbolically computed and
-compared with previous available results."  Their method depends on
-some algebraic manipulation, and the main point is that automation
-gives a simpler formulation of the problem.}}
-
-@ARTICLE{Handy:87,
- AUTHOR = "N. C. Handy",
- TITLE = "The Derivation of Vibration-Rotation Kinetic Energy Operators,
-in Internal Coordinates",
- JOURNAL = "Mol. Phys.",
- YEAR = 1987, VOLUME = 61, PAGES = "207-223",
- COMMENT = {{REDUCE USED} to produce a straightforward method for the
-derivation of kinetic energy operators in molecular vibration-rotation.  He
-notes in the introduction "The purpose of this paper is to derive a simple and
-straightforward procedure for which it is possible to make the
-computer do all the hard work.  After many years of investigating this
-problem, this author believes that this must be the reliable way to
-proceed."}}
-
-@PHDTHESIS{Harper:87,
- AUTHOR = "David Harper",
- TITLE = "Dynamics of the Outer Satellites of Saturn",
- SCHOOL = "Univ. of Liverpool, England",
- YEAR = 1987}
-
-@TECHREPORT{Harper:89,
- AUTHOR = "David Harper and Chris Wooff and David Hodgkinson",
- TITLE = "A Guide to Computer Algebra Systems",
- INSTITUTION = "Computer Laboratory, The University of Liverpool,
-Liverpool, England", YEAR = 1989, MONTH = "September", TYPE = "Report"}
-
-@ARTICLE{Harper:89a,
- AUTHOR = "David Harper",
- TITLE = "{Vector33:}  A {REDUCE} Program for Vector Algebra and Calculus
-in Orthogonal Curvilinear Coordinates",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1989, VOLUME = 54, NUMBER = "2 and 3", PAGES = "295-305",
- MONTH = "June and July"}
-
-@ARTICLE{Harrington:77,
- AUTHOR = "Steven J. Harrington",
- TITLE = "A Symbolic Limit Evaluation Program in {REDUCE}",
- YEAR = 1977,
- ABSTRACT = {A program for the automatic evaluation of algebraic
-limits, implemented in {MODE-REDUCE}, is described.  The program
-incorporates many of the techniques previously employed, including
-the top-down recursive evaluation, power series expansion, and
-L'Hopital's rule.  It also introduces the concept of a special
-algebraic form for limits.}}
-
-@ARTICLE{Harrington:77a,
- AUTHOR = "S. J. Harrington",
- TITLE = "{REDUCE} Solution to Problem \#8",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = "1977 and 1978", VOLUME = "11 and 12", NUMBER = "4 and 1",
- PAGES = "7-8", MONTH = "November and February"}
-
-@ARTICLE{Harrington:79,
- AUTHOR = "Steven J. Harrington",
- TITLE = "A New Symbolic Integration System in {REDUCE}",
- JOURNAL = "Comp. Journ.",
- YEAR = 1979, VOLUME = 22, NUMBER = 2, PAGE = "127-131",
- ABSTRACT = {A new integration system, employing both algorithmic and
-pattern match integration schemes is presented.  The organization of the
-system differs from that of earlier programs in its emphasis on the
-algorithmic approach to integration, its modularity, and its ease of
-revision.  The new {Norman-Risch} algorithm and its implementation at the
-University of Cambridge are employed, supplemented by a powerful
-collection of simplification and transformation rules.  The facility for
-user defined integrals and functions is also included.  The program is
-both fast and powerful, and can be easily modified to incorporate
-anticipated developments in symbolic integration.}}
-
-@ARTICLE{Harrington:79a,
- AUTHOR = "Steven J. Harrington",
- TITLE = "A Symbolic Limit Evaluation Program in {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1979, VOLUME = 13, NUMBER = 1, PAGES = "27-31", MONTH = "February"}
-
-@ARTICLE{Hartley:91,
- AUTHOR = "David Hartley and Robin W. Tucker",
- TITLE = "A Constructive Implementation of the {Cartan-K{\"a}hler} Theory
-of Exterior Differential Systems",
- JOURNAL = "J. Symb. Comp.",
- YEAR = 1991, VOLUME = 12, NUMBER = 6, PAGES = "655-667",
- MONTH = "December",
- ABSTRACT = {An efficient algorithm for the construction of a regular chain
-of involutive integral elements for a general exterior differential system
-is presented.  It is based upon the existence theorems of the
-{Cartan-}K{"\a}hler theory, and may be used to analyse partial differential
-equations by formulating them as exterior differential systems.}}
-
-@ARTICLE{Hasenfratz:80,
- AUTHOR = "Anna Hasenfratz and Peter Hasenfratz",
- TITLE = "The Connection Between the Parameters of Lattice and
-Continuum {QCD}",
- JOURNAL = "Phys. Lett.",
- YEAR = 1980, VOLUME = "93B", NUMBER = "1,2", PAGES = "165-169",
- MONTH = "June"}
-
-@INPROCEEDINGS{Hearn:68,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "{REDUCE}: A User-Oriented Interactive System for Algebraic
-Simplification",
- YEAR = 1968, PAGES = "79-90",
- EDITOR = "M. Klerer and J. Reinfelds",
- BOOKTITLE = "Interactive Systems for Experimental Applied Mathematics",
- PUBLISHER = "Academic Press", ADDRESS = "New York"}
-
-@ARTICLE{Hearn:69,
- AUTHOR = "A. C. Hearn and P. K. Kuo and D. R. Yennie",
- TITLE = "Radiative Corrections to an Electron-Positron Scattering
-Experiment",
- JOURNAL = "Phys. Rev.",
- YEAR = 1969, VOLUME = 187, PAGES = "2088-2096"}
-
-@INPROCEEDINGS{Hearn:69a,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "The Problem of Substitution",
- YEAR = 1969, PAGES = "3-19",
- EDITOR = "R.G. Tobey",
- BOOKTITLE = "Proc. of the 1968 Summer Institute on Symbolic Mathematical
-Computation",
- PUBLISHER = "IBM Boston Prog. Center", ADDRESS = "Cambridge, Mass",
- COMMENT = "IBM Programming Laboratory Report No. FSC-69-0312"}
-
-@ARTICLE{Hearn:71,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "Applications of Symbolic Manipulation in Theoretical Physics",
- JOURNAL = "Comm. ACM",
- YEAR = 1971, VOLUME = 14, PAGES = "511-516"}
-
-@INPROCEEDINGS{Hearn:71a,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "{REDUCE} 2: A System and Language for Algebraic Manipulation",
- YEAR = 1971, PAGES = "128-133",
- EDITOR = "S.R. Petrick",
- BOOKTITLE = "Proc. of Second Symposium on Symbolic and
-Algebraic Manipulation",
- PUBLISHER = "ACM, New York"}
-
-@INPROCEEDINGS{Hearn:71b,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "Calculation of Traces of Products of Gamma Matrices",
- YEAR = 1971, PAGES = "I-30 - I-44",
- BOOKTITLE = "Proc. of the Second Colloquium on Advanced Computing
-Methods in Theoretical Physics, {CNRS}, Marseilles",
- ABSTRACT = {A survey of the algorithms available for the calculation of
-traces of products of Dirac gamma matrices is presented.}}
-
-@INPROCEEDINGS{Hearn:71c,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "The Computer Solution of Algebraic Problems by Pattern Matching",
- YEAR = 1971, PAGES = "I-45 - I-57",
- BOOKTITLE = "Proc. of the Second Colloquium on Advanced Computing
-Methods in Theoretical Physics, {CNRS}, Marseilles",
- ABSTRACT = {This paper discusses computer techniques for the solution of
-algebraic  problems in theoretical physics and related areas by pattern
-matching.}}
-
-@INPROCEEDINGS{Hearn:72,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "Computer Solution of Symbolic Problems in Theoretical Physics",
- YEAR = 1972, PAGES = "567-596",
- BOOKTITLE = "Computing as a Language of Physics, {IAEA}, Vienna",
- ABSTRACT = {A survey of the computing techniques currently available for
-the solution of nonnumerical problems in theoretical physics and related
-areas is presented.}}
-
-@ARTICLE{Hearn:72a,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "Improved Non-modular Polynomial {GCD} Algorithm",
- JOURNAL = "SIGSAM Bulletin",
- YEAR = 1972, PAGES = "10-15",
- ABSTRACT = {An improved non-modular algorithm for the calculation of the
-greatest common divisor of two multivariate polynomials is presented.}}
-
-@ARTICLE{Hearn:72b,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "A {REDUCE} Solution of Problem \#2 - The {Y(2n)} Functions",
- JOURNAL = "SIGSAM Bulletin",
- YEAR = 1972, VOLUME = 14,
- ABSTRACT = {A {REDUCE} solution to {SIGSAM} Problem \#2 is described.}}
-
-@INPROCEEDINGS{Hearn:73,
- AUTHOR = "Anthony C. Hearn and R{\"u}diger G. K. Loos",
- TITLE = "Extended Polynomial Algorithms",
- YEAR = 1973, PAGES = "147-152",
- BOOKTITLE = "Proc. {ACM} 73",
- ABSTRACT = {It is shown that standard polynomial algorithms may be
-applied to a much wider class of functions by making a straightforward
-generalization of the concept of the exponent.  The implementation of a
-computer algebra system from a standard set of polynomial programs which
-allows for any coefficient or exponent structure is also discussed.}}
-
-@INPROCEEDINGS{Hearn:73a,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "The {REDUCE} Program for Computer Algebra",
- YEAR = 1973,
- BOOKTITLE = "Proc. of the Third Colloquium on Advanced Computing Methods
-in Theoretical Physics, {CNRS}, Marseilles",
- ABSTRACT = {The status of the {REDUCE} program for computer algebra in 1973
-is illustrated by a discussion of some aspects of its design philosophy.}}
-
-@INPROCEEDINGS{Hearn:74,
- AUTHOR = "Anthony C. Hearn",
- TITLE = " Polynomial and Rational Function Representations",
- YEAR = 1974, PAGE = "211",
- BOOKTITLE = "Proc. Math Software II, Purdue University",
- ABSTRACT = {A survey of some current methods for computer manipulation of
-polynomials and rational functions is presented.  Particular emphasis
-is placed on the desirability of writing programs which avoid explicit
-reference to the data structures used in the manipulation."}}
-
-@INPROCEEDINGS{Hearn:74a,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "A Mode Analyzing Algebraic Manipulation Program",
- YEAR = 1974, PAGES = "722-724",
- BOOKTITLE = "Proc. {ACM} 74",
- COMMENT = {Describes a version of the {REDUCE} program for algebraic
-manipulation which performs a complete mode analysis as a separate extension
-of the parse.}}
-
-@ARTICLE{Hearn:76,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "Scientific Applications of Symbolic Computation",
- JOURNAL = "Computer Science and Scientific Comp.",
- YEAR = 1976, PAGES = "83-108",
- ABSTRACT = {This paper reviews the use of symbolic computation systems for
-problem solving in scientific research.}}
-
-@INPROCEEDINGS{Hearn:76a,
- AUTHOR = "A. C. Hearn",
- TITLE = "A New {REDUCE} Model for Algebraic Simplification",
- YEAR = 1976, PAGES = "46-52",
- BOOKTITLE = "Proc. {SYMSAC} 76, {ACM}",
- ABSTRACT = {This paper shows how the general concepts of mode analysis can
-play a useful role in the design and implementation of programs
-for algebraic simplification.}}
-
-@INPROCEEDINGS{Hearn:76b,
- AUTHOR = "A. C. Hearn",
- TITLE = "Symbolic Computation",
- YEAR = 1976, PAGES = "201-211",
- BOOKTITLE = "Proc. {CERN} 1976 Computing School, {CERN} Geneva",
- COMMENT = {Lecture Notes.}}
-
-@INPROCEEDINGS{Hearn:77,
- AUTHOR = "A. C. Hearn",
- TITLE = "The Structure of Algebraic Computations",
- YEAR = 1977, PAGES = "1-15",
- BOOKTITLE = "Proc. of the Fourth Colloquium on Advanced Comp.
-Methods in Theor. Physics. St. Maximin, France",
- ABSTRACT = {Most algebraic computations which arise from physical problems
-have considerable structure in their specification because of the many
-physical conservation laws and the nature of our approximation techniques.
-The exploitation of this structure is often the reason why hand
-calculations of non-trivial problems are possible.  However, most
-available algebra systems do not preserve such structure in a consistent
-manner, and consequently produce results which are far less comprehensible
-than equivalent hand calculations.  In this paper we shall describe
-techniques which can utilize the algebraic structure more effectively and
-apply them to several examples.}}
-
-@INPROCEEDINGS{Hearn:78,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "Algebraic Manipulation by Computer",
- YEAR = 1978, PAGES = "96-116",
- BOOKTITLE = "Proc. Intern. Meeting on Programm. and Math. Meth. for
-Solving Phys. Probs., Dubna, USSR",
- ABSTRACT = {This paper reviews the use of algebraic manipulation by computer
-as a tool for scientific problem solving.}}
-
-@INPROCEEDINGS{Hearn:79,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "Non-Modular Computation of Polynomial {GCDs} Using Trial
-Division",
- YEAR = 1979, VOLUME = 72, PAGES = "227-239",
- BOOKTITLE = "Proc. {EUROSAM} 79",
- ABSTRACT = {This paper describes a new algorithm for the determination of
-the {GCD} of two multivariate polynomials by non-modular means.}}
-
-@ARTICLE{Hearn:79a,
- AUTHOR = "Anthony C. Hearn and Arthur C. Norman",
- TITLE = "A One-Pass Prettyprinter",
- JOURNAL = "Sigplan Notices, ACM 12",
- YEAR = 1979, VOLUME = 14, PAGES = "50-58",
- ABSTRACT = {We propose a new method for program formatting which is
-described in terms of two coroutines.}}
-
-@INPROCEEDINGS{Hearn:80,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "The Personal Algebra Machine",
- YEAR = 1980, PAGES = "621-628",
- BOOKTITLE = "Information Processing 80, Proc. {IFIP}
-Congress 80"}
-
-@ARTICLE{Hearn:81,
- AUTHOR = "Anthony C. Hearn and S. Watanabe",
- TITLE = "Analytic Integration by Computer",
- JOURNAL = "Information Processing Society of Japan 22",
- YEAR = 1981, PAGES = "639-650"}
-
-@INPROCEEDINGS{Hearn:81a,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "Symbolic Computation and its Application to
-High-Energy Physics",
- YEAR = 1981, PAGES = "390-406",
- BOOKTITLE = "Proc. 1980 {CERN} School of Computing, Geneva"}
-
-@INPROCEEDINGS{Hearn:82,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "{REDUCE} - A Case Study in Algebra System Development",
- YEAR = 1982, VOLUME = 144, PAGES = "263-272",
- BOOKTITLE = "Proc. of {EUROCAM} '82, Lecture Notes on Comp.
-Science"}
-
-@INPROCEEDINGS{Hearn:82a,
- AUTHOR = "Anthony C. Hearn and M. L. Griss and E. Benson",
- TITLE = "Current Status of a Portable {LISP} Compiler",
- YEAR = 1982,
- BOOKTITLE = "Proc. {SIGPLAN} '82 Symp. on Compiler
-Construction, ACM", PAGES = "276-283"}
-
-@INPROCEEDINGS{Hearn:85,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "Structure:  The Key to Improved Algebraic Computation",
- YEAR = 1985,
- BOOKTITLE = "Proc. of the Second {RIKEN} International
-Symposium on Symbolic and Algebraic Computation by Computers",
- PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "215-230"}
-
-@INPROCEEDINGS{Hearn:86,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "Optimal Evaluation of Algebraic Expressions",
- BOOKTITLE = "Proc. {AAECC}-3, Lecture Notes on Comp. Science",
- PUBLISHER = "Springer Verlag",
- YEAR = 1986, VOLUME = 229, PAGES = "392-403"}
-
-@TECHREPORT{Hearn:91,
- AUTHOR = "Anthony C. Hearn",
- TITLE = "{REDUCE} User's Manual, {Version} 3.6",
- INSTITUTION = "RAND",
- YEAR = 1995, TYPE = "Report",
- NUMBER = "CP 78", MONTH = "July"}
-
-@INPROCEEDINGS{Hearn:93,
- AUTHOR = "Anthony C. Hearn and Eberhard Schr{\"u}fer",
- TITLE = "An Order-sorted Approach to Algebraic Computation",
- BOOKTITLE = "Proc. {DISCO '93}, Lecture Notes on Comp. Science",
- YEAR = 1993, VOLUME = 722, PAGES = "134-144",
- PUBLISHER = "Springer-Verlag",
- ABSTRACT = {This paper presents the prototype design of an algebraic
-computation system that manipulates algebraic quantities as generic objects
-using order-sorted algebra as the underlying model.  The resulting programs
-have a form that is closely related to the algorithmic description of a
-problem, but with the secruity of full type checking in a compact, natural
-style.}}
-
-@ARTICLE{Hearn:95,
- AUTHOR = "Anthony C. Hearn and Eberhard Schr{\"u}fer",
- TITLE = "A Computer Algebra System based on Order-sorted Algebra",
- JOURNAL = "Journ. Symbolic Computation",
- YEAR = 1995, VOLUME=19, PAGES = "65-77",
- ABSTRACT = "This paper presents the prototype design of an algebraic
-computation system that manipulates algebraic quantities as generic
-objects using order-sorted algebra as the underlying model.  The resulting
-programs have a form that is closely related to the algorithmic
-description of a problem, but with the security of full type checking in a
-compact, natural style."}
-
-@ARTICLE{Hehl:92,
- AUTHOR = "Friedrich W. Hehl and Hartmut Meyer",
- TITLE = "Mit Buchstaben auf dem Computer rechnen",
- JOURNAL = "Physikalische {Bl\"{a}tter}",
- YEAR = 1992, VOLUME = "48", PAGES = "377-381",
- COMMENT = {(in German) Describes the application of
- symbolic computation using examples coded in {REDUCE}. The CA systems
- of interest for physicists are classified. A series of problems
- from physics which have successfully been solved with CA methods
- is given}}
-
-@BOOK{Hehl:92a,
- AUTHOR = "F.W. Hehl and V. Winkelmann and H. Meyer",
- TITLE = "Computer-Algebra. Ein Kompaktkurs {\"{u}ber} die Anwendung von
-REDUCE",
- PUBLISHER = "Springer-Verlag, Berlin, Heidelberg, New York,
-   ISBN 3-540-55724-5",
- YEAR = 1992}
-
-@ARTICLE{Hermann:83,
- AUTHOR = "R. Hermann",
- TITLE = "Geometric Construction and Properties of Some Families of
-Solutions of Nonlinear Partial Differential Equations",
- JOURNAL = "J. Math. Phys.",
- YEAR = 1983,  VOLUME = 24, NUMBER = "3", PAGES = "510-521",
- COMMENT = {First of series of papers on 19th century pde theory.  The
-presentation is aimed at including systems such as {MACSYMA} and {REDUCE}
-as tools.  This paper is on Lagrange-Charpit method. "I have in mind
-developing the differential algebraic aspects of the formalism, going
-beyond the 19th century with the aid of symbolic computer systems".}}
-
-@ARTICLE{Hess:84,
- AUTHOR = "P. O. Hess and W. Greiner",
- TITLE = "The Collective Modes of Nuclear Molecules",
- JOURNAL = "Il Nuovo Cimento",
- YEAR = 1984, VOLUME = "83A", PAGES = "76-177",
- COMMENT = {A long paper, admits use of {REDUCE} (on page 101) to invert
-11 x 11 matrix.}}
-
-@TECHREPORT{Hettich:77,
- AUTHOR = "R. P. Hettich and J. A. van Hulzen",
- TITLE = "Approximation with a Class of Rational Functions",
- INSTITUTION = "Department of Applied Mathematics, Twente
-University of Technology, The Netherlands",
- YEAR = 1977, TYPE = "Memorandum",
- NUMBER = 165, MONTH = "May"}
-
-@ARTICLE{Hietarinta:83,
- AUTHOR = "J. Hietarinta",
- TITLE = "A search for integrable two-dimensional {Hamiltonian} systems
-with polynomial potential",
- JOURNAL = "Phys. Lett.",
- YEAR = 1983, VOLUME = "96A", PAGES = "273-278",
- COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
-
-@ARTICLE{Hietarinta:83a,
- AUTHOR = "J. Hietarinta",
- TITLE = "Integrable Families of {Henon-Heiles} Type {Hamiltonians} and a
-New Duality",
- JOURNAL = "Phys. Rev. A",
- YEAR = 1983, VOLUME = 28, PAGES = "3670-3672",
- COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
-
-@ARTICLE{Hietarinta:84,
- AUTHOR = "J. Hietarinta",
- TITLE = "Classical versus quantum integrability",
- JOURNAL = "J. Math. Phys.",
- YEAR = 1984, VOLUME = 25, PAGES = "1833-1840",
- COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
-
-@ARTICLE{Hietarinta:84a,
- AUTHOR = "J. Hietarinta",
- TITLE = "New integrable {Hamiltonians} with transcendental invariants",
- JOURNAL = "Phys. Rev. Lett.",
- YEAR = 1984, VOLUME = 52, PAGES = "1057-1060",
- COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
-
-@ARTICLE{Hietarinta:84b,
- AUTHOR = "J. Hietarinta and B. Grammaticos and B. Dorizzi and A. Ramani",
- TITLE = "Coupling-Constant Metamorphosis and Duality between
-Integrable {Hamiltonian} Systems",
- JOURNAL = "Phys. Rev. Lett.",
- YEAR = 1984, VOLUME = 53, PAGES = "1707-1710",
- COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
-
-@ARTICLE{Hietarinta:85,
- AUTHOR = "J. Hietarinta",
- TITLE = "How to construct integrable {Fokker-Planck} and
-electromagnetic {Hamiltonians} from ordinary integrable {Hamiltonians}",
- JOURNAL = "J. Math. Phys.",
- YEAR = 1985, VOLUME = 26, PAGES = "1970-1975",
- COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
-
-@ARTICLE{Hietarinta:87,
- AUTHOR = "J. Hietarinta",
- TITLE = "Direct methods for the search of the second invariant",
- JOURNAL = "Physics Reports",
- YEAR = 1987, VOLUME = 147, PAGES = "87-154",
- COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
-
-@ARTICLE{Hietarinta:87a,
- AUTHOR = "J. Hietarinta",
- TITLE = "A search of bilinear equations passing {Hirota's} three-soliton
-condition: {I.} {KdV}-type bilinear equations",
- JOURNAL = "J. Math. Phys.",
- YEAR = 1987, VOLUME = 28, PAGES = "1732-1742",
- COMMENT = {{REDUCE} is used to check when polynomials in 6 to 12 variables
-vanish on a affine manifold defined by {LET-rules}.  Large scale
-computation.}}
-
-@ARTICLE{Hietarinta:87b,
- AUTHOR = "J. Hietarinta",
- TITLE = "A search of bilinear equations passing {Hirota's} three-soliton
-condition: {II.} {mKdV}-type bilinear equations",
- JOURNAL = "J. Math. Phys.",
- YEAR = 1987, VOLUME = 28, PAGES = "2094-2101",
- COMMENT = {{REDUCE} is used to check when polynomials in 6 to 12 variables
-vanish on a affine manifold defined by {LET-rules}.  Large scale
-computation.}}
-
-@ARTICLE{Hietarinta:87c,
- AUTHOR = "J. Hietarinta",
- TITLE = "A search of bilinear equations passing {Hirota's} three-soliton
-condition: {III.} {Sine-Gordon}-type bilinear equations",
- JOURNAL = "J. Math. Phys.",
- YEAR = 1987, VOLUME = 28, PAGES = "2586-2592",
- COMMENT = {{REDUCE} is used to check when polynomials in 6 to 12 variables
-vanish on a affine manifold defined by {LET-rules}.  Large scale
-computation.}}
-
-@ARTICLE{Hietarinta:88,
- AUTHOR = "J. Hietarinta",
- TITLE = "A search of bilinear equations passing {Hirota's} three-soliton
-condition: {IV.} Complex bilinear equations",
- JOURNAL = "J. Math. Phys.",
- YEAR = 1988, VOLUME = 29, PAGES = "628-635",
- COMMENT = {{REDUCE} is used to check when polynomials in 6 to 12 variables
-vanish on a affine manifold defined by {LET-rules}.  Large scale computation.
-computation.}}
-
-@ARTICLE{Hietarinta:89,
- AUTHOR = "J. Hietarinta and B. Grammaticos",
- TITLE = "On the $\hbar^{2}$-correction terms in quantum integrability",
- JOURNAL = "J. Phys. A: Mat. Gen.",
- YEAR = 1989, VOLUME = "TBD", PAGES = "TBD",
- COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
-
-@INPROCEEDINGS{Hietarinta:91,
- AUTHOR = "J. Hietarinta",
- TITLE = "From an analytical formula to a movie by way of {REDUCE} and {C}",
- BOOKTITLE = "Proc. of the Workshop on Symbolic and Numeric Computation",
- PUBLISHER = "Research Reports, Computing Centre of Helsinki University",
- YEAR = 1991, PAGES = "117-126"}
-
-@TECHREPORT{Hietarinta:92,
- AUTHOR = "Jarmo Hietarinta",
- TITLE = "Solving the {Yang-Baxter} equation in 2 dimensions with massive
-use of factorizing Gr{"\o}bner basis computations",
- INSTITUTION = "University of Turku, Finland", YEAR = 1992,
- MONTH = "January", TYPE = "Preprint",
- COMMENT = {Submitted to ISSAC '92},
- ABSTRACT = {The complete solution to the constant (quantum) Yang-Baxter
-equation was recently obtained in the two dimensional case
-(= all indices range over 1,2).  This amounts to solving a set of 64
-equations in 16 variables.  We describe here how the problem was solved,
-first by breaking it into smaller subproblems by using the symmetries of
-the equation, and then by solving each subproblem by computing the
-factorized Gr{"\o}bner basis using the {'grobner'-}package written by Melenk,
-M{"\o}ller and Neun for REDUCE 3.4.}}.
-
-@TECHREPORT{Hietarinta:92a,
- AUTHOR = "Jarmo Hietarinta",
- TITLE = "Solving the two-dimensional constant quantum {Yang-Baxter}
-  equation",
- INSTITUTION = "University of Turku, Finland", YEAR = 1992,
- MONTH = "May", TYPE = "Report", NUMBER = "TURKU-FL-R7"}
-
-@BOOK{Hirota:89,
- AUTHOR = "Ryogo Hirota and Masaaki Ito",
- TITLE = "Introduction to {REDUCE --- Doing} Symbolic Computation on {PC}",
- PUBLISHER = "Science sha, Tokyo", MONTH = "June", YEAR = 1989,
- COMMENT = {(In Japanese).}}
-
-@TECHREPORT{Horowitz:75,
- AUTHOR = "E. Horowitz and D. R. Musser",
- TITLE = "The Synthesis and Use of Algebraic Specifications of Data
-Structures",
- INSTITUTION = "University of Southern California",
- YEAR = 1975, TYPE = "Preprint"}
-
-@ARTICLE{Horwitz:83,
- AUTHOR = "B. Horwitz",
- TITLE = "Unequal Diameters and Their Effects on Time Varying Voltages
-in Branched Neurons",
- JOURNAL = "BioPhys. J.",
- YEAR = 1983, VOLUME = 41, PAGES = "51-66",
- COMMENT = {Theoretical biophysics.  Much algebra, and used {REDUCE} to
-decrease mental labor.  "Crucial point is that the existence of such computer
-techniques allows higher-order correction terms to be used."}}
-
-@ARTICLE{Hughes:90,
- AUTHOR = "D. I. Hughes",
- TITLE = "Symbolic Computation with Fermions",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1990, VOLUME = 10, NUMBER = 6, PAGES = "657-664", MONTH = "December",
- ABSTRACT = {A set of {REDUCE} routines for manipulating operators which
-anticommute amongst themselves is described.  These routines have
-applications in theories such as supergravity where anticommuting operators
-are used to represent fermions.  The Dirac bracket of the supersymmetry
-constraints arising in a quantum cosmological model based on N = 1
-supergravtiy coupled to a massless scalar multiplet is calculated as an
-example.}}
-
-@INPROCEEDINGS{Hulshof:84,
- AUTHOR = "B. J. A. Hulshof and J. A. van Hulzen",
- TITLE = "Automatic Error Cumulation Control",
- BOOKTITLE = "Proc. {EUROSAM} 1984, Lecture Notes
-in Computer Science", YEAR = 1984, VOLUME = 174, PAGES = "260-271",
- PUBLISHER = "Springer-Verlag"}
-
-@INPROCEEDINGS{Hulshof:85,
- AUTHOR = "B. J. A. Hulshof and J. A. van Hulzen",
- TITLE = "An Expression Compression Package for {REDUCE} based on
-Factorization and Controlled Expansion",
- BOOKTITLE = "Proc. {EUROCAL} 1985, Lecture Notes
-in Computer Science", YEAR = 1985, VOLUME = 204, PAGES = "315-316",
- PUBLISHER = "Springer-Verlag"}
-
-@TECHREPORT{Hulshof:81,
- AUTHOR = "B. J. A. Hulshof and J. A. van Hulzen and J. Smit",
- TITLE = "Code Optimization Facilities Applied in the {Netform} Context",
- INSTITUTION = "Department of Applied Mathematics, Twente
-University of Technology, The Netherlands",
- YEAR = 1981, TYPE = "Memorandum", NUMBER = 368,
- MONTH = "December"}
-
-@ARTICLE{Hulshof:83,
- AUTHOR = "B. J. A. Hulshof and J. A. van Hulzen",
- TITLE = "Some {REDUCE} Facilities for Pretty Printing Subscripts and Formal
-Derivatives",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "16-20", MONTH = "February"}
-
-@ARTICLE{Hunt:91,
- AUTHOR = "R. E. Hunt and D. G. Crighton",
- TITLE = "Instability of flows in spatially developing media",
- JOURNAL = "Proc. Roy. Soc. Lond. A",
-YEAR = 1991, VOLUME = 435, PAGES = "109-128",
- COMMENT = {Uses {REDUCE} to find series solutions for two fluid-dynamical
-  problems, and then condenses the series into exact solutions}}
-
-@TECHREPORT{Husberg:81,
- AUTHOR = "N. Husberg",
- TITLE = "Preliminary {II} {REDUCE}-2 and {Analitik-74}, a Comparison",
- INSTITUTION = "Helsinki University of Technology Computing
-Center", YEAR = 1981, MONTH = "November"}
-
-%                          REDUCE BIBLIOGRAPHY
-
-%                              Part 3:  I-O
-
-% Copyright (c) 1993 RAND.  All Rights Reserved.
-
-% Additions and corrections are solicited.  Please send them, in the
-% same format as these entries if possible, to reduce at rand.org.
-
-
-@TECHREPORT{Idesawa:77,
- AUTHOR = "M. Idesawa and T. Yatagai",
- TITLE = "General Theory of Projection-Type {Moir\'e} Topography",
- INSTITUTION = "Institute of Physical and Chemical Research,
-Wako-Shi, Saitama", YEAR = 1977, TYPE = "Scientific Papers",
- NUMBER = 71,
- ABSTRACT = {The configuration of equi-order surfaces in the projection-type
-{Moire} topography is described in terms of system parameters
-without any restrictions on the measurement condition.}}
-
-@INPROCEEDINGS{Ilyin:87,
- AUTHOR = "V. A. Ilyin and A. P. Kryukov",
- TITLE = "{DIMREG} - The Package for Calculations in the Dimensional
-Regularization with {4-dimensional} $\gamma^{5}$ -matrix in Quantum Field
-Theory",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "225-232",
- PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{Ilyin:89,
- AUTHOR = "V. A. Ilyin and A. P. Kryukov and A. Ya. Rodioniov and
-A. Yu. Taranov",
- TITLE = "Fast Algorithm for Calculation of {Dirac}'s Gamma-Matrices Traces",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1989, VOLUME = 23, NUMBER = 4, PAGES = "15-24", MONTH = "October"}
-
-@INPROCEEDINGS{Ilyin:91,
- AUTHOR = "V. A. Ilyin and A. P. Kryukov",
- TITLE = "Symbolic Simplification of Tensor Expressions Using Symmetries,
-Dummy Indices and Identities",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- EDITOR = "Stephen M. Watt",
- PUBLISHER = "ACM Press", ADDRESS = "Maryland", PAGES = "224-228",
- YEAR = 1991,
- ABSTRACT = {The algorithm based on simple geometrical ideas is suggested
-for simplification of tensor expressions which takes into account
-symmetries, dummy indices, and linear identities with many terms.  The
-results of the realization in REDUCE system are adduced.}}
-
-@INPROCEEDINGS{Ilyin:91a,
- AUTHOR = "V. A. Ilyin and A. P. Kryukov and A. Ya. Rodionov and A Yu.
-Taranov",
- TITLE = "{PC} Implementation of Fast {Dirac} Matrix Trace Calculations",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- EDITOR = "Stephen M. Watt",
- PUBLISHER = "ACM Press", ADDRESS = "Maryland", PAGES = "456-457",
- YEAR = 1991,
- COMMENT = {We present an implementation of fast algorithm for Dirac
-matrix trace calculations.  This implementation is made for {IBM}       i
-compatible {PC} and works under {REDUCE 3.3.1}.  Name of package is
-{CVIT}.  The algorithm itself was described in [1].  It is based on intense
-use of Fierz identities in N-dimensional space (N is arbitrary natural
-number or symbol) and may be considered as an extension of well known
-Kahane algorithm [2] on higher space dimensions.}}
-
-@TECHREPORT{Inada:80,
- AUTHOR = "Nobuyuki Inada",
- TITLE = "Fortran-Based {LISP} System for {REDUCE}",
- INSTITUTION = "Information Science Laboratory, The Institute
-of Physical and Chemical Research",
- YEAR = 1980}
-
-@TECHREPORT{Ioakimidis:90,
- AUTHOR = "N. I. Ioakimidis",
- TITLE = "Construction of the Equation of Caustics in Dynamic Plane
-Elasticity Problems with the Help of {REDUCE}",
- INSTITUTION = "Division of Applied Mathematics and Mechanics, School of
-Engineering, University of Patras, Greece",
- YEAR = 1990}
- ABSTRACT = {The method of caustics has become a very efficient tool in
-crack, hole and many additional plane elasticity problems.  Unfortunately,
-the fundamental equation of the caustics frequently requires complicated
-algebraic computations including that of a Jacobian determinant.  Here we
-show that computer algebra software can prove very efficient in these
-computations, using as a vehicle for this illustration the already known
-fundamental equation of caustics in dynamic plane elasticity (both for crack
-problems in fracture mechanics as well as for hole and additional problems).
-We have used the programming capabilities of {REDUCE}, a very popular
-computer algebra system, for our algebraic computations.  Moreover, we
-illustrate the "learning" abilities of {REDUCE} especially for the
-derivation of the complex form of this equation.  The case of static plane
-elasticity results simply as a special case of dynamic plane elasticity.
-Additional possibilities are suggested in brief.}}
-
-@TECHREPORT{Ioakimidis:90a,
- AUTHOR = "N. I. Ioakimidis",
- TITLE = "Construction of Singular Integral Equations for Interacting
-Straight Cracks by Using {REDUCE}",
- INSTITUTION = "Division of Applied Mathematics and Mechanics, School of
-Engineering, University of Patras, Greece",
- YEAR = 1990}
- ABSTRACT = {The method of singular integral equations has been applied to
-the solution of crack problems in plane and antiplane elasticity
-hundreds of times during the last twenty years.  Here we revisit the case of
-an arbitrary number of interacting straight cracks in plane elasticity and
-we illustrate the possibility of constructing (algebraically) the
-corresponding system of singular integral equations by using computer
-algebra software.  We present a procedure (computer program) by using
-{REDUCE} as well as several examples of application of the present approach,
-extensions and generalizations of which follow rather trivially.}}
-
-@ARTICLE{Ito:85,
- AUTHOR = "M. Ito",
- TITLE = "A {REDUCE} Program for Evaluating a {Lax} Pair Form",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1985, VOLUME = 34, PAGES = "325-331",
- COMMENT = {{REDUCE} in nonlinear equations.}}
-
-@ARTICLE{Ito:85a,
- AUTHOR = "M. Ito and F. Kako",
- TITLE = "A {REDUCE} Program for Finding Conserved Densities of Partial
-Differential Equations with Uniform Rank",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1985, VOLUME = 38, PAGES = "415-419"}
-
-@ARTICLE{Ito:88,
- AUTHOR = "Masaaki Ito",
- TITLE = "A {REDUCE} Program for {Hirota's} Bilinear Operator and
-{Wronskian} Operations",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1988, VOLUME = 50, NUMBER = 3, PAGES = "321-330", MONTH = "August"}
-
-@ARTICLE{Ito:90,
- AUTHOR = "Nobuyasu Ito and Tetsuhiko Chikyu",
- TITLE = "Multi-Spin-Flip Dynamics of the {Ising} Chain",
- JOURNAL = "Physica A",
- YEAR = 1990, VOLUME = 166, PAGES = "193-205",
- ABSTRACT = {Two kinds of multi-spin-flip discrete-time dynamics of the
-Ising chain are solved analytically.  One dynamics is the two sublattice
-type flip and each sublattice contains {\em n} sequential spins
-alternately.  The other has the overlapped multi-spin-flip sequence.  The
-state of {\em n} spins at the next time step is selected from ${2}^{n}$
-states using the heat-bath type transition probability.  These dynamics of
-the Ising chain are equivalent to the statics of the square-lattice Ising
-model with a 1 x 2 unit cell or of the triangular-lattice Ising model.
-The analytic solutions of the single spin relaxation time of these
-dynamics are obtained using these equivalences.}}
-
-@ARTICLE{Ito:90a,
- AUTHOR = "Nobuyasu Ito",
- TITLE = "Discrete-Time and Single-Spin-Flip Dynamics of the {Ising} Chain",
- JOURNAL = "Progress of Theoretical Physics",
- YEAR = 1990, VOLUME = 83, NUMBER = 4, PAGES = "682-692", MONTH = "April",
- ABSTRACT = {Some stochastic dynamics of the Ising chain are discussed
-analytically and their flip-sequence dependences are studied in the
-present paper.  The dynamics are the discrete-time and single-spin-flip
-dynamics.  The flip sequence is of sequential or sublattice-type.  Their
-relaxation times of single spin expectation functions are calculated.  The
-sequential-flip dynamics of {\em n}-site chain has the same correlation
-time as the {\em n}-sublattice dynamics.  The relaxation becomes slow when
-this {\em n} is made large.  The static models equivalent to these dynamic
-models are the Ising models on a triangular lattice with a skew boundary
-condition which has the same couplings in two directions.  Spin-spin
-correlation lengths in the direction perpendicular to the anisotropic
-direction are obtained for these equivalent models.  They depend only on
-the ratio of the lattice width to boundary skew.}}
-
-@ARTICLE{Ito:94,
- AUTHOR = "Masaaki Ito",
- TITLE = "{SYMCD} - a {REDUCE} package for finding symmetries and conserved
-densitites of systems of nonlinear evolution equations",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1994, VOLUME = 79, NUMBER = 3, PAGES = "547-554", MONTH = "May"}
-
-@ARTICLE{Jansen:86,
- AUTHOR = "Paul Jansen and Peter Weidner",
- TITLE = "High-Accuracy Arithmetic Software--Some Tests of the
-{ACRITH} Problem-Solving Routines",
- JOURNAL = "{ACM} {TOMS}",
- YEAR = 1986, VOLUME = 12, NUMBER = 1, PAGES = "62-70", MONTH = "March",
- COMMENT = {A criticism of {ACRITH}, shows {REDUCE} bigfloats are more
-accurate and comparable in speed.}}
-
-@ARTICLE{Janssen:87,
- AUTHOR = "M. H. M. Janssen and D. H. Parker and S. Stolte",
- TITLE = "Saturation in Laser-Induced Fluorescence:  Effects on
-Alignment Parameters",
- JOURNAL = "Chemical Phys.",
- YEAR = 1987, VOLUME = 113, PAGES = "357-382",
- COMMENT = {"Computer algebra programs are used to generate simple analytical
-expressions which account for the influence of saturation on
-determining alignment parameters."  The system is {REDUCE}.}}
-
-@ARTICLE{Jeffrey:84,
- AUTHOR = "D. J. Jeffrey and Y. Onishi",
- TITLE = "The Forces and Couples Acting on Two Nearly Touching Spheres
-in Low-{Reynolds}-Number Flow",
- JOURNAL = "Z. Ang. Math. Phys.",
- YEAR = 1984, VOLUME = 35, PAGES = "634-641",
- COMMENT = {Extends previous result from linear term to
-O$\epsilon$ in $\epsilon$.  "Otherwise the only new principle in the
-calculation is the handling of long algebraic expressions, which was
-accomplished by using the computer algebra systems {CAMAL} and {REDUCE}."}}
-
-@ARTICLE{Kadlecsik:88,
- AUTHOR = "J. Kadlecsik",
- TITLE = "New Approaches to the Axisymmetric Vacuum",
- JOURNAL = "Zeitschrift {f\"{u}r} Physik C. Particles and Fields",
- YEAR = 1988, VOLUME = 41, PAGES = "265-269"}
-
-@TECHREPORT{Kadlecsik:92,
- AUTHOR = "Jo{\'o}zsef Kadlecsik",
- TITLE = "Tensor Manipulation Package for General Relativity Calculations",
- INSTITUTION = "Central Research Institute for Physics, Budapest",
- YEAR = 1992, TYPE = "Preprint", NUMBER = "KFKI-1992-05/B+M",
- ABSTRACT = {An experimental computer program is presented, which manipulates
-tensor expressions symbolically in general relativity calculations.}}
-
-@ARTICLE{Kagan:85,
- AUTHOR = "Y. Y. Kagan and L. Knopoff",
- TITLE = "The First-Order Statistical Moment of the Seismic Moment Tensor",
- JOURNAL = "Geophys. J. R. Astron. Soc.",
- YEAR = 1985, VOLUME = 81, PAGES = "429-444"}
-
-@ARTICLE{Kagan:88,
- AUTHOR = "Y. Y. Kagan",
- TITLE = "Static Sources of Elastic Deformation in a Homogeneous
-Half-Space",
- JOURNAL = "J. Geophys. Res.",
- YEAR = 1988, VOLUME = 93, NUMBER = "B9", PAGES = "10,560-10,574",
- MONTH = "September"}
-
-@TECHREPORT{Kahn:69,
- AUTHOR = "M. E. Kahn",
- TITLE = "The Near-Minimum-Time Control of Open Loop Articulated
-Kinematic Chains",
- INSTITUTION = "Stanford University, Computer Science Dept.",
- YEAR = 1969, TYPE = "Report", NUMBER = "AIM-106"}
-
-@TECHREPORT{Kamal:81,
- AUTHOR = "A. N. Kamal and J. Kodaira and T. Muta",
- TITLE = "Gluon Jets From Heavy Paraquarkonium",
- INSTITUTION = "University of Alberta, Canada and Stanford
-University, California and  Fermi National Accelerator
-Laboratory, Illinois",
- YEAR = 1981, NUMBER = "SLAC-PUB-2725", MONTH = "April"}
-
-@TECHREPORT{Kamel:69,
- AUTHOR = "A. A. Kamel",
- TITLE = "Perturbation Method in the Theory of Non-Linear Oscillations",
- INSTITUTION = "Stanford University, Dept. of Aeronautics
-and Astronautics", YEAR = 1969, TYPE = "Report"}
-
-@TECHREPORT{Kamel:69a,
- AUTHOR = "A. A. Kamel",
- TITLE = "Perturbation Theory Based on {Lie} Transforms and Its
-Application to the Stability of Motion Near {Sun}-Perturbed
-{Earth-Moon} Triangular Libration Points",
- INSTITUTION = "Stanford University, Dept. of Aeronautics and
-Astronautics", YEAR = 1969, TYPE = "Report", NUMBER = "391"}
-
-@INPROCEEDINGS{Kamel:78,
- AUTHOR = "A. A. Kamel",
- TITLE = "Synchronous Satellite Ephemeris Due to Earth's
-Triaxiality and Luni-Solar Effects",
- YEAR = 1978, MONTH = "August",
- BOOKTITLE = "{AIAA/AAS} Astrodynamics Conference,
-Palo Alto, CA",
- COMMENT = {Synchronous satellite ephemeris is developed in terms of
-non-singular orbital elements.}}
-
-@ARTICLE{Kanada:81,
- AUTHOR = "Yasumasa Kanada and Tateaki Sasaki",
- TITLE = "{LISP-based} {big-float} system is not slow",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1981, VOLUME = 15, NUMBER = 2, PAGES = "13-19", MONTH = "May"}
-
-@TECHREPORT{Kanada:75,
- AUTHOR = "Y. Kanada",
- TITLE = "Implementation of {HLISP} and Algebraic Manipulation
-Language {REDUCE} 2",
- INSTITUTION = "University of Tokyo Information Science Lab",
- YEAR = 1975, TYPE = "Report", NUMBER = "75-01"}
-
-@ARTICLE{Kaneko:89,
- AUTHOR = "Toshiaki Kaneko and Setsuya Kawabata",
- TITLE = "A Preprocessor for {Fortran} Source Code Produced by {REDUCE}",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1989, VOLUME = 55, NUMBER = 2, PAGES = "141-147",
- MONTH = "September", PUBLISHER = "North Holland Publishing Company"}
-
-@ARTICLE{Kaps:85,
- AUTHOR = "P. Kaps and S. W. H. Poon and T. D. Bui",
- TITLE = "Rosenbrock Methods for Stiff {ODEs}:  A Comparison of {Richardson}
-Extrapolation and Embedding Techniques",
- JOURNAL = "Computing",
- YEAR = 1985, VOLUME = 34, PAGES = "17-40",
- COMMENT = {Reference to {REDUCE} but not in text.}}
-
-@INPROCEEDINGS{Karr:85,
- AUTHOR = "Michael Karr",
- TITLE = "Canonical Form for Rational Exponential Expressions",
- BOOKTITLE = "Proc. {EUROCAL} 1985, Lecture Notes
-in Computer Science", YEAR = 1985, VOLUME = 204, PAGES = "585-594",
- PUBLISHER = "Springer-Verlag"}
-
-@INPROCEEDINGS{Katsura:85,
- AUTHOR = "Shigetoshi Katsura",
- TITLE = "Application of the Formula Manipulating System to Statistical
- Mechanics", YEAR = 1985,
- BOOKTITLE = "Proc. of the Second {RIKEN} International
-Symposium on Symbolic and Algebraic Computation by Computers",
- PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "155-180"}
-
-@PHDTHESIS{Kauffman:73,
- AUTHOR = "S. K. Kauffman",
- TITLE = "Ortho-Positronium Annihilation:  Steps Toward Computing
-the First Order Radiative Corrections",
- SCHOOL = "California Institute of Technology",
- YEAR = 1973}
-
-@INPROCEEDINGS{Kazasov:87,
- AUTHOR = "C. Kazasov",
- TITLE = "Laplace Transformations in {REDUCE} 3",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "132-133",
- PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{Keady:85,
- AUTHOR = "Grant Keady",
- TITLE = "The Power Concavity of Solutions of Some Semilinear Elliptic
-{Boundary-Value} Problems",
- JOURNAL = "Bull. Austral. Math. Soc.",
- YEAR = 1985, VOLUME = 31, PAGES = "181-184"}
-
-@ARTICLE{Keener:83,
- AUTHOR = "James P. Keener",
- TITLE = "Oscillatory coexistence in the {chemostat:} a codimension two
-unfolding",
- JOURNAL = "{SIAM} J. Appl. Math.",
- YEAR = 1983, VOLUME = 43, NUMBER = 5, PAGES = "1005-1018"}
-
-@ARTICLE{Keener:85,
- AUTHOR = "James P. Keener",
- TITLE = "Oscillatory coexistence in a food chain model with competing
-predators",
- JOURNAL = "J. Math. Biology",
- YEAR = 1985, VOLUME = 22, PAGES = "123-135"}
-
-@ARTICLE{Keener:89,
- AUTHOR = "James P. Keener",
- TITLE = "Knotted scroll wave filaments in excitable media",
- JOURNAL = "Physica D 34",
- YEAR = 1989, PAGES = "378-390"}
-
-@ARTICLE{Keener:90,
- AUTHOR = "James P. Keener",
- TITLE = "Knotted vortex filaments in an ideal fluid",
- JOURNAL = "J. Fluid Mech.",
- YEAR = 1990, VOLUME = 211, PAGES = "629-651"}
-
-@ARTICLE{Kendall:88,
- AUTHOR = "W. S. Kendall",
- TITLE = "Symbolic Computation and the Diffusion of Shapes of Triads",
- JOURNAL = "Adv. Appl. Prob.",
- YEAR = 1988, VOLUME = 20, PAGES = "775-797"}
-
-@TECHREPORT{Kendall:89,
- AUTHOR = "W. S. Kendall",
- TITLE = "The Diffusion of {Euclidean} Shape",
- INSTITUTION = "University of Warwick, Dept. of Statistics", YEAR = 1989,
- TYPE = "Research Report", NUMBER = 161}
-
-@TECHREPORT{Kendall:89a,
- AUTHOR = "W. S. Kendall",
- TITLE = "Probability, Convexity, and Harmonic Maps with Small Image I:
-Uniqueness and Fine Existence",
- INSTITUTION = "University of Warwick, Dept. of Statistics", YEAR = 1989,
- TYPE = "Research Report", NUMBER = 162}
-
-@ARTICLE{Kendall:90,
- AUTHOR = "W. S. Kendall",
- TITLE = "Computer Algebra and Stochastic Calculus",
- JOURNAL = "Notices A.M.S.",
- YEAR = 1990, VOLUME = 37, PAGES = "1254-1256"}
-
-@TECHREPORT{Kendall:91,
- AUTHOR = "Wilfred S. Kendall",
- TITLE = "Computer Algebra and Stochastic Calculus",
- INSTITUTION = "University of Warwick, Dept. of Statistics", YEAR = 1991,
- TYPE = "Research Report", NUMBER = 203}
-
-@TECHREPORT{Kendall:91a,
- AUTHOR = "Wilfred S. Kendall",
- TITLE = "Symbolic {It\^{o}} Calculus:  An Introduction",
- INSTITUTION = "University of Warwick, Dept. of Statistics", YEAR = 1991,
- TYPE = "Research Report", NUMBER = 217}
- ABSTRACT = {The ito procedures are an implementation of stochastic calculus
-for the computer algebra package {REDUCE}.  In this paper it is explained
-how the implementation of ito grows naturally out of the formulation of
-stochastic calculus using modules of stochastic differentials.  Two examples
-are given of ito in action:  a simple example concerning various exponential
-martingales and a more involved example concerning the escape rate of the
-Bessel process of dimension exceeding 2.  A basic subset of the ito
-procedures is listed in six appendices; details are given of how to obtain
-the full set from the author.}}
-
-@TECHREPORT{Kendall:93a,
- AUTHOR = "Wilfred S. Kendall",
- TITLE = "Probability, Convexity, and Harmonic Maps II:  Smoothness via
-Probabilistic Gradient Inequalities",
- INSTITUTION = "University of Warwick, Dept. of Statistics", YEAR = 1993,
- MONTH = "October", TYPE = "Research Report", NUMBER = 260,
- ABSTRACT = {A conformal change of metric is used to construct a coupling
-of two time-changed Riemannian Brownian motions, such that there is an
-upper bound on the prabability of no coupling before either process leaves
-a small geodesic ball, with the bound being linear in the distance between
-the two starting points.  This coupling is a more geometric (and
-probabilistically less technical) alternative to that introduced by
-Cranston (1991).  Together with some modifications it is used to provide a
-probabilistic approach to the regularity of harmonic maps, thus completing
-the probabilistic construction of solutions to small-image harmonic map
-Dirichlet problems described in Kendall (1990).  The approach includes a
-mild generalization to the case of harmonic maps defined using
-non-Riemannian connections in the target manifold and smooth strictly
-elliptic second-order differential operators in the domain.}}
-
-@INPROCEEDINGS{Kerner:75,
- AUTHOR = "W. Kerner and R. C. Grimm",
- TITLE = "{MHD} Spectra for {Tokamaks} with Non-circular Cross Sections",
- YEAR = 1975,
- BOOKTITLE = "Proc. Seventh Conference on
-Numerical Simulation of Plasmas, Courant Institute, {NYU}"}
-
-@ARTICLE{Kersten:83,
- AUTHOR = "P. H. M. Kersten",
- TITLE = "Infinitesimal Symmetries and Conserved Currents for Nonlinear
-{Dirac} Equation",
- JOURNAL = "J. Math. Phys.",
- YEAR = 1983, VOLUME = 24, PAGES = "2374-2376",
- COMMENT = {Harrison-Estabrook and computer algebra, in {REDUCE}.  Very like
-{EXCALC} but predates it.}}
-
-@ARTICLE{Kersten:84,
- AUTHOR = "P. Kersten and R. Martini",
- TITLE = "The Harmonic Map and Killing Fields for Self-Dual {SU(3)}
-{Yang-Mills} Equations",
- JOURNAL = "J. Phys. A",
- YEAR = 1984, VOLUME = 17, PAGES = "L227-L230",
- COMMENT = {%"{\ldots}and the determination of the general solution of the
-killing fields have been achieved by symbolic computations in a semi-automatic
-way using software developed in the symbolic language {REDUCE}{\ldots}"}}
-
-@ARTICLE{Kersten:86,
- AUTHOR = "P. H. M. Kersten",
- TITLE = "Creating and Annihilating {Lie-B\"acklund} Transformations
-of the {Federbush} Model",
- JOURNAL = "J. Math. Phys.",
- YEAR = 1986, VOLUME = 27, PAGES = "1139-1144",
- COMMENT = {"We want to stress that all computations have been worked out on
-a {DEC-20} computer using {REDUCE} and a software package to do these
-calculations."  Lie algebra and Gragert's package.}}
-
-@ARTICLE{Kersten:86a,
- AUTHOR = "P. H. M. Kersten and H. M. M. Ten Eikelder",
- TITLE = "Infinite Hierarchies of t-independent and t-dependent
-Conserved Functionals of the {Federbush} Model",
- JOURNAL = "J. Math. Phys.",
- YEAR = 1986, VOLUME = 27, PAGES = "2140-2145",
- COMMENT = {"We want to stress that all computations have been worked out on
-a {DEC-20} computer using {REDUCE} and a software package to do these
-calculations."}}
-
-@ARTICLE{Kersten:86b,
- AUTHOR = "P. H. M. Kersten and H. M. M. Ten Eikelder",
- TITLE = "An Infinite Number of Infinite Hierarchies of Conserved
-Quantities of the {Federbush} Model",
- JOURNAL = "J. Math. Phys.",
- YEAR = 1986, VOLUME = 27, PAGES = "2791-2796"}
-
-@ARTICLE{Killalea:80,
- AUTHOR = "M. K. Killalea and B. J. McCoy",
- TITLE = "Concentration Distribution and Spatial Moments of
-Moving Macromolecules Undergoing Isomerization",
- JOURNAL = "Biopolymers",
- YEAR = 1980, VOLUME = 19, PAGES = "1875-1886"}
-
-@TECHREPORT{Kinoshita:72,
- AUTHOR = "T. Kinoshita and P. Cvitanovic",
- TITLE = "Sixth Order Radiative Corrections to the Electron Magnetic Moment",
- INSTITUTION = "Cornell Lab. for Nuclear Studies", YEAR = 1972,
- TYPE = "Report", NUMBER = "CLNS-197", MONTH = "October"}
-
-@TECHREPORT{Kinoshita:73,
- AUTHOR = "T. Kinoshita and P. Cvitanovic",
- TITLE = "Feynman-{Dyson} Rules in Parametric Space",
- INSTITUTION = "Cornell Lab. for Nuclear Studies", YEAR = 1973,
- TYPE = "Report", NUMBER = "CLNS-209", MONTH = "January"}
-
-@ARTICLE{Kitatani:86,
- AUTHOR = "H. Kitatani and S. Miyashita and M. Suzuki",
- TITLE = "Reentrant Phenomena in Some {Ising} Spin Systems - Rigorous
-Results and Effects of an External Field",
- JOURNAL = "J. Phys. S. Japan",
- YEAR = 1986, VOLUME = 55, NUMBER = 3, PAGES = "865-876",
- COMMENT = {{REDUCE} used to calculate formula before numerical
-calculation.}}
-
-@ARTICLE{Klimov:93,
- AUTHOR = "D. M. Klimov and V. V. Leonov and V. M. Rudenko",
- TITLE = "The Study of Motion for a Gyroscope with Gimbal Suspension:
-Obtaining the Highest Approximations for a Drift of Magnus",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1993, VOLUME = 15, NUMBER = 1, PAGES = "73-78", MONTH = "January",
- COMMENT = {Here we give a solution to the classic problem of the applied
-mechanics of the gyroscope.  The problem is reduced to using the computer
-algebra system {REDUCE}.  We show that symbolic computation is very
-convenient for applied mechanics.}}
-
-@TECHREPORT{Kobayashi:84,
- AUTHOR = "Hidestune Kobayashi",
- TITLE = "Weierstrass Points on a Curve, $X^{7}_{0}+X^{7}_{1}
-+X^{7}_{2}=0$",
- INSTITUTION = "Research Institute of Science and Technology, Nihon
-University", YEAR = 1984, TYPE = "Preprint", NUMBER = 28, MONTH = "March"}
-
-@INPROCEEDINGS{Kobayashi:88,
- AUTHOR = "H. Kobayashi and S. Moritsugu and R. W. Hogan",
- TITLE = "Solving Systems of Algebraic Equations",
- BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
- YEAR = 1988, VOLUME = 358, PAGES = "139-149"}
-
-@INPROCEEDINGS{Kodaira:85,
- AUTHOR = "Hiroshi Kodaira and Hiroshi Toshima",
- TITLE = "Gini Coefficient of Wealth in Life Cycle Model",
- YEAR = 1985,
- BOOKTITLE = "Proc. of the Second {RIKEN} International
-Symposium on Symbolic and Algebraic Computation by Computers",
- PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "119-151"}
-
-@ARTICLE{Koh:82,
- AUTHOR = "I. G. Koh and Y. D. Kim and Y. J. Park and C. H. Kim and
-Y. S. Kim",
- TITLE = "Complete Set of {SU(5)} Monopole Solution",
- JOURNAL = "J. Math. Phys.",
- YEAR = 1982, VOLUME = 23, PAGES = "1210-1212",
- COMMENT = {Calculation checked by {REDUCE} after hand calculation.}}
-
-@ARTICLE{Koelbig:81,
- AUTHOR = "K. S. K{\"o}lbig and F. Schwarz",
- TITLE = "On Positive Function Series",
- JOURNAL = "Computing",
- YEAR = 1981, VOLUME = 27, PAGES = "319-337",
- COMMENT = {{REDUCE} for algebra on constraints on a functional form and
-Jacobi polynomials.}}
-
-@ARTICLE{Koelbig:81b,
- AUTHOR = "K. S. K{\"o}lbig",
- TITLE = "A Program for Computing the Conical functions of the
-First Kind ${P}^{m}_{-1/2+i\tau}(x)$ for $m = 0$ and $m = 1$",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1981, VOLUME = 23, PAGES = "51-61",
- PUBLISHER = "North Holland Publishing Company"}
-
-@ARTICLE{Koelbig:82,
- AUTHOR = "K. S. K{\"o}lbig",
- TITLE = "Closed Expressions for $\int_{0}^{1} t^{-1} $log$^{n-1}t\,
- $log$^{p}(1 - t) dt$",
- JOURNAL = "Math. Comp.",
- YEAR = 1982, VOLUME = 39, NUMBER = 160, PAGES = "647-654",
- MONTH = "October",
- COMMENT = {Closed form of integral for easy calculation.  Used {REDUCE} for
-manipulations.  This class includes dilog, Spence functions etc.
-Remarks that {REDUCE} is easier than {FORTRAN}.}}
-
-@ARTICLE{Koelbig:82a,
- AUTHOR = "K. S. K{\"o}lbig and W. R{\"u}hl",
- TITLE = "Complex Zeros of the Partition Function for
-Two-Dimensional {U(N)} Lattice Gauge Theories",
- JOURNAL = "Z. Phys. C - Particles and Fields",
- YEAR = 1982, VOLUME = 12, PAGES = "135-143",
- COMMENT = {The Complex Zeros of the Partition Function for Two-Dimensional
-U(N) Lattice Gauge Theories.}}
-
-@ARTICLE{Koelbig:83,
- AUTHOR = "K. S. K{\"o}lbig",
- TITLE = "On the Integral $\int_{0}^{\pi/2} $log$^{n}$cos$\,x\,$
-log$^{p}$sin$\,x\,dx$",
- JOURNAL = "Math. Comp.",
- MONTH = "April",
- YEAR = 1983, VOLUME = 40, PAGES = "565-570",
- COMMENT = {A formula is derived for the integral in the title which allows
-easy evaluation by formula manipulation on a computer.}}
-
-@ARTICLE{Koelbig:83a,
- AUTHOR = "K. S. K{\"o}lbig",
- TITLE = "On the Integral $\int_{0}^{\infty} e^{-\mu t} t^{\nu -1}
-   $log$^{m} t dt$",
- JOURNAL = "Math. Comp.",
- YEAR = 1983, VOLUME = 41, PAGES = "171-182",
- COMMENT = {A recurrence relation is given for the integral in the title.}}
-
-@ARTICLE{Koelbig:84,
- AUTHOR = "K. S. K{\"o}lbig and B. Schorr",
- TITLE = "Asymptotic Expansions for the {Landau} Density and
-Distribution Function",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1984, VOLUME = 32, PAGES = "121-131"}
-
-@ARTICLE{Koelbig:84a,
- AUTHOR = "K. S. K{\"o}lbig and B. Schorr",
- TITLE = "A Program Package for the {Landau} Distribution",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1984, VOLUME = 31, PAGES = "97-111"}
-
-@TECHREPORT{Koelbig:84b,
- AUTHOR = "K. S. K{\"o}lbig",
- TITLE = "Some Problems Involving Special Functions
-Arising From Physics at {CERN}",
- INSTITUTION = "CERN, Data Handling Division",
- YEAR = 1984, NUMBER = "DD 84-14", MONTH = "September"}
-
-@TECHREPORT{Koelbig:85,
- AUTHOR = "K. S. K{\"o}lbig",
- TITLE = "On the Integral $\int_{0}^{1} x^{\nu -1} (1 - x)^{-\lambda}
- $ln$^{m} x dx$",
- INSTITUTION = "CERN, Data Handling Division",
- YEAR = 1985, NUMBER = "DD/85/18", MONTH = "September"}
-
-@ARTICLE{Koelbig:85a,
- AUTHOR = "K. S. K{\"o}lbig",
- TITLE = "Explicit Evaluation of Certain Definite Integrals Involving
-Powers of Logarithms",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1985, VOLUME = 1, NUMBER = 1, PAGES = "109-114", MONTH = "March"}
-
-@ARTICLE{Koelbig:86,
- AUTHOR = "K. S. K{\"o}lbig",
- TITLE = "On the Integral $\int_{0}^{\infty} x^{\nu -1}
- (1 + \beta x)^{-\lambda} $ln$^{m} x dx$",
- JOURNAL = "Journal of Comp. and Appl. Math.",
- YEAR = 1986, VOLUME = 14, PAGES = "319-344"}
-
-@TECHREPORT{Koepf:94,
- AUTHOR = "Wolfram Koepf and Dieter Schmersau",
- TITLE = "Spaces of Functions Satisfying Simple Differential Equations",
- INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
- YEAR = 1994, MONTH = "March", TYPE = "Preprint", NUMBER = "TR 94-2"}
-
-@TECHREPORT{Koepf:94a,
- AUTHOR = "Wolfram Koepf",
- TITLE = "Algebraische Darstellung transzendenter Funktionen (in {German})",
- INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
- YEAR = 1994, MONTH = "October", TYPE = "Preprint", NUMBER = "SC 94-24"}
-
-@TECHREPORT{Koepf:94b,
- AUTHOR = "Wolfram Koepf",
- TITLE = "Algorithms for the Indefinite and Definite Summation",
- INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
- YEAR = 1994, MONTH = "December", TYPE = "Preprint", NUMBER = "SC 94-33"}
-
-@ARTICLE{Koepf:95,
- AUTHOR = "Wolfram Koepf",
- TITLE = "{REDUCE} package for the Indefinite and Definite Summation",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1995, VOLUME = 29, NUMBER = 1, PAGES = "14-30", MONTH = "January",
-Abstract ={The {REDUCE} package {ZEILBERG} is a careful implementation of
-the Gosper and Zeilberger algorithms for indefinite, and definite
-summation of hypergeometric terms respectively.  An expression $a_k$ is
-called a hypergeometric term (or closed form) if $a_k/a_{k-1}$ is a
-rational function with respect to $k$.  Typical hypergeometric terms are
-ratios of products of powers, factorial, Gamma function terms, binomial
-coefficients, and shifted factorials (Pochhammer symbols) that are
-integer-linear in their arguments.  The package covers further extensions
-of both Gosper's and Zeilberger's algorithms.}}
-
-@TECHREPORT{Koepf:95a,
- AUTHOR = "Wolfram Koepf",
- TITLE = "Identities for families of orthogonal polynomials and special
-functions",
- INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
- YEAR = 1995, MONTH = "January", TYPE = "Preprint", NUMBER = "SC 95-1",
- ABSTRACT = {In this article we present new results for families of
-orthogonal polynomials and special functions, that are determined by
-algorithmical approaches.
-
-In the first section, we present new results, especially for discrete
-families of orthogonal polynomials, obtained by an application of the
-celebrated Zeilberger algorithm.
-
-Next, we present algorithms for holonomic families $f(n,x)$ of special
-functions which possess a derivative rule.  We call those families
-admissible.  A family $f(n,x)$ is holonomic if it satisfies a holonomic
-recurrence equation with respect to n, and a holonomic differential
-equation with respect to x, i.e. linear homogeneous equations with
-polynomial coefficients.
-
-The rather rigid property of admissibility has many interesting
-consequences, that can be used to generate and verify identities for these
-functions by linear algebra techniques.  On the other hand, many families
-of special functions, in particular families of orthogonal polynomials, are
-admissible.  We moreover present a method that generates the derivative
-rule from the holonomic representation of a holonomic family.
-
-As examples, we find new identities for the Jacobi polynomials and for the
-Whittaker functions, and for families of discrete orthogonal polynomials by
-the given approach.
-
-Finally, we present representations for the parameter derivatives of the
-Gegenbauer and the generalized Laguerre polynomials.}}
-
-@ARTICLE{Koike:92,
- AUTHOR = "F. Koike",
- TITLE = "Explicit formulae of angular momentum coupling coefficients",
- JOURNAL = "Comp. Phys. Commun.",
- YEAR = 1992, VOLUME = 72, NUMBERS = "2 and 3", PAGES = "154-164",
- MONTH = "November",
- COMMENT = {A program has been developed to generate algebraic formulae of
-the coupling coefficients of angular momenta.  The algebraic programming
-system {REDUCE} version 3.3 is used for programming.  The program
-consists of several {REDUCE} prefix operators.  They carry out symbolic
-reductions of Clebsch-Gordan coefficients.  Racah coefficients,
-X-coefficients, and related coefficients.  Both variables and values of
-angular momentum can be their arguments.  The program allows one to use
-these operators in the same way as the {REDUCE} built-in operators.}}
-
-@ARTICLE{Kolar:90,
- AUTHOR = "M. Kol{\'a}\u{r} and M. K. Ali",
- TITLE = "Trace maps associated with general {two-letter} substitution
-rules",
- JOURNAL = "Physical Review {A}",
- YEAR = 1990, VOLUME = 42, NUMBER = 12, PAGES = "7112-7124",
- MONTH = "December",
- ABSTRACT = {Spectral properties, as determined by trace maps, of the
-one-dimensional chains (layered structures) constructed according to
-general two-letter substitution rules are investigated.  In all trace maps
-thus obtained an important role is played by the quantity
-$I=x^{2}+y^{2}+z^{2}-xyz-4$ However, only a very small fraction of all
-such trace maps are similar to the Fibonacci golden-mean trace map in that
-I is their invariant.  In addition to the known case of the precious-mean
-lattices (precious means are ratios of the form
-$^{1}_{2}[m+(m^{2}+4)^{1/2}]$, m being any positive integer; m=1 gives the
-golden mean), we have identified two new large clases of substitution
-rules that give trace maps with invariant I.  One of them is a superset of
-the precious-mean lattices.  All other cases represent a vast assortment
-of different trace maps (and thus the potential for various hitherto
-unexplored spectral properties) with a unifying feature that the set I=0
-plays the role of an attractor in the trace space.  In most (but not all)
-cases, two chains with identical trace maps (and thus identical spectra)
-are locally isomorphic.  Generally, local isomorphism equivalence classes
-seem to be subsets of identical spectrum equivalence classes.}}
-
-@TECHREPORT{Kornyak:87,
- AUTHOR = "V. V. Kornyak and R. N. Fedorova",
- TITLE = "A {REDUCE} Program to Calculate Determining Equations of
-{Lie-Baecklund} Symmetries of Differential Equations",
- INSTITUTION = "J.I.N.R., Dubna",
- YEAR = 1987, NUMBER = "P11-87-19"}
-
-@ARTICLE{Kotorynski:86,
- AUTHOR = "W. P. Kotorynski",
- TITLE = "Steady Laminar Flow Through a Twisted Pipe of Elliptical
-Cross-Section",
- JOURNAL = "Computers and Fluids",
- YEAR = 1986, VOLUME = 14, PAGES = "433-444",
- COMMENT = {Used {REDUCE} to perform the calculations for steady flow through
-twisted pipes, but who also remarked that the techniques he developed
-for this problem are applicable to a variety of other pipe flow tasks.}}
-
-@ARTICLE{Krack:82,
- AUTHOR = "K. Krack",
- TITLE = "Rechnerunterst{\"u}tzte {Entwicklung} der {Mittelbreitenformeln}
-und Absch{\"a}tzung ihrer ellipsoidischen {Anteile} zur L{\"o}sung der
-zweiten geod{\"a}tischen {Hauptaufgabe} auf dem {Rotationsellipsoid}",
- JOURNAL = "Z. Vermessungswes.",
- YEAR = 1982, VOLUME = 107, PAGES = "502-513",
- COMMENT = {(In German) Used {REDUCE} to develop the Gauss mid-latitude
-formulae for inverse positioning to the 7th order (Geodesy).}}
-
-@PHDTHESIS{Kraus:73,
- AUTHOR = "J. Kraus",
- TITLE = "Delbr{\"u}ckstreuung und Pr{\"u}fung der
-Quantenelektrodynamik",
- SCHOOL = "Ludwig-Maximilians-Universit{\"a}t zu M{\"u}nchen",
- YEAR = 1973}
-
-@ARTICLE{Kredel:88,
- AUTHOR = "Heinz Kredel",
- TITLE = "Admissible termorderings used in Computer Algebra Systems",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1988, VOLUME = 22, NUMBER = 1, PAGES = "28-31", MONTH = "January"}
-
-@ARTICLE{Kruse:83,
- AUTHOR = "Hans-Guenther Kruse and Karin Ohlsen",
- TITLE = "About the Realization of an Extended, but Really Interactive
-{REDUCE} by Integration of a Small Editing and Executing System",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "21-25", MONTH = "February"}
-
-@TECHREPORT{Kryukov,
- AUTHOR = "A. P. Kryukov and A. Ya. Rodionov",
- TITLE = "Usage of {REDUCE} for Computations of Group-Theoretical Weight of
-{Feynman} Diagrams in Non-Abelian Gauge Theories",
- INSTITUTION = "Institute of Nuclear Physics, Moscow, USSR", YEAR = "TBD"}
-
-@ARTICLE{Kryukov:84,
- AUTHOR = "A. P. Kryukov",
- TITLE = "An Antitranslator of the {RLISP} Language",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1984, VOLUME = 18, NUMBER = 3, PAGES = "12-15", MONTH = "August"}
-
-@ARTICLE{Kryukov:85,
- AUTHOR = "A. P. Kryukov and A. Ya. Rodionov",
- TITLE = "Dynamic-Debugging System for the {REDUCE} Programs",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1985, VOLUME = 19, NUMBER = 2, PAGES = "34-37", MONTH = "May"}
-
-@ARTICLE{Kryukov:85a,
- AUTHOR = "A. P. Kryukov and A. Ya. Rodionov",
- TITLE = "Interactive {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1985, VOLUME = 19, NUMBER = 3, PAGES = "43-45", MONTH = "August"}
-
-@TECHREPORT{Kryukov:87,
- AUTHOR = "A. P. Kryukov and A. Ya. Rodionov and V. A. Rostovtsev",
- TITLE = "Pattern Compilation in {REDUCE}",
- INSTITUTION = "J.I.N.R., Dubna",
- YEAR = 1987, NUMBER = "P11-87-302"}
-
-@INPROCEEDINGS{Kryukov:87a,
- AUTHOR = "A. P. Kryukov and A. Ya. Rodionov",
- TITLE = "{CTS} - Algebraic Debugging System for {REDUCE} Programs",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "233-243",
- PUBLISHER = "Springer-Verlag"}
-
-@TECHREPORT{Kryukov:88,
- AUTHOR = "A. P. Kryukov and A. Ya. Rodionov and V. A. Rostovtsev",
- TITLE = "New Programming Tools for Computing Substitution
-Rules in {REDUCE} System",
- INSTITUTION = "J.I.N.R., Dubna",
- YEAR = 1988, NUMBER = "P11-88-402",
- COMMENT = {New programming tools allowing to compile patterns in
-{REDUCE} system are described.  A guide for using
-these tools and examples of their working are presented.}}
-
-@ARTICLE{Kryukov:88a,
- AUTHOR = "A. P. Kryukov and A. Ya. Rodionov",
- TITLE = "Program {``COLOR''} for Computing the Group-Theoretic Weight
-of {Feynman} Diagrams in {Non-Abelian} Gauge Theories",
- JOURNAL = "Comp. Phys. Commun.",
- YEAR = 1988, VOLUME = 48, NUMBER = 2, PAGES = "327-334", MONTH = "February"}
-
-@TECHREPORT{Kryukov:88b,
- AUTHOR = "A. P. Kryukov and D. A. Slavnov",
- TITLE = "The Role of the $gg \rightarrow c\overline{c}g$ Process in the
-Cross Section of Production of Charmed Particles (in {Russian})",
- INSTITUTION = "Moscow State University",
- YEAR = 1988, NUMBER = "88-49/70", TYPE = "Preprint"}
-
-@BOOK{Kryukov:91,
- AUTHOR = "A. P. Kryukov and A. Ya. Rodionov and A. Yu. Taranov and
-E. Shablygin",
- TITLE = "Programming in R-Lisp",
- PUBLISHER = "Radio and Connective Publishers, Moscow", YEAR = 1991,
- ABSTRACT = {Various Lisp dialects become more and more popular as
-high-level programming languages.  In this book basic Lisp concepts, its
-data structures and build in functions are introduced using R-Lisp.
-R-Lisp is the implementation language of a famous REDUCE computer algebra
-system.  All concepts are illustrated by simple but by no means trivial
-programming examples.  The description of compiler and full function
-reference are included.  The book will be interesting for beginners as
-well as Lisp programmers. In Russian}}
-
-@TECHREPORT{Kuppers:71,
- AUTHOR = "G. Kuppers and D. Pfirsch and H. Tasso",
- TITLE = "{M.H.D.} - Stability of Axisymmetric Plasmas",
- INSTITUTION = "Max-Planck-Institut fuer Plasmaphysik",
- YEAR = 1971, TYPE = "Report", NUMBER = "CN -28/F-14"}
-
-@ARTICLE{Lambin:84,
- AUTHOR = "P. Lambin and J. P. Vigneron",
- TITLE = "Computation of Crystal {Green's} Functions in the Complex-Energy
-Plane with the Use of the Analytical Tetrahedron Method",
- JOURNAL = "Phys. Rev. B",
- YEAR = 1984, VOLUME = 29, NUMBER = 6, PAGES = "3430-3437",
- COMMENT = {Crystallography, {REDUCE}, quantum theory.}}
-
-@TECHREPORT{Lang:79,
- AUTHOR = "C. B. Lang and W. Porod",
- TITLE = "Symmetry Breaking and $\pi$ {K} Amplitudes in the Unphysical
-Region",
- INSTITUTION = "Institut f{\"u}r Theor. Physik, Univ. Graz",
- YEAR = 1979, TYPE = "Report", NUMBER = "UNIGRAZ-UTP 08/79",
- ABSTRACT = {We apply two different methods of analytic continuation
-(fixed-t and hyperbolic dispersion relations with discrepancy) to
-determine the expansion parameters of the pi K amplitudes in the
-unphysical region near the symmetry point.},
- COMMENT = {To be published in Phys. Rev. D, September, 1979.}}
-
-@TECHREPORT{Laursen:79,
- AUTHOR = "M. L. Laursen and M. A. Samuel",
- TITLE = "The n-Bubble Diagram Contribution to the g-2 of the Electron -
-{Mathematical} Structure of the Analytical Expression",
- INSTITUTION = "Oklahoma State Univ. Quantum Theoretical Research Group",
- YEAR = 1979, TYPE = "Research Note", NUMBER = "96",
- ABSTRACT = {We obtain an exact integrated expression for the contribution
-of the mass-independent n-bubble diagram to the leptonic g-2.}}
-
-@TECHREPORT{Laursen:80,
- AUTHOR = "Morten L. Laursen and Mark A. Samuel",
- TITLE = "Borel Transform Technique and the {n-Bubble} Diagram
-Contribution to the Lepton Anomaly",
- INSTITUTION = "Oklahoma State Univ. Quantum Theoretical Research Group",
- YEAR = 1980, TYPE = "Research Note", NUMBER = 10, MONTH = "August",
- ABSTRACT = {By using the {Borel} transform technique we calculate
-analytically the muon anomaly from the mass-dependent n-bubble diagram in the
-limit where the mass ratio is large.}}
-
-@ARTICLE{Laursen:81,
- AUTHOR = "M. L. Laursen and M. A. Samuel",
- TITLE = "The n-bubble Diagram Contribution to g-2",
- JOURNAL = "J. Maths. Phys.",
- YEAR = 1981, VOLUME = 22, PAGES = "1114-1126",
- COMMENT = {Exact integration for contribution to mass indep. {n-bubble}
-diagram to {leptonic g-2}.  {REDUCE} used to calculate explicitly to {n=13},
-involves summing series and rational coefficients.}}
-
-@ARTICLE{Lecourtier:85,
- AUTHOR = "Y. Lecourtier and A. Raksanyi",
- TITLE = "Algebraic Manipulation Routines for Testing Structural Properties",
- JOURNAL = "IFAC Identification and System Parameter Estimation",
- YEAR = 1985, PAGES = "543-549"}
-
-@ARTICLE{Lee:85,
- AUTHOR = "H-C Lee and M. S. Milgram",
- TITLE = "On the Axial Gauge:  Ward Identities and the Separation of
-Infrared and Ultraviolet Singularities by Analytical Regularization",
- JOURNAL = "J. Math. Phys.",
- YEAR = 1985, VOLUME = 26, PAGES = "1793-1804",
- COMMENT = {Yang-Mills theories on the axial gauge.  Uses {SCHOONSCHIP} and
-{REDUCE}.}}
-
-@ARTICLE{Leler:85,
- AUTHOR = "Wm Leler and Neil Soiffer",
- TITLE = "An Interactive Graphical Interface for {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1985, VOLUME = 19, NUMBER = 3, PAGES = "17-23", MONTH = "August"}
-
-@ARTICLE{Lepage:83,
- AUTHOR = "G. P. Lepage and P. B. Mackenzie and K. H. Streng and
-P. M. Zernas",
- TITLE = "Multiphoton Decays of Positronium",
- JOURNAL = "Phys. Rev. A",
- YEAR = 1983, VOLUME = 28, PAGES = "3090-3091",
- COMMENT = {Same as Adkins and Brown (1983) but independent of it.}}
-
-@INPROCEEDINGS{Levi:70,
- AUTHOR = "I. Levi and N. Hoff",
- TITLE = "Non-Symmetric Creep Buckling of Circular
-Cylindrical Shells in Axial Compression",
- YEAR = 1970, MONTH = "August",
- BOOKTITLE = "Proc. Intern. Symp. in Creep Effect in Structures,
-Gotenburg, Sweden"}
-
-@INPROCEEDINGS{Levi:71,
- AUTHOR = "I. M. Levi",
- TITLE = "Symbolic Algebra by Computer - Applications to
-Structural Mechanics",
- YEAR = 1971, MONTH = "April",
- BOOKTITLE = "{AIAA/ASME} 12th Structures, Structural Dynamics
-and Materials Conference, Anaheim, California"}
-
-@ARTICLE{Liebermann:75,
- AUTHOR = "R. Liebermann",
- TITLE = "Traces of High Energy Processes in Strong Magnetic Fields",
- JOURNAL = "J. Comp. Phys.",
- YEAR = 1975}
-
-@ARTICLE{Liska:84,
- AUTHOR = "R. Liska",
- TITLE = "Program for Stability and Accuracy Analysis of
-Finite Difference Methods",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1984, VOLUME = 34, PAGES = "175-186"}
-
-@INPROCEEDINGS{Liska:87,
- AUTHOR = "R. Liska and D. Drska",
- TITLE = "Evaluation of Plasma Fluid Equations Collision Integrals Using
-{REDUCE}",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = 178,
- PUBLISHER = "Springer-Verlag"}
-
-@InProceedings{Liska90,
-  author =      "R. Liska and L. Drska",
-  title =       "{FIDE}: A {REDUCE} package for automation of {FI}nite
-                 difference method for solving {pDE}",
-  booktitle =   "Proceedings of the 1990 International Symposium on
-                 Symbolic and Algebraic Computation",
-  year =        "1990",
-  editor =      "S. Watanabe and Morio Nagata",
-  pages =       "169-176",
-  organization =        "ACM",
-  publisher =   "Addison-Wesley"
-}
-
-@INPROCEEDINGS{Liska:91,
- AUTHOR = "Richard Liska and Michail Yu. Shashkov",
- TITLE = "Algorithms for Difference Schemes Construction on Non-orthogonal
-Logically Rectangular Meshes",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- EDITOR = "Stephen M. Watt",
- PUBLISHER = "ACM Press", ADDRESS = "Maryland", PAGES = "419-426",
- YEAR = 1991,
- ABSTRACT = {The paper deals with the formalization of the basic operator
-method for construction of difference schemes for the numerical solving
-of partial differential equations.  The strength of the basic operator
-method lies on the fact that it produces fully conservative difference
-schemes.  The difference mesh can be non-orthogonal but has to be logically
-orthogonal.  Algorithms for working with grid functions and grid operators
-in symbolic form which are necessary in the basic operator method are
-described.  The algorithms have been implemented in the computer algebra
-system REDUCE.}}
-
-@ARTICLE{Lloyd:90,
- AUTHOR = "N. G. Lloyd and J. M. Pearson",
- TITLE = "{REDUCE} and the Bifurcation of Limit Cycles",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1990, VOLUME = 9, NUMBER = 2, PAGES = "215-224", MONTH = "February"}
-
-@INPROCEEDINGS{Loe:85,
- AUTHOR = "Kia Fock Loe and Noritaka Ohsawa and Eiichi Goto",
- TITLE = "Circuit Simulation Code Generation by Computer Algebra",
- YEAR = 1985,
- BOOKTITLE = "Proc. of the Second {RIKEN} International
-Symposium on Symbolic and Algebraic Computation by Computers",
- PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "87-103"}
-
-@INPROCEEDINGS{London:74,
- AUTHOR = "R. London and D. R. Musser",
- TITLE = "The Application of a Symbolic Mathematical System
-to Program Verification",
- YEAR = 1974, PAGES = "265-273",
- BOOKTITLE = "Proc. {ACM} 74"}
-
-@ARTICLE{Loos:72,
- AUTHOR = "R{\"u}diger Loos",
- TITLE = "Analytic Treatment of Three Similar {Fredholm} Integral
-Equations",
- JOURNAL = "SIGSAM Bulletin",
- YEAR = 1972, VOLUME = 11, PAGES = "32-40",
- ABSTRACT = {A {REDUCE} solution to {SIGSAM} Problem \#1 is presented.}}
-
-@INPROCEEDINGS{Lottati,
- AUTHOR = "Itzhak Lottati and Isaac Elishakoff",
- TITLE = "Refined Dynamical Theories of Beams, Plates
-and Shells and Their Applications",
- BOOKTITLE = "Proc. Euromech-Colloquium 219"}
-
-@ARTICLE{Louw:86,
- AUTHOR = "J. A. Louw and F. Schwarz and W. H. Steeb",
- TITLE = "First Integrals and {Yoshida} Analysis of {Nahm}'s Equation",
- JOURNAL = "J. Phys. A",
- YEAR = 1986, VOLUME = 19, PAGES = "L569-L573",
- COMMENT = {Monopole solutions in Yang-Mills theories explicitely given in
-special cases.  {REDUCE} used for polynomial first integrals and
-Kowalewski exponents.  An application of spde.}}
-
-@ARTICLE{Luegger:73,
- AUTHOR = "J. Luegger and H. Melenk",
- TITLE = "Darstellung und {Bearbeitung} Umfangreicher {LISP-Programme}",
- JOURNAL = "Angewandte Informatik",
- YEAR = 1973, MONTH = "June", PAGES = "257-263"}
-
-@TECHREPORT{Luegger:91,
- AUTHOR = "Joachim L{\"u}gger and Wolfgang Dalitz",
- TITLE = "Verteilung mathematischer {Software} mittels elektronischer
-{Netze:} {Die} elektronische {Softwarebibliothek} {eLib}",
- INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
- YEAR = 1991, MONTH = "February", TYPE = "Preprint", NUMBER = "TR 91-2"}
-
-@TECHREPORT{Lukacs,
- AUTHOR = "B. Luk{\'a}cs and Z. Perj{\'e}s and
-A. Sebesty{\'e}n and A. Valentini",
- TITLE = "Stationary Vacuum Fields with a Conformally Flat
-Three-Space, II. Proof of Axial Symmetry",
- INSTITUTION = "Central Research Institute for Physics,
-Budapest, Hungary",
- YEAR = 1982, NUMBER = "KFKI-1982-19"}
-
-@ARTICLE{Lukaszuk:87,
- AUTHOR = "L. L{\'u}kaszuk and D. M. Siemienczuk and L. Szymanowski",
- TITLE = "Evaluation of Helicity Amplitudes",
- JOURNAL = "Phys. Rev. D",
- YEAR = 1987, VOLUME = 35, PAGES = "326-329"}
-
-@PHDTHESIS{Lux:75,
- AUTHOR = "Augustin Lux",
- TITLE = "Etude d'un Modele Abstrait pour une Machine {LISP} et de
-son Implantation",
- SCHOOL = "Universit{\'e} Scientifique et Medicale de Grenoble",
- YEAR = 1975, MONTH = "March",
- COMMENT = {Thesis presented to Universit{\'e} Scientifique et Medicale de
-Grenoble, Institut National Polytechnique de Grenoble.}}
-
-@BOOK{MacCallum:86,
- AUTHOR = "M. A. H. MacCallum",
- TITLE = "Dynamical Spacetimes and Numerical Relativity",
- PUBLISHER = "Cambridge University Press", YEAR = 1986}
-
-@TECHREPORT{MacCallum:86a,
- AUTHOR = "M. A. H. MacCallum",
- TITLE = "Algebraic Computing in Relativity",
- INSTITUTION = "Queen Mary College, University of London",
- YEAR = 1986, NUMBER = "TAU 86-04"}
-
-@INPROCEEDINGS{MacCallum:87,
- AUTHOR = "M. A. H. MacCallum",
- TITLE = "Symbolic Computation in Relativity Theory",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "34-43",
- PUBLISHER = "Springer-Verlag"}
-
-@INPROCEEDINGS{MacCallum:88,
- AUTHOR = "M. A. H. MacCallum",
- TITLE = "An Ordinary Differential Equation Solver for {REDUCE}",
- BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
- YEAR = 1988, VOLUME = 358, PAGES = "196-205"}
-
-@ARTICLE{MacCallum:89,
- AUTHOR = "Malcolm A. H. MacCallum",
- TITLE = "Comments on the performance of algebra systems in general
-relativity and a recent paper by {Nielsen} and {Pedersen}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1989, VOLUME = 23, NUMBER = 2, PAGES = "22-25", MONTH = "April"}
-
-@BOOK{MacCallum:91,
- AUTHOR = "Malcolm MacCallum and Francis Wright",
- TITLE = "Algebraic Computing with {REDUCE}",
- PUBLISHER = "Oxford University Press", YEAR = 1991,
- ISBN = "0-19-853444-2, 0-19-853443-4 (paperback)"}
-
-@ARTICLE{MacCallum:92,
- AUTHOR = "M. A. H. MacCallum and S. T. C. Siklos",
- TITLE = "Algebraically special hypersurface-homogeneous {Einstein} spaces
-in general relativity",
- JOURNAL = "Journal of Geometry and Physics",
- YEAR = 1992, VOLUME = 8, PAGES = "221-242"}
-
-@BOOK{MacDonald:94,
-  AUTHOR = "N. MacDonald",
-  TITLE = "{REDUCE} for Physics",
-  PUBLISHER = "Institute of Physics Publishing",
-  ADDRESS = "Bristol, England",
-  YEAR = 1994, MONTH = "March",
-  NOTE = "ISBN 0 7503 0277 1",
-  COMMENT = {This book provides an introduction to {REDUCE} with the needs
-of physicists primarily in mind.  Each chapter introduces some aspects of
-{REDUCE} and illustrates them with applications from various branches of
-physics including mechanics, dynamics, dimensional analysis, quantum
-mechanics, plasma physics.  Exercises to test understanding are included
-throughout.  The emphasis is on hands-on working with {REDUCE} as a tool to
-tackle real physical problems.  The book takes account of changes to
-{REDUCE} for Version 3.4.
-Students and researchers in the physical sciences and engineering using
-{REDUCE} for the first time should find this book useful.}}
-
-@PHDTHESIS{Mack:73,
- AUTHOR = "D. Mack",
- TITLE = "Nichtnumerische Verfahren und deren Anwendung
-in der Elementarteilchen-Physik",
- SCHOOL = "University of Tuebingen",
- YEAR = 1973}
-
-@ARTICLE{Mack:73a,
- AUTHOR = "D. Mack and H. Mitter",
- TITLE = "Calculation of Electron-Electron-Bremsstrahlung Cross-Sections",
- JOURNAL = "Phys. Lett.",
- YEAR = 1973, VOLUME = "44A", PAGES = "71-72"}
-
-@ARTICLE{Maclaren:89,
- AUTHOR = "N. M. Maclaren",
- TITLE = "The Generation of Sequences of Multiple Independent Sequences
-of Pseudorandom Numbers",
- JOURNAL = "Applied Statistics {JRSS Series C}",
- YEAR = 1989, VOLUME = 38, NUMBERS = 2, PAGES = "351-359"}
-
-@MASTERSTHESIS{Maguire:81,
- AUTHOR = "Gerald Quentin {Maguire Jr.}",
- TITLE = "Program Transformation in {REDUCE} Using Rule Sequencing",
- SCHOOL = "Department of Computer Science, The University of Utah",
- YEAR = 1981, MONTH = "March"}
-
-@INPROCEEDINGS{Malm:82,
- AUTHOR = "Bengt Malm",
- TITLE = "A Program in {REDUCE} for Finding Explicit Solutions",
- BOOKTITLE = "Proc. {EUROCAM} 1982, Lecture Notes
-in Computer Science", YEAR = 1982, VOLUME = 144, PAGES = "289-293",
- PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{Man:93,
- AUTHOR = "Yiu-Kwong Man",
- TITLE = "On Computing Closed Forms for Indefinite Summations",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1993, MONTH = "October", VOLUME = 16, NUMBER = 4, PAGES = "355 - 376",
- COMMENT = {A decision procedure for finding closed forms for indefinite
-summation of polynomials, rational functions, quasipolynomials and
-quasirational functions is presented.  It is also extended to deal with
-some non-hypergeometric sums with rational inputs, which are not summable
-by means of Gosper's algorithm.  Discussion of its implementation, analysis
-of degree bounds and some illustrative examples are included.}}
-
-@ARTICLE{Man:93a,
- AUTHOR = "Yiu-Kwong Man",
- TITLE = "Computing Closed Form Solutions of First Order {ODE}s Using the
-{Prelle-Singer} Procedure",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1993, MONTH = "November", VOLUME = 16, NUMBER = 5, PAGES = "423 - 443",
- COMMENT = {The {Prelle-Singer} procedure is an important method for formal
-solution of first order ODEs.  Two different REDUCE implementations (PSODE
-versions 1 & 2) of this procedure are presented in this paper.  The aim is
-to investigate which implementation is more efficient in solving different
-types of ODEs (such as exact, linear, separable, linear in coefficients,
-homogeneous or Bernoulli equations).  The test pool is based on Kamke's
-collection of first order and first degree ODEs.  Experimental results,
-timings and comparison of efficiency and solvability with the present
-REDUCE differential equation solver (ODESOLVE) and a MACSYMA implementation
-(ODEFI) of the {Prelle-Singer} procedure are provided.  Discussion of
-technical difficulties and some illustrative examples are also included.}}
-
-@InProceedings{Man:94,
-  author =       {Yiu-Kwong Man and Francis J. Wright},
-  title =        {Fast Polynomial Dispersion Computation and its
-		 Application to Indefinite Summation},
-  booktitle =    {Symbolic and Algebraic Computation},
-  editor =       {},
-  series =       {ISSAC},
-  year =         {1994},
-  organization = {SIGSAM},
-  publisher =    {ACM},
-  pages =        {175--180}
-}
-
-@ARTICLE{Marti:78,
- AUTHOR = "Jed Marti",
- TITLE = "The {META/REDUCE} Translator Writing System",
- JOURNAL = "Sigplan Notices",
- YEAR = 1978, VOLUME = 13, PAGES = "42-49",
- COMMENT = {The {META/REDUCE} translator writing system operates in a
-{LISP} and {REDUCE} syntax.  The language supports: {BNF} like syntax,
-recursive descent parsing schemes, lexical primitives, symbol table
-primitives and automatic syntax error message generation.}}
-
-@ARTICLE{Marti:79,
- AUTHOR = "J. B. Marti and A. C. Hearn and M. L. Griss and C. Griss",
- TITLE = "Standard {Lisp} Report",
- JOURNAL = "Sigplan Notices, ACM",
- YEAR = 1979, VOLUME = 14, NUMBER = 10, PAGES = "48-68",
- ABSTRACT = {A description of Standard {LISP} primitive data structures and
-functions is presented.}}
-
-@ARTICLE{Marti:80,
- AUTHOR = "J. Marti and A. C. Hearn and M. L. Griss and C. Griss",
- TITLE = "Standard {Lisp} Report",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1980, VOLUME = 14, NUMBER = 1, PAGES = "23-41", MONTH = "February"}
-
-@ARTICLE{Marti:83,
- AUTHOR = "Jed Marti and John Fitch",
- TITLE = "{REDUCE} 2 for {CP/M}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "26-27", MONTH = "February"}
-
-@ARTICLE{Marti:85,
- AUTHOR = "Jed B. Marti and Anthony C. Hearn",
- TITLE = "{REDUCE} as a {LISP} Benchmark",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1985, VOLUME = 19, NUMBER = 3, PAGES = "8-16", MONTH = "August"}
-
-@INPROCEEDINGS{Marti:85a,
- AUTHOR = "Jed B. Marti",
- TITLE = "The Role of Explanation in Symbolic Computation",
- YEAR = 1985,
- BOOKTITLE = "Proc. of the Second {RIKEN} International
-Symposium on Symbolic and Algebraic Computation by Computers",
- PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "13-34"}
-
-@INPROCEEDINGS{Marti:88,
- AUTHOR = "J. Marti",
- TITLE = "A Graphics Interface to {REDUCE}",
- BOOKTITLE = "Proc. {AAECC-6} 1988, Lecture Notes in Computer Science",
- YEAR = 1988, VOLUME = 357, PAGES = "274-296",
- PUBLISHER = "Springer-Verlag"}
-
-@BOOK{Marti:93a,
-  AUTHOR = "Jed Marti",
-  TITLE = "{RLISP} '88 An Evolutionary Approach to Program Design and Reuse",
-  PUBLISHER = "World Scientific",
-  ADDRESS = "Singapore",
-  YEAR = 1993,
-  NOTE = "SBN 981-02-14790"}
-
-@INPROCEEDINGS{Marzinkewitsch:91,
- AUTHOR = "Reiner Marzinkewitsch",
- TITLE = "Operating Computer Algebra Systems by Handprinted Input",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
- PAGES = "411-413", YEAR = 1991,
- ABSTRACT = {A prototype of a workstation is presented for calculation
-with mathematical formulas by hand and support by computer algebra systems.
-Keywords:  Character recognition, neural network, computer algebra system,
-context free grammar, parsing of two dimensional structures.}}
-
-@ARTICLE{Matveev:87,
- AUTHOR = "V. A. Matveev and Ya. Z. Darbaidze and
-Z. V. Merebashvili and L. A. Slepchenko",
- TITLE = "Gluon Fusion in {SUSY QCD}",
- JOURNAL = "Phys. Lett. B",
- YEAR = 1987, VOLUME = 191, NUMBER = "1 and 2", PAGES = "179-181",
- MONTH = "June"}
-
-@ARTICLE{Maurer:86,
- AUTHOR = "M. Maurer and A. Hayd and H. J. Kaeppeler",
- TITLE = "Quasi-Analytical Method for Solving Nonlinear Differential
-Equations for Turbulent Self-Confined Magneto-Plasma",
- JOURNAL = "J. Comp. Phys.",
- YEAR = 1986, VOLUME = 66, PAGES = "151-172",
- COMMENT = {Mixed {REDUCE} and {FORTRAN}.  Enthusiastic about this style of
-mixed working.}}
-
-@TECHREPORT{Mazepa:85,
- AUTHOR = "N. E. Mazepa and S. I. Serdyukova",
- TITLE = "The Stability Investigation of Some Difference Boundary Problem
-with the Application of Symbolic Computation System",
- INSTITUTION = "J.I.N.R., Dubna",
- YEAR = 1985, NUMBER = "E5-85-39"}
-
-@ARTICLE{Mazzarella:85,
- AUTHOR = "Giuseppe Mazzarella",
- TITLE = "Improved Simplification of Odd and Even Functions in {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1985, VOLUME = 19, NUMBER = 2, PAGES = "29-30", MONTH = "May"}
-
-@ARTICLE{McCrea:81,
- AUTHOR = "J. D. McCrea",
- TITLE = "The {Petrov} Type of a Static Vacuum Spacetime Near a
-Normal-Dominated Singularity",
- JOURNAL = "J. Phys.",
- YEAR = 1981, VOLUME = "A14", PAGES = "1351-1356"}
-
-@ARTICLE{McCrea:82,
- AUTHOR = "J. D. McCrea",
- TITLE = "A Stationary Cylindrically Symmetric Electrovac Spacetime",
- JOURNAL = "J. Phys.",
- YEAR = 1982, VOLUME = "A15", PAGES = "1587-1590"}
-
-@ARTICLE{McCrea:83,
- AUTHOR = "J. D. McCrea",
- TITLE = "Static, Vacuum, Cylindrical and Plane Symmetric Solutions
-of the Quadratic {Poincar{\'e}} Gauge Field Equations",
- JOURNAL = "J. Phys.",
- YEAR = 1983, VOLUME = "A16", PAGES = "997-1004"}
-
-@ARTICLE{McCrea:84,
- AUTHOR = "J. D. McCrea",
- TITLE = "A {NUT}-Like Solution of the Quadratic-{Poincar{\'e}} Gauge
-Field Equations",
- JOURNAL = "Phys. Lett.",
- YEAR = 1984, VOLUME = "100A", PAGES = "397-399"}
-
-@INPROCEEDINGS{McCrea:84a,
- AUTHOR = "J. D. McCrea",
- TITLE = "The Use of {REDUCE} in Finding Exact Solutions of the
-Quadratic {Poincar{\'e}} Gauge Field Equations",
- BOOKTITLE = "Classical General Relativity",
- PUBLISHER = "Cambridge University", YEAR = 1984, PAGES = "173-182"}
-
-@INPROCEEDINGS{McCrea:87,
- AUTHOR = "J. D. McCrea",
- TITLE = "{Poincar{\'e}} Gauge Theory of Gravitation:  Foundations,
-Exact Solutions and Computer Algebra",
- YEAR = 1987, PAGES = "16",
- BOOKTITLE = "Differential Geometric Methods in Mathematical
-Physics, Proc. {14th} International Conference,
-Salamanca, 1985 (Springer Lecture Notes in Mathematics, No. 1251)"}
-
-@ARTICLE{McCrea:87a,
- AUTHOR = "J. D. McCrea and P. Baekler and M. Guerses",
- TITLE = "A {Kerr}-Like Solution of the {Poincar{\'e}} Gauge Field
-Equations",
- JOURNAL = "Il Nuovo Cim",
- YEAR = 1987, VOLUME = "99B", PAGES = "171-177"}
-
-@ARTICLE{McCrea:88,
- AUTHOR = "J. D. McCrea and E. W. Mielke and F. W. Hehl",
- TITLE = "A Remark on the Axisymmetric {Chen} et al. Solution of the
-{Poincar{\'e}} Gauge Theory",
- JOURNAL = "Phys. Lett.",
- YEAR = 1988, VOLUME = "127A", PAGES = "65-69"}
-
-@ARTICLE{McIsaac:85,
- AUTHOR = "Kevin McIsaac",
- TITLE = "Pattern Matching Algebraic Identities",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1985, VOLUME = 19, NUMBER = 2, PAGES = "4-13", MONTH = "May"}
-
-@TECHREPORT{Melenk:88,
- AUTHOR = "H. Melenk and H. M. M{\"o}ller and W. Neun",
- TITLE = "On {Gr{\"o}bner} Bases Computation on a Supercomputer
-Using {REDUCE}",
- INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik
-Berlin",
- YEAR = 1988, TYPE = "Preprint", NUMBER = "SC 88-2", MONTH = "January"}
-
-@ARTICLE{Melenk:89,
- AUTHOR = "H. Melenk and H. M. M{\"o}ller and W. Neun",
- TITLE = "Symbolic Solution of Large Stationary Chemical
-Kinetics Problems",
- JOURNAL = "Impact of Computing in Science and Engineering",
- YEAR = 1989, VOLUME = 1, NUMBER = 2, PAGES = "138-167", MONTH = "June"}
-
-@TECHREPORT{Melenk:89a,
- AUTHOR = "Herbert Melenk and Winfried Neun",
- TITLE = "Implementation of {Portable Standard LISP} for the {SPARC}
-Processor",
- INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin",
- YEAR = 1989, TYPE = "Preprint", NUMBER = "SC 89-6", MONTH = "July"}
-
-@ARTICLE{Melenk:89b,
- AUTHOR = "Herbert Melenk and Winfried Neun",
- TITLE = "Parallel Polynomial Operations in the Large {Buchberger}
-Algorithm",
- JOURNAL = "Computer Algebra and Parallelism", EDITOR = "J. Della Dora
-and J. Fitch",
- YEAR = 1989, PAGES = "143-158", PUBLISHER = "Academic Press, London"}
-
-@ARTICLE{Melenk:90,
- AUTHOR = "H. Melenk",
- TITLE = "Solving Polynomial Equation Systems by {Groebner} Type Methods",
- JOURNAL = "CWI Quarterly",
- YEAR = 1990, VOLUME = 3, NUMBER = 2, PAGES = "121-136", MONTH = "June"}
-
-@INPROCEEDINGS{Melenk:91,
- AUTHOR = "H. Melenk",
- TITLE = "Practical Application of {Gr{\"o}bner} Bases for the Solution
-  of Polynomial Equation Systems",
- BOOKTITLE = "IV. International Conference on Computer Algebra in
- Physical Research, 1990",
- EDITOR = "D. V. Shirkov, V. A. Tostovtsev, V. P. Gerdt",
- YEAR = "1991", PAGES = "230-235", PUBLISHER="World Scientific",
- ADDRESS="Singapore"}
-
-@TECHREPORT{Melenk:93,
- AUTHOR = "Herbert Melenk",
- TITLE = "Algebraic Solution of Nonlinear Equation Systems in {REDUCE}",
- INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin",
- YEAR = 1993, TYPE = "Preprint", NUMBER = "TR 93-2", MONTH = "January"}
-
-@InProceedings{Melenk:93a,
-  author =      "H. Melenk",
-  title =       "Automatic Symbolic Solution of Nonlinear Equation Systems in
-		 {REDUCE}",
-  booktitle =   "Proceedings of the 1993 International IMACS Symposium on
-                 Symbolic Computation",
-  year =        "1993",
-  editor =      "G. Jacob and N. E. Oussous and S. Steinberg",
-  pages =       "175-180",
-  organization ="IMACS",
-  publisher =   "Laboratoire d'Informatique Fondamentale de Lille, France",
-  comment =     {Mathematical background and algorithmic structure of the
-                 nonlinear system part of the {REDUCE} 3.4.1 SOLVE package.}
-}
-
-@TECHREPORT{Melenk:94,
- AUTHOR = "Herbert Melenk",
- TITLE = "The Complexity Barrier in {REDUCE} a Case Study",
- INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin",
- YEAR = 1994, TYPE = "Preprint", NUMBER = "TR 94-6", MONTH = "January"}
-
-@ARTICLE{melfo:92,
- AUTHOR = "A. Melfo and L. A. N\'u\~nez",
- TITLE =  "Checking Collineation Vectors with {REDUCE}",
- JOURNAL = "Gen. Rel. Grav.",
- YEAR = "1992",
- VOLUME = "24",
- NUMBER = "11",
- PAGES = "1125--1129",
- NOTE  = "A package of programs for writing and checking the solutions
-to the equations for various types of collineations (symmetries of the
-metric, christoffel, riemman and ricci tensors) is presented. Some
-examples of previously found  collineations that have been checked are
-given, and new results reported."}
-
-@ARTICLE{Mirie:84,
- AUTHOR = "R. M. Mirie and C. H. Su",
- TITLE = "Internal Solitary Waves and Their Head-On Collision Part I",
- JOURNAL = "J. Fluid Mechanics",
- YEAR = 1984, VOLUME = 147, PAGES = "213-231",
- COMMENT = {Lengthy calculation "acknowledge the use of {REDUCE-2}."
-Perturbation and integration.}}
-
-@INPROCEEDINGS{Molenkamp:91,
- AUTHOR = "J.H.J. Molenkamp and V.V. Goldman and J.A. van Hulzen",
- TITLE = "An Improved Approach to Automatic Error Cumulation Control",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
- PAGES = "414-418", YEAR = 1991,
- ABSTRACT = {For evaluation of arithmetical expressions using multiple
-precision floating-point arithmetic, a method is given to automatically
-perform error cumulation control prior to the actual computations.
-Individual errors and their effects are identified, and it is shown how to
-compute these effects efficiently via automatic differentiation.  In the
-presented approach these effects are used to determine which precisions have
-to be chosen during the real computations, in order to limit error cumulation
-to admissible, user chosen error bounds.}}
-
-@TECHREPORT{Moller:89,
- AUTHOR = "H. Michael M{\"o}ller",
- TITLE = "Multivariate Rational Interpolation Reconstruction of Rational
-Functions",
- INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik
-Berlin",
- YEAR = 1989, TYPE = "Preprint", NUMBER = "SC 89-4", MONTH = "July"}
-
-@TECHREPORT{Moller:92,
- AUTHOR = "H. Michael M{\"o}ller",
- TITLE = "On Decomposing Systems of Polynomial Equations With Finitely
-Many Solutions",
- INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik
-Berlin",
- YEAR = 1992, TYPE = "Preprint", NUMBER = "SC 92-15", MONTH = "June"}
-
-@INPROCEEDINGS{Moritsugu:85,
- AUTHOR = "S. Moritsugu and N. Inada and E. Goto",
- TITLE = "Symbolic {Newton} Iteration and its Application",
- YEAR = 1985,
- BOOKTITLE = "Proc. of the Second {RIKEN} International
-Symposium on Symbolic and Algebraic Computation by Computers",
- PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "105-117"}
-
-@TECHREPORT{Moritsugu:88,
- AUTHOR = "S. Moritsugu and E. Goto",
- TITLE = "A Proposal for Improvement of Facilities of {REDUCE}",
- INSTITUTION = "Department of Information Science,
-University of Tokyo, Japan",
- YEAR = 1988, MONTH = "December"}
-
-@ARTICLE{Moritsugu:89,
- AUTHOR = "Shuichi Moritsugu and Eiichi Goto",
- TITLE = "A Note on the Preconditioning for Factorization of Homogeneous
-Polynomials",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1989, VOLUME = 23, NUMBER = 1, PAGES = "9-12", MONTH = "January"}
-
-@ARTICLE{Moritsugu:89a,
- AUTHOR = "Shuichi Moritsugu and Makoto Matsumoto",
- TITLE = "A Note on the Numerical Evaluation of Arctangent Function",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1989, VOLUME = 23, NUMBER = 3, PAGES = "8-12", MONTH = "July"}
-
-@ARTICLE{Muroa:91,
- AUTHOR = "Hirokazu Murao",
- TITLE = "Vectorization of symbolic determinant calculation",
- JOURNAL = "Supercomputer",
- YEAR = 1991, VOLUME = "43,VIII-3", PAGES = "36-48"}
-
-@ARTICLE{Mueller:81,
- AUTHOR = "R. M{\"u}ller and H. J. W. M{\"u}ller-Kirsten",
- TITLE = "Iteration of Single- and Two-Channel {Schr{\"o}dinger} Equations",
- JOURNAL = "J. Math. Phys.",
- YEAR = 1981, VOLUME = 22, PAGES = "733-749",
- ABSTRACT = {{\dots} we describe an iteration procedure which has already
-been applied to a large number of other problems.  With the help of
-{REDUCE} it is now possible to do these algebraic computations on the
-computer, so that the necessary expressions are obtained within a
-reasonable time.}}
-
-@InProceedings{Mueller-Hoissen:93,
-  author =      "F. Mueller-Hoissen",
-  title =       "Noncommutative Differential Calculus, Quantum Groups and
-                 Computer Algebra",
-  booktitle =   "Proceedings of the 1993 International IMACS Symposium on
-                 Symbolic Computation",
-  year =        "1993",
-  editor =      "G. Jacob and N. E. Oussous and S. Steinberg",
-  pages =       "97-102",
-  organization ="IMACS",
-  publisher =   "Laboratoire d'Informatique Fondamentale de Lille, France"
-}
-
-@ARTICLE{Murzin:85,
- AUTHOR = "F. A. Murzin",
- TITLE = "Syntactic Properties of the {REFAL} Language",
- JOURNAL = "Int. J. Computer Maths.",
- YEAR = 1985, VOLUME = 17, PAGES = "123-139",
- COMMENT = {{SNOBOL-like} special purpose algebra system.  Designed for
-Cartan  work.  "{REFAL} is rather an unusual programming language.  It is
-natural to ask in which situations it is useful."  Concludes {MACSYMA}
-or {REDUCE} for standard manipulations, {REFAL} for nonstandard.}}
-
-@TECHREPORT{Nagata:82,
- AUTHOR = "Morio Nagata and Makoto Shibayama",
- TITLE = "{COSMOS:}  A Conversational Algebraic System",
- INSTITUTION = "Department of Administration Engineering,
-Keio University",
- YEAR = 1982, TYPE = "Technical Report", NUMBER = "No. 8201",
- MONTH = "March"}
-
-@INPROCEEDINGS{Nagata:85,
- AUTHOR = "Morio Nagata and Makoto Shibayama",
- TITLE = "An Interactive Algebraic System for Personal Computing",
- YEAR = 1985,
- BOOKTITLE = "IEEE International Symposium on New Directions
-in Computing"}
-
-@BOOK{Nakamura:89,
- AUTHOR = "Hideharu Nakamura and Shouichi Matsui",
- TITLE = "Symbolic Computation in Structural Mechanics using {REDUCE}",
- PUBLISHER = "Gihodo Shuppan Company Ltd.", ADDRESS = "1-11-41,
-Akasaka, Minato-Ku, 107 Tokyo, {Japan}", YEAR = 1989}
-
-@ARTICLE{Nakashima:84,
- AUTHOR = "T. T. Nakashima and R. E. D. McClung and B. K. John",
- TITLE = "A Simple Method for the Determination of the Deuterium
-Decoupler Pulse Angle",
- JOURNAL = "J. Magnetic Resonance",
- YEAR = 1984, VOLUME = 56, PAGES = "262-274",
- COMMENT = {{REDUCE} used in theoretical part.  "All density matrix
-calculations presented here were performed on a digital computer using
-REDUCE-2." Essentially matrix products.}}
-
-@ARTICLE{Nakashima:84a,
- AUTHOR = "T. T. Nakashima and R. E. D. McClung and B. K. John",
- TITLE = "Experimental and Theoretical Investigation of
-$_{2}D-_{13}C$ DEPT Spectra on $CD_{N}$",
-JOURNAL = "J. Magnetic Resonance",
- YEAR = 1984, VOLUME = 58, PAGES = "27-36",
- COMMENT = {"All calculations were performed using {REDUCE-2}."}}
-
-@ARTICLE{Namba:86,
- AUTHOR = "Kenji Namba",
- TITLE = "Some Improvements on {Utah} {Standard} {Lisp}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1986, VOLUME = 20, NUMBER = "1 and 2", PAGES = "29-36",
- MONTH = "February and May"}
-
-@ARTICLE{Nemeth:82,
- AUTHOR = "G. N{\'e}meth and M. Zim{\'a}nyi",
- TITLE = "Polynomial Type {Pad\'e} Approximants",
- JOURNAL = "Math. Comp.",
- YEAR = 1982, VOLUME = 38, PAGES = "553-565",
- COMMENT = {Looking for approximants where $R_{n}(x)$ is
-$P_{n}(x)$/P_{n-1}(x)$.  Applied in special functions.  Used
-REDUCE and FORMAC mainly for bignum calculations.}}
-
-@INPROCEEDINGS{Nemeth:87,
- AUTHOR = "G. N{\'e}meth and M. Zim{\'a}nyi",
- TITLE = "Computation of Generalized {Pad\'e} Approximants",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "450-451",
- PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{Neun:89,
- AUTHOR = "W. Neun and H. Melenk",
- TITLE = "Implementation of the {LISP-}Arbitrary Precision Arithmetic
-for a vector Processor",
- JOURNAL = "Computer Algebra and Parallelism", EDITOR = "J. Della Dora
-and J. Fitch",
- YEAR = 1989, PAGES = "75-89", PUBLISHER = "Academic Press, London"}
-
-@ARTICLE{Neutsch:85,
- AUTHOR = "W. Neutsch and E. Schr{\"u}fer and A. Jessner",
- TITLE = "Note on Efficient Integration on the Hypersphere",
- JOURNAL = "J. Comp. Phys.",
- YEAR = 1985, VOLUME = 59, PAGES = "167-175",
- COMMENT = {{REDUCE} used for integration on 4-D hypersphere.  {REDUCE}
-use rather small.}}
-
-@ARTICLE{Neutsch:86,
- AUTHOR = "W. Neutsch and E. Schr{\"u}fer",
- TITLE = "Simple Integrals for Solving {Kepler}'s Equation",
- JOURNAL = "Astrophysics and Space Science",
- YEAR = 1986, VOLUME = 125, PAGES = "77-83",
- COMMENT = {Uses {REDUCE} to verify calculations to give integral form which
-is numerically good, involving only rationals and exponentials.}}
-
-@ARTICLE{Ng:89,
- AUTHOR = "Tze Beng Ng",
- TITLE = "Computation of the Cohomology of ${B\hat{S}O_{n}<16>}$ for
-$23 \leq n \leq 26$ using {REDUCE}",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1989, VOLUME = 7, NUMBER = 1, PAGES = "93-99", MONTH = "January"}
-
-@ARTICLE{Niki:84,
- AUTHOR = "Naoto Niki and Sadanori Konishi",
- TITLE = "Higher Order Asymptotic Expansions for the
-Distribution of the Sample Correlation Coefficient",
- JOURNAL = "Comm. Statist.-Simula. Comp.",
- YEAR = 1984, VOLUME = 13, NUMBER = 2, PAGES = "169-182"}
-
-@TECHREPORT{Nikityuk:87,
- AUTHOR = "N. M. Nikityuk",
- TITLE = "Some Questions of Using Coding Theory and Analytical
-Calculation Methods on Computers",
- INSTITUTION = "J.I.N.R., Dubna",
- YEAR = 1987, NUMBER = "E11-87-10"}
-
-@ARTICLE{Noor:79,
- AUTHOR = "A. K. Noor and C. M. Andersen",
- TITLE = "Computerized Symbolic Manipulation in Structural Mechanics -
-Progress and Potential",
- JOURNAL = "Computers and Structures",
- YEAR = 1979, VOLUME = 10, PAGES = "95-118",
- COMMENT = {Concentrates on {MACSYMA} but mentions {FORMAC} and {REDUCE}
-as also having been used in structures.  Mainly finite elements.  Includes
-program and output.}}
-
-@INPROCEEDINGS{Norman:77,
- AUTHOR = "A. C. Norman and P. M. A. Moore",
- TITLE = "Implementing the New {Risch} Integration Algorithm",
- YEAR = 1977, MONTH = "March",
- BOOKTITLE = "Proc. of the Fourth Colloquium on Advanced Comp.
-Methods in Theor. Phys., St. Maximin, France"}
-
-@ARTICLE{Norman:78,
- AUTHOR = "Arthur Norman",
- TITLE = "Towards a {REDUCE} solution to {SIGSAM} Problem 7",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1978, VOLUME = 12, NUMBER = 4, PAGES = "14-18", MONTH = "November"}
-
-@INPROCEEDINGS{Norman:79,
- AUTHOR = "A. C. Norman and J. H. Davenport",
- TITLE = "Symbolic Integration - The Dust Settles?",
- BOOKTITLE = "Proc. {EUROSAM} 1979, Lecture Notes
-in Computer Science", YEAR = 1979, VOLUME = 72, PAGES = "398-407",
- PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{Norman:83,
- AUTHOR = "Arthur C. Norman and Paul S. Wang",
- TITLE = "A Comparison of {Vaxima} and {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "28-30",
- MONTH = "February"}
-
-@InProceedings{Norman90,
-  author =      "A. C. Norman",
-  title =       "A Critical-Pair/Completion based Integration Algorithm",
-  booktitle =   "Proceedings of the International Symposium on
-                 Symbolic and Algebraic Computation",
-  year =        "1990",
-  editor =      "S. Watanabe and Morio Nagata",
-  pages =       "201-205",
-  organization =        "ACM",
-  publisher =   "Addison-Wesley"
-}
-
-@INPROCEEDINGS{Norman:93,
- AUTHOR = "A. C. Norman",
- TITLE = "Compact Delivery Support for {REDUCE}",
- BOOKTITLE = "Proc. {DISCO '93}, Lecture Notes on Comp. Science",
- YEAR = 1993, VOLUME = 722, PAGES = "331-340",
- PUBLISHER = "Springer-Verlag",
- ABSTRACT = {The {CSL} Lisp system is one designed primarily for delivering
-Lisp applications to users.  It thus emphasises robustness, portability and
-small size rather than support for an integrated programming environment.
-Both portability and compactness are served by making CSL compile the bulk
-of applications code into a compact byte-code instruction set which is then
-emulated.  The speed penalities inherent in this are offset by providing
-instrumentation that makes it easy to identify code hot-spots, and a second
-compiler that translates critical parts of the original Lisp into C for
-incorporation in the CSL kernel.  For use with REDUCE it is found that
-compiling about 5% of the source code into C led to overall performance
-competetive with other Lisp implementations.}}
-
-@ARTICLE{Norman:95,
- AUTHOR = "A.C. Norman",
- TITLE = "Compact Delivery Support for {REDUCE}",
- JOURNAL = "Journ. Symbolic Computation",
- YEAR = 1995, VOLUME=19, PAGES = "133-143",
- ABSTRACT = "{CSL} is a {Lisp} system specifically designed to support the
-{REDUCE} algebra system.  This paper views the {Lisp} system upon which a
-{Lisp-coded} algebra system is coded as in effect a micro-kernel -- it
-provides basic compilation, storage management and extended arithmetic
-capabilities that algebra needs, but is not much concerned with higher level
-algebraic algorithms or with user interfaces.  The description of {CSL}
-given here discusses the major design decisions embodied in the system, and
-shows the extent to which it has been possible to resolve conflicting goals
-of simplicity, small size, portability and high performance."}
-
-@ARTICLE{Norton:80,
- AUTHOR = "Lewis M. Norton",
- TITLE = "A Note About {Laplace} Transform Tables for Computer Use",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1980, VOLUME = 14, NUMBER = 2, PAGES = "30-31", MONTH = "May"}
-
-@TECHREPORT{Nucci:90,
- AUTHOR = "M. C. Nucci",
- TITLE = "Interactive {REDUCE} Programs for Calculating Classical,
-Non-Classical and {Lie-B{\"a}cklund} Symmetries of Differential Equations",
- INSTITUTION = "Georgia Institute of Technology, School of Mathematics",
- YEAR = 1990, TYPE = "Preprint", NUMBER = "Math: 062090-051"}
-
-@BOOK{Ochiai:90,
- AUTHOR = "Mitsuyuki Ochiai and Kiyokazu Nagatomo",
- TITLE = "Linear Algebra using {REDUCE}",
- PUBLISHER = "Kindai Kagaku sha, Tokyo", MONTH = "January", YEAR = 1990,
- COMMENT = {In Japanese.}}
-
-@ARTICLE{Ogilvie:82,
- AUTHOR = "J. F. Ogilvie",
- TITLE = "Applications of Computer Algebra in Physical Chemistry",
- JOURNAL = "Computers in Chemistry",
- YEAR = 1982, VOLUME = 6, NUMBER = 4, PAGES = "169-172",
- COMMENT = {After distinguishing between algebraic and numerical
-computing, the author outlines the facilities of some
-algebraic or symbolic processors and provides some
-instances of how some important features can be applied
-to problems in physical chemistry.}}
-
-@ARTICLE{Ogilvie:89,
- AUTHOR = "J. F. Ogilvie",
- TITLE = "Computer algebra in modern physics",
- JOURNAL = "Computers in Physics",
- YEAR = 1989, MONTH = "January/February", PAGES = "66-74"}
-
-@TECHREPORT{Ono:1979,
- AUTHOR = "Kiyoshi Ono",
- TITLE = "{BFORT} -- A {Fortran} System with Arbitrary
-Precision Integer and Real Arithmetic",
- INSTITUTION = "Department of Physics, University of Tokyo",
- YEAR = 1979, MONTH = "January"}
-
-@TECHREPORT{Ozieblo,
- AUTHOR = "A. Ozieblo",
- TITLE = "Application of {REDUCE 2} in General Theory of Relativity",
- INSTITUTION = "Cyfronet - Krakow, Poland",
- COMMENT = {Application of {REDUCE 2} in all calculations typical for
-General Theory of Relativity is shown here.  The most
-spectacular usage of {REDUCE 2} appears to be in various
-aspects of tensor calculus including differentiation
-operations.}}
-
-%                          REDUCE BIBLIOGRAPHY
-
-%                              Part 4:  P-Z
-
-% Copyright (c) 1993 RAND.  All Rights Reserved.
-
-% Additions and corrections are solicited.  Please send them, in the
-% same format as these entries if possible, to reduce at rand.org.
-
-
-@InProceedings{Padget90,
-  author =      "Julian Padget and Alan Barnes",
-  title =       "Univariate Power Series Expansions in {REDUCE}",
-  booktitle =   "Proceedings of the International Symposium on
-                 Symbolic and Algebraic Computation",
-  year =        "1990",
-  editor =      "S. Watanabe and Morio Nagata",
-  pages =       "82-87",
-  organization =        "ACM",
-  publisher =   "Addison-Wesley"
-}
-
-@ARTICLE{Pankau:73,
- AUTHOR = "E. Pankau and W. Nakel",
- TITLE = "Measurement of the Absolute Cross Section of the
-Elementary Process of Electron-Electron Bremsstrahlung at 300 {keV}",
- JOURNAL = "Phys. Lett.",
- YEAR = 1973, VOLUME = "44A", PAGES = "65-67"}
-
-@ARTICLE{Pankau:73a,
- AUTHOR = "E. Pankau and W. Nakel",
- TITLE = "Eine {Koinzidenzmessung} zum {Elementarprozess}
-der {Elektron-Elektron-Bremsstrahlung} bei 300 {keV}",
- JOURNAL = "Z. Physik",
- YEAR = 1973, VOLUME = 264, PAGES = "139-153"}
-
-@ARTICLE{Parsons:68,
- AUTHOR = "R. G. Parsons",
- TITLE = "An Estimate of the Sixth Order Contribution to the
-Anomalous Magnetic Moment of the Electron",
- JOURNAL = "Phys. Rev.",
- YEAR = 1968, VOLUME = 168, PAGES = "1562-1567"}
-
-@TECHREPORT{Parsons:71,
- AUTHOR = "R. G. Parsons",
- TITLE = "S-Channel Transformation Matrices for Helicity and
-Invariant Amplitudes for lambda + N to O + B",
- INSTITUTION = "Center for Particle Theory, University of Texas",
- YEAR = 1971, TYPE = "Memo", NUMBER = "CPT-88", MONTH = "January"}
-
-@ARTICLE{Pasini:91,
- AUTHOR = "P. Pasini and F. Semeria and C. Zannoni",
- TITLE = "Symbolic computation of orientational correlation function
-moments",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1991, VOLUME = 12, NUMBER = 2, PAGES = "221-231", MONTH = "August"}
- COMMENTS = {Symbolic manipulation (REDUCE and SCHOONSCHIP) has been
-applied to the analytic evaluation of the coefficients in the Taylor series
-expansion of time-correlation functions.  These expressions are derived
-for cylindrically and biaxially symmetric particles reorienting in a
-uniaxial fluid.  The possibility of using computer algebra to determine
-correlation-function moments should make it applicable to various problems
-in statistical physics.}}
-
-@ARTICLE{Pattnaik:83,
- AUTHOR = "P. C. Pattnaik and G. Fletcher and J. L. Fry",
- TITLE = "Improved Numerical Stability for Norm-Conserving ion-{Ure}
-Pseudopotentials",
- JOURNAL = "Phys. Rev. B",
- YEAR = 1983, VOLUME = 28, NUMBER = 6, PAGES = "3364-3365",
- COMMENT = {{REDUCE} and {FORTRAN}; inverting a matrix algebraically would
-be more accurate than a numerical inverse, and used {REDUCE} for this part of
-their work.}}
-
-@ARTICLE{Pearce:81,
- AUTHOR = "P. D. Pearce and R. J. Hicks",
- TITLE = "The Application of Algebraic Optimisation Techniques to
-Algebraic Mode Programs for {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1981, VOLUME = 15, NUMBER = 4, PAGES = "15-22",
- MONTH = "November"}
-
-@ARTICLE{Pearce:83,
- AUTHOR = "P. D. Pearce and R. J. Hicks",
- TITLE = "Data Structures and Execution Times of Algebraic Mode
-Programs for {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "31-37", MONTH = "February"}
-
-@ARTICLE{Perjes:84,
- AUTHOR = "Z. Perj{\'e}s",
- TITLE = "Stationary Vacuum Fields with a Conformally Flat
-Three-Space.  {III}. {Complete} Solution",
- JOURNAL = "General Relativity and Gravitation",
- YEAR = 1984, VOLUME = 18, PAGES = "531-547",
- COMMENT = {{REDUCE} used to perform the necessary calculations.}}
-
-@ARTICLE{Perjes:84a,
- AUTHOR = "Z. Perj{\'e}s and B. Luk{\'a}cs and A. Sebesty{\'e}n
-and A. Valentini",
- TITLE = "Solution of the Stationary Vacuum Equations of
-Relativity for Conformally Flat 3-Spaces",
- JOURNAL = "Phys. Lett.",
- YEAR = 1984, VOLUME = {100A}, NUMBER = 8, PAGES = "405-406",
- MONTH = "February"}
-
-@TECHREPORT{Perjes:84b,
- AUTHOR = "Z. Perj{\'e}s",
- TITLE = "Improved Characterization of the {Kerr} Metric",
- INSTITUTION = "Hungarian Academy of Sciences, Central
-Research Institute for Physics",
- YEAR = 1984, NUMBER = "KFKI-1984-115"}
-
-@TECHREPORT{Perjes:84c,
- AUTHOR = "Z. Perj{\'e}s",
- TITLE= "Stationary Vacuum Fields with a Conformally Flat Three-Space.
-{IV}. {Complete} Solution",
- INSTITUTE = "Institute for Nuclear Study, University of Tokyo",
- YEAR = 1984,  NUMBER = "INS-REP.-487", MONTH = "January"}
-
-@TECHREPORT{Perjes:86,
- AUTHOR = "Z. Perj{\'e}s",
- TITLE = "Ernst Coordinates",
- INSTITUTION = "Hungarian Academy of Sciences, Central
-Research Institute for Physics",
- YEAR = 1986, TYPE = "Preprint", NUMBER = "KFKI-1986-33/B"} ,
-
-@ARTICLE{Perjes:86a,
- AUTHOR = "Z. Perj{\'e}s",
- TITLE = "Stationary Vacuum Fields with a Conformally
-Flat Three-Space.  {II}. {Proof} of Axial Symmetry",
- JOURNAL = "General Relativity and Gravitation",
- YEAR = 1986, VOLUME = 18, NUMBER = 5, PAGES = "511-530",
- MONTH = "May"}
-
-@ARTICLE{Perjes:88,
- AUTHOR = "Z. Perj{\'e}s",
- TITLE  = "Approaches to  Axisymmetry by  Man and  Machine",
- JOURNAL = "Relativity Today",
- YEAR = 1988, EDITOR = "Z. Perjes", PUBLISHER = "World Scientific,
- Singapore"}
-
-@ARTICLE{Perlt:90,
- AUTHOR = "H. Perlt and J. Ranft and J. Heinrich",
- TITLE = "Calculation of {QED} graphs with the {Spinor} technique",
- JOURNAL = "Comp. Phys. Commun.",
- YEAR = 1990, VOLUME = 56, NUMBER = 3, PAGES = "385-390", MONTH = "January"}
-
-@TECHREPORT{Perrottet:78,
- AUTHOR = "M. Perrottet",
- TITLE = "Signature for {W} Boson Production From Jet Analysis
-In e+e- $\rightarrow$ {W+W-} $\rightarrow$ Hadrons",
- INSTITUTION = "CPT 2, CNRS, Marseille", YEAR = 1978,
- TYPE = "Preprint", NUMBER = "78/P.1019", MONTH = "June",
- ABSTRACT = {We have computed the ratio
-o(e+e- $\rightarrow$ W+W- $\rightarrow$ Hadrons)/ o(e+e- $\rightarrow$
-G,Z $\rightarrow$ Hadrons) as a function of the {CM} energy in the
-Weinberg-Salam model.}}
-
-@TECHREPORT{Pesic:73,
- AUTHOR = "P. D. Pesic",
- TITLE = "Two-Photon Cross Section for {W}-Pair Production
-by Colliding Beams",
- INSTITUTION = "Stanford University", YEAR = 1973, TYPE = "Report",
-NUMBER = "SLAC-PUB-1188",
- COMMENT = {Stanford University Linear Accelerator Report.}}
-
-@PHDTHESIS{Pictiaw:69,
- AUTHOR = "Chen Pictiaw",
- TITLE = "An Analytical Investigation of Infinitesimal Spatial
-Motion Theory and its Application to Three-Dimensional Linkages",
- SCHOOL = "Dept. of Mech. Eng., Stanford University",
- YEAR = 1969, MONTH = "March"}
-
-@ARTICLE{Piessens:84,
- AUTHOR = "R. Piessens",
- TITLE = "A Series Expansion for the First Positive Zero of the {Bessel}
-Function",
- JOURNAL = "Math. Comp.",
- YEAR = 1984, VOLUME = 42, PAGES = "195-197",
- COMMENT = {Gives explicit series for first positive zero for 4 terms, using
-{REDUCE}.}}
-
-@ARTICLE{Piessens:86,
- AUTHOR = "R. Piessens and S. Ahmed",
- TITLE = "Note on Approximation for the Turning Points of {Bessel}
-Functions",
- JOURNAL = "J. Comp. Phys.",
- YEAR = 1986, VOLUME = 64, PAGES = "253-257",
- COMMENT = {{REDUCE} used to differentiate and give expansions.}}
-
-@ARTICLE{Pignataro:85,
- AUTHOR = "M. Pignataro and A. Luongo and N. Rizzi",
- TITLE = "On the Effect of the Local Overall Interaction on the
-Postbuckling of Uniformly Compressed Channels",
- JOURNAL = "Thin-Walled Structures",
- YEAR = 1985, VOLUME = 3, PAGES = "292-321",
- COMMENT = {{REDUCE} generating {FORTRAN}, but also used to investigate the
-form of the solutions.}}
-
-@MASTERSTHESIS{Podgorzak:84,
- AUTHOR = "E. Podg{\'o}rak and I. Romanowska",
- TITLE = "Application of {REDUCE} 2 to the Construction of
-Recurrence Relations",
- SCHOOL = "Institute of Computer Science, University of Wroclaw",
- YEAR = "1984"}
-
-@ARTICLE{Price:84,
- AUTHOR = "S. L. Price and A. J. Stone and M. Alderton",
- TITLE = "Explicit Formulae for the Electrostatic Energy, Forces and
-Torques Between a Pair of Molecules of Arbitrary Symmetry",
- JOURNAL = "Molecular Phys.",
- YEAR = 1984, VOLUME = 52, PAGES = "987-1001",
- COMMENT = {"The substitution of the complex multipoles and the S
-functions into the expression for the electrostatic energy was
-facilitated by the use of the symbolic algebraic manipulation program
-{REDUCE}."  Involves heavy calculations.}}
-
-@TECHREPORT{Quarton,
- AUTHOR = "D. C. Quarton and A. D. Garrad",
- TITLE = "Some Comments on the Stability Analysis of Horizontal
-Axis Wind Turbines",
- INSTITUTION = "Wind Energy Group, Taylor Woodrow Construction Ltd."}
-
-@TECHREPORT{Quarton:84,
- AUTHOR = "D. C. Quarton and A. D. Garrad",
- TITLE = "Symbolic Computing as a Tool in Wind Turbine Dynamics",
- INSTITUTION = "Wind Energy Group, Taylor Woodrow Construction Ltd.",
- YEAR = 1984,
- COMMENT = {Presented at the European Wind Energy Conference and Exhibition
-22-26 Oct 1984, Hamburg.}}
-
-@MASTERSTHESIS{Rao:85,
- AUTHOR = "R. H. Rao",
- TITLE = "Deformation of a Fluid-Filled Cylindrical Membrane by a
-Slow Viscous Shear Flow",
- SCHOOL = "Washington University",
- ADDRESS = "Dept. of Mech. Eng., Washington University, St. Louis",
- YEAR = "1985",
- COMMENT = {Draws attention to the use of classical perturbation
-techniques combined with computer algebra as an alternative to
-numerical calculation.}}
-
-@BOOK{Rayna:87,
- AUTHOR = "G. Rayna",
- TITLE = "{REDUCE}:  A System for Computer Algebra",
- PUBLISHER = "Springer-Verlag",
- YEAR = 1987}
-
-@INPROCEEDINGS{Renner:91,
- AUTHOR = "Friedrich Renner",
- TITLE = "Nonlinear Evolution Equations and the {Painlev{\'e}} Analysis:
-A constructive Approach with {REDUCE}",
- YEAR = 1991, MONTH = "July",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
- PAGES = "289-294",
- ABSTRACT = {A number of necessary conditions for a class of nonlinear
-partial differential equations to pass the Painlev{\'e} test with the
-Kruskal ansatz is given.  Using these we can (theoretically) construct all
-evolution equations of certain form and this property with a computer algebra
-package based on {REDUCE}.}}
-
-@ARTICLE{Renner:92,
- AUTHOR = "Friedrich Renner",
- TITLE = "A constructive {REDUCE} package based upon the {Painlev{\'e}}
-analysis of nonlinear evolutions equations in Hamiltonian and/or normal
-form",
- JOURNAL = "Computer Physics Communications",
- YEAR = 1992, VOLUME = 70, NUMBER = 2, PAGES = "409-416", MONTH = "June",
- ABSTRACT = {A number of necessary conditions for scalar nonlinear evolution
-equations of normal or certain Hamiltonian form to pass the {Painlev{\'e}}
-test in one (or two) branches with the Kruskal ansatz is used to write a
-{REDUCE} package able to construct (theoretically) all equations with this
-property.  Starting with a given leading order, a degree of homogeneity
-and (in the Hamiltonian case) a skew-adjoint differential operator, the
-system generates al admissible resonance patterns, adapts (if possible)
-the free parameters of the equation according to the chosen pattern and the
-constraints of the compatibility conditions.  In the {Painlev{\'e}} case,
-the general inhomogeneous equation is generated and also examined.  For
-help and further investigations a set of utility procedures is supplied.}}
-
-@ARTICLE{Reusch:86,
- AUTHOR = "M. F. Reusch and G. H. Neilson",
- TITLE = "Torodially Symmetric Polynomial Multipole Solutions
-of the Vector {Laplace} Equation",
- JOURNAL = "J. Comp. Phys.",
- YEAR = 1986, VOLUME = 64, PAGES = "416-432",
- COMMENT = {{REDUCE} (plasma MHD) algebraic form of multipoles, then
-numerical.}}
-
-Marcelo Ribeiro
-Departamento de Astrofisica
-Observatorio Nacional - CNPq
-Rua General Jose Cristino 77
-Rio de Janeiro, RJ 20921-400
-BRAZIL
-;N arpa mbr obsn.on.br
-
-@PHDTHESIS{Rink:71,
- AUTHOR = "R. A. Rink",
- TITLE = "Application of a Digital Computer to Solve Analytically
-Special Classes of Linear and Nonlinear Differential Equations",
- SCHOOL = "Stanford University",
- YEAR = 1971}
-
-@ARTICLE{Rizzi:85,
- AUTHOR = "N. Rizzi and A. Tatone",
- TITLE = "Symbolic Manipulation in Buckling and Postbuckling Analysis",
- JOURNAL = "Computers and Structures",
- YEAR = 1985, VOLUME = 21, PAGES = "691-700",
- COMMENT = {Gives {REDUCE} program and output for generating {FORTRAN}.}}
-
-@ARTICLE{Rodionov:84,
- AUTHOR = "A. Ya. Rodionov",
- TITLE = "Work with {non-commutative} variables in the {REDUCE-2}
-system for analytical calculations",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1984, VOLUME = 18, NUMBER = 3, PAGES = "16-19", MONTH = "August"}
-
-@ARTICLE{Rodionov:87,
- AUTHOR = "A. Ya. Rodionov and A. Yu. Taranov",
- TITLE = "Computation of Covariant Derivatives of the Geodetic
-Interval within the Coincident Arguments",
- JOURNAL = "Class. Quantum Grav.",
- YEAR = 1987, VOLUME = 4, PAGES = "1767-1775",
- COMMENT = {Used {REDUCE} to calculate the geodetic interval of the
-Riemannian manifold by calculating the multiple covariant derivatives of
-orders 7 and 8.  Direct use of {REDUCE} was not sufficient, but some
-investigations of the structure of the problem produced some
-recurrence relations.}}
-
-@INPROCEEDINGS{Rodionov:87a,
- AUTHOR = "A. Ya. Rodionov and A. Yu. Taranov",
- TITLE = "Combinatorial Aspects of Simplification of Algebraic Expressions",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "192-201",
- PUBLISHER = "Springer-Verlag"}
-
-@TECHREPORT{Rodionov:88,
- AUTHOR = "A. Ya. Rodionov and A. Yu. Taranov",
- TITLE = "{RTENSOR - Packet} for work with tensoric expressions",
- INSTITUTION = "Moscow State University, Scientific Research Institute
-of Nuclear Physics", YEAR = 1988, TYPE = "Preprint", NUMBER = "88-29/50"}
-
-@INPROCEEDINGS{Roelofs:91,
- AUTHOR = "Marcel Roelofs and Peter K.H. Gragert",
- TITLE = "Implementation of multilinear operators in {REDUCE} and
-applications in mathematics",
- YEAR = 1991, MONTH = "July",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
- PAGES = "390-396",
- ABSTRACT = {In this paper we introduce and implement a concept for dealing
-with mathematical bases of linear spaces and mappings (multi)linear with
-respect to such bases, in {REDUCE}.  Using this concept we give some
-examples how to implement some well known (multi)linear mappings in
-mathematics with very little effort.  Moreover we implement a procedure
-operatorcoeff similar to the standard {REDUCE} procedure coeff, but now
-for linear spaces instead of polynomial rings.}}
-
-@BOOK{Rogers:89,
- AUTHOR = "C. Rogers and W. F. Ames",
- TITLE = "Nonlinear Boundary Value Problems in Science and Engineering",
- PUBLISHER = "Academic Press, Inc.",
- YEAR = 1989}
-
-@ARTICLE{Roque:88,
- AUTHOR = "Waldir L. Roque and Renato P. dos Santos",
- TITLE = "Computa\c{c}\~{a}o alg\'{e}brica: ``um assistente matem\~{a}tico''",
- JOURNAL = "Ci\^{e}ncia e Cultura",
- YEAR = 1988, VOLUME = 40, NUMBER = 9, PAGES = "843-852", MONTH =
-"September",
- ABSTRACT = {In this paper we discuss in a simple and
-informative way the theme ``algebraic computing'' in an attempt to encourage
-the Brasilian scientific community to make use of this new tool{\ldots}. Many
-algebraic computing systems have been developed in a variety of research
-fields. Some of these systems, their main characteristics and applications
-will be discussed.},
- COMMENT = {In Portuguese}}
-
-@ARTICLE{Roque:91,
- AUTHOR = "Waldir L. Roque and Renato P. dos Santos",
- TITLE = "Computer algebra in spacetime embedding",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1991, VOLUME = 12, NUMBER = 3, PAGES = "381-389", MONTH =
-"September",
- ABSTRACT = {In this paper we describe an algorithm to determine the vectors
-normal to a space-time ${V}_{4}$ embedded in a pseudo-Euclidean manifold
-${M}_{4+N}$.  An application of this algorithm is given considering the
-Schwarzchild spacetime geometry embedded in a 6 dimensional pseudo-Euclidean
-manifold, using the algebraic computing system REDUCE.}}
-
-@ARTICLE{Ronveaux:88,
- AUTHOR = "A. Ronveaux and G. Thiry",
- TITLE = "Polynomial Solution of Recurrence Relation and Differential
-Equation",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1988, VOLUME = 22, NUMBER = 4, PAGES = "9-19", MONTH = "October"}
-
-@ARTICLE{Ronveaux:89,
- AUTHOR = "A. Ronveaux and G. Thiry",
- TITLE = "Differential Equations of Some Orthogonal Families in {REDUCE}",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1989, VOLUME = 8, NUMBER = 5, PAGES = "537-541", MONTH = "November"}
-
-@INPROCEEDINGS{Rudenko:91,
- AUTHOR = "V.M. Rudenko and V.V. Leonov and A.F. Bragazin and
-I.P Shmyglevsky",
- TITLE = "Application of Computer Algebra to the Investigation of the
-Orbital Satellite Motion",
- YEAR = 1991, MONTH = "July",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
- PAGES = "450-451"}
-
-@ARTICLE{Saez:83,
- AUTHOR = "A. E. Saez and B. J. McCoy",
- TITLE = "Transient Analysis of Packed-Bed Thermal Storage Systems",
- JOURNAL = "Int. J. Heat Mass Transfer",
- YEAR = 1983, VOLUME = 26, NUMBER = 1, PAGES = "49-54"}
-
-@ARTICLE{Sage:88,
- AUTHOR = "Martin L. Sage",
- TITLE = "An Algebraic Treatment of Quantum Vibrations",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1988, VOLUME = 5, NUMBER = 3, PAGES = "377-384", MONTH = "June"}
-
-@ARTICLE{Sarlet:92,
- AUTHOR = "W. Sarlet and J. Vanden Bonne",
- TITLE = "{REDUCE-}procedures for the study of adjoint symmetries of
-second-order differential equations",
- JOURNAL = "J. Symbolic Computation",
- VOLUME = 13, NUMBER = 6, YEAR = 1992, MONTH = "June", PAGES = "683-693",
- ABSTRACT = {Two {REDUCE} programs are presented which should be of
-assistance in computing and studying so-called adjoint symmetries of
-second-order ordinary differential equations.  The first program essentially
-serves to construct the determining equations for adjoint symmetries,
-whose leading coefficients are allowed to be polynomial functions of the
-velocities.  The second program runs various tests concerning the possible
-construction of a first integral or a lagrangian for the given system.}}
-
-@INPROCEEDINGS{Sasaki:79,
- AUTHOR = "Tateaki Sasaki",
- TITLE = "An Arbitrary Precision Real Arithmetic Package in {REDUCE}",
- BOOKTITLE = "Proc. {EUROSAM} 1979, Lecture Notes
-in Computer Science", YEAR = 1979, VOLUME = 72, PAGES = "358-368",
- PUBLISHER = "Springer-Verlag",
- ABSTRACT = {A {REDUCE} arbitrary precision real arithmetic package is
-described which will become a part of the kernel of an algebraic-numeric
-system being developed for {REDUCE}.}}
-
-@ARTICLE{Savage:90,
- AUTHOR = "Stuart B. Savage",
- TITLE = "Symbolic computation of the flow of granular avalanches",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1990, VOLUME = 9, NUMBER = 4, PAGES = "515-530", MONTH = "April"}
-
-@ARTICLE{Sayers:87,
- AUTHOR = "C. M. Sayers",
- TITLE = "The Elastic Anisotropy of Polycrystalline Aggregates
-of Zirconium and Its Alloys",
- JOURNAL = "J. Nuclear Materials",
- YEAR = 1987, VOLUME = 144, PAGES = "211-213",
- COMMENT = {Used {REDUCE} for calculations of tensor products.}}
-
-@ARTICLE{Sayers:87a,
- AUTHOR = "C. M. Sayers",
- TITLE = "Elastic Wave Anisotropy in the Upper Mantle",
- JOURNAL = "Geophysical J. R. Ast. Soc.",
- YEAR = 1987, VOLUME = 88, PAGES = "417-424",
- COMMENT = {Used {REDUCE} in calculations.  "Theoretical expressions for
-angular dependence of the longitudinal and shear wave velocities in an
-axially symmetric aggregate{\ldots}"}}
-
-@INPROCEEDINGS{Schlegel:91,
- AUTHOR = "H. Schlegel",
- TITLE = "Determination of the Root System of Semisimple {Lie} Algbras from
-the {Dynkin} Diagram",
- YEAR = 1991, MONTH = "July",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
- PAGES = "239-240"}
-
-@INPROCEEDINGS{Schmuck:77,
- AUTHOR = "P. Schmuck",
- TITLE = "Verification of the Transient, Two Phase Fluid
-Flow Program {Kachina} using Computerized Similarity Analysis",
- YEAR = 1977, MONTH = "October",
- BOOKTITLE = "Second {GAMM} Conference on Numerical Methods
-in Fluid Mechanics, k{\"o}ln"}
-
-@TECHREPORT{Schoebel:92,
- AUTHOR = "Franziska Schoebel",
- TITLE = "The Symbolic Classification of Real Four-Dimensional
-   Lie Algebras", NUMBER = "Preprint 27/92", YEAR = 1992,
- INSTITUTION = "Naturwissenschaftlich-Theoretisches Zentrum, Universitaet
-    Leipzig, Germany"}
-
-@TECHREPORT{Schoepf:91,
- AUTHOR = "Rainer Sch{\"o}pf and Peter Deuflhard",
- TITLE = "{OCCAL} A mixed symbolic-numeric {Optimal Control CALculator}",
- INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin",
- YEAR = 1991, TYPE = "Preprint", NUMBER = "SC 91-13", MONTH = "December",
- ABSTRACT = {The numerical solution of optimal control problems by indirect
-methods (such as multiple shooting or collocation) requires a considerable
-amount of analytic calculation to establish a numerically tractable system.
-These analytic calculations, though being rather tedious in realistic
-examples, are nowadays mostly still done by hand--and thus prone to
-calculation errors.  The paper aims at automating this analytic processing
-to a reasonable extent by means of a modern symbolic manipulation language
-(here:  REDUCE).  In its present stage of development the package OCCAL
-(mnemotechnically for Optimal Control CALculator) permits an interactive
-use, covering tasks like automatic determination of control and, in case of a
-singular control, of its order.  In simpler problems, the present version of
-OCCAL automatically produces the full subroutine input for a MULtiple
-shooting code (MULCON) with adaptive numerical CONtinuation.
-
-In more complicated problems where singular sub-arcs may occur or where the
-sequence of sub-arcs of the optimal trajectory is unclear OCCAL is a
-significant help in reducing analytic pre-processing.  Examples illustrate
-the performance of OCCAL/MULCON.}}
-
-@ARTICLE{Schruefer:81,
- AUTHOR = "E. Schr{\"u}fer and H. Heintzmann",
- TITLE = "Lorentz-Covariant Eikonal Method in Magnetohydrodynamics
-{II} - The Determination of the Wave Amplitude",
- JOURNAL = "Phys. Lett.",
- YEAR = 1981, VOLUME = {81A}, NUMBER = 9, PAGES = "501-506",
- MONTH = "February",
- COMMENT = {Used {REDUCE} for "rather tedious algebra."}}
-
-@ARTICLE{Schruefer:82,
- AUTHOR = "E. Schr{\"u}fer",
- TITLE = "An Implementation of the Exterior Calculus in {REDUCE:}
-A Status Report",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1982, VOLUME = 16, NUMBER = 4, PAGES = "27-31", MONTH = "November"}
-
-@ARTICLE{Schruefer:87,
- AUTHOR = "E. Schr{\"u}fer and F. W. Hehl and J. D. McCrea",
- TITLE = "Exterior Calculus on the Computer:  The {REDUCE}-Package
-{EXCALC} Applied to General Relativity and to the {Poincar{\'e}}
-Gauge Theory",
- JOURNAL = "General Relativity and Gravitation",
- YEAR = 1987, VOLUME = 19, NUMBER = 2, PAGES = "197-218",
- MONTH = "February",
- COMMENT = {Application of {EXCALC/REDUCE}, including review of other
-systems, and description of {EXCALC}.}}
-
-@ARTICLE{Schruefer:88,
- AUTHOR = "E. Schr{\"u}fer",
- TITLE = "A Note on {Einstein} Metrics",
- JOURNAL = "SIGSAM Bulletin",
- YEAR = 1988, VOLUME = 22, NUMBER = 3, PAGES = "22-26", MONTH = "July"}
-
-@ARTICLE{Schwarz:80,
- AUTHOR = "F. Schwarz",
- TITLE = "An Approximation Scheme for Constructing $\pi_{0}\pi$
-Amplitudes from {ACU} Requirements",
- JOURNAL = "Fortschritte der Physik",
- YEAR = 1980, VOLUME = 28, PAGES = "201-235",
- COMMENT = {"To derive the equations expressing the threshold and the
-asymptotic behaviour one relies heavily on the programming system
-{REDUCE}."}}
-
-@ARTICLE{Schwarz:82,
- AUTHOR = "F. Schwarz",
- TITLE = "Symmetries of the Two Dimensional {Korteweg-De Vries} Equation",
- JOURNAL = "J. Phys. S. Japan",
- YEAR = 1982, VOLUME = 51, NUMBER = 8, PAGES = "2387-2388",
- COMMENT = {{REDUCE} used in the {SPDE} package.}}
-
-@ARTICLE{Schwarz:82a,
- AUTHOR = "F. Schwarz",
- TITLE = "A {REDUCE} Package for Determining {Lie} Symmetries of
-Ordinary and Partial Differential Equations",
- JOURNAL = "Computer Physics Communications",
- YEAR = 1982,  VOLUME = 27, PAGES = "179-186",
- COMMENT = {Preliminary description of {REDUCE} packages {SODE} and
-{SPDE}.}}
-
-@ARTICLE{Schwarz:83,
- AUTHOR = "Fritz Schwarz",
- TITLE = "A {REDUCE} Package for Series Analysis by {Hadamard's}
-Theorem and {QD} Schemes",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "38-44", MONTH = "February"}
-
-@INPROCEEDINGS{Schwarz:83a,
- AUTHOR = "Fritz Schwarz",
- TITLE = "Automatically Determining Symmetries of Ordinary Differential
-Equations",
- BOOKTITLE = "Proc. {EUROCAL} 1983, Lecture Notes
-in Computer Science", YEAR = 1983, VOLUME = 162, PAGES = "45-54",
- PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{Schwarz:84,
- AUTHOR = "F. Schwarz",
- TITLE = "The {Riquier-Janet} Theory and Its Application to Nonlinear
-Evolution Equations",
- JOURNAL = "Physica",
- YEAR = 1984, VOLUME = "11D", PAGES = "243-251",
- COMMENT = {Prologation methods in {REDUCE}.  Points to existence of
-{REDUCE} system.}}
-
-@ARTICLE{Schwarz:84a,
- AUTHOR = "F. Schwarz and W. H. Steeb",
- TITLE = "Symmetries and First Integrals for Dissipative Systems",
- JOURNAL = "J. Phys. {A:}  Math. Gen.",
- YEAR = 1984, VOLUME = 17, PAGES = "L819-L823"}
-
-@ARTICLE{Schwarz:85,
- AUTHOR = "F. Schwarz",
- TITLE = "Automatically Determining Symmetries of Partial Differential
-Equations",
- JOURNAL = "Computing",
- YEAR = 1985, VOLUME = 34, PAGES = "91-106",
- COMMENT = {Describes the {SPDE} package for {REDUCE}.}}
-
-@ARTICLE{Schwarz:85a,
- AUTHOR = "Fritz Schwarz",
- TITLE = "An Algorithm for Determining Polynomial First Integrals of
-Autonomous Systems of Ordinary Differential Equations",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1985, VOLUME = 1, NUMBER = 2, PAGES = "229-233", MONTH = "June"}
-
-@ARTICLE{Schwarz:86,
- AUTHOR = "F. Schwarz",
- TITLE = "A {REDUCE} Package for Determining First Integrals of
-Autonomous Systems of Ordinary Differential Equations",
- JOURNAL = "Computer Physics Communications",
- YEAR = 1986, VOLUME = 39, PAGES = "285-296",
- COMMENT = {Description of package {DISSYS} in {REDUCE}.}}
-
-@INPROCEEDINGS{Schwarz:87,
- AUTHOR = "F. Schwarz",
- TITLE = "Symmetries and Involution Systems: Some Experiments in
-Computer Algebra",
- YEAR = 1987, MONTH = "August",
- BOOKTITLE = "Topics in Soliton Theory and Exactly Solvable Nonlinear
-Equations", PUBLISHER = "World Science Press", ADDRESS = "Singapore",
- COMMENT = {Description of algorithm {INVSYS} and applications.}}
-
-@ARTICLE{Schwarz:88,
- AUTHOR = "F. Schwarz",
- TITLE = "Symmetries of Differential Equations: From {Sophus Lie} to
-Computer Algebra",
- JOURNAL = "Siam Review",
- YEAR = 1988, VOLUME = 30, PAGES = "450-481",
- COMMENT = {Review article on applying the {REDUCE} package {SPDE}.}}
-
-@ARTICLE{Schwarz:94,
- AUTHOR = "F. Schwarz",
- TITLE = "Efficient Factorization of Linear {ODE's}",
- JOURNAL = "Sigsam Bulletin",
- YEAR = 1994, VOLUME = 28, NUMBER = 1, PAGES = "9-17",
- ABSTRACT = {Factorization and testing for irreducibility has turned out to
-be one of the most important algorithms for handling linear ode's.  The
-main hindrance for applying it is its trmendous complexity originating to a
-large extent from solving certain Riccati equations which occur during the
-factorization.  The solution procedure for these Riccati equations is much
-more manageable if it is subdivided into two major parts.  At first so
-called solution candidates are determined each of which depends only on the
-parameters of a single irreducible denominator or the behavior at infinity.
-In a second step it is tried to complete each candidate into a genuine
-solution of the Riccati equation, possibly including an unspecified number
-of additional first order poles.  Furthermore a scheme is proposed for
-running the factorization procedure in parallel on a two-processor machine
-in which possible factors are searched for both from the right and the left
-at the same time.}}
-
-@ARTICLE{Seiler:91,
- AUTHOR = "Werner M. Seiler",
- TITLE = "{SUPERCALC-} a {REDUCE} package for commutator calculations",
- JOURNAL = "Computer Physics Communications",
- YEAR = 1991, VOLUME = 66, PAGES = "363-376",
- COMMENT = {A {REDUCE} package for commutator calculations in sypersymmetric
-theories (including ordered products) and for infinite sums is presented
-and an application to the computation of anomalies in string theory is
-given.}}
-
-@INPROCEEDINGS{Shablygin:87,
- AUTHOR = "E. Shablygin",
- TITLE = "Integral Equation with Hidden Eigenparameter Solver:
-{REDUCE} and {FORTRAN} in Tandem",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "186-191",
- PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{Shmueli:83,
- AUTHOR = "U. Shmueli and A. J. C. Wilson",
- TITLE = "Generalized Intensity Studies:  The Subcentric Distribution
-and Effects of Dispersion",
- JOURNAL = "Acta Cryst.",
- YEAR = 1983, VOLUME = "A39", PAGES = "225-233",
- COMMENT = {Uses {REDUCE} for series expansion to high order as convergence
-is slow.}}
-
-@ARTICLE{Shmueli:83a,
- AUTHOR = "U. Shmueli and U. Kaldor",
- TITLE = "Moments of the Trigonometric Structure Factor",
- JOURNAL = "Acta Cryst.",
- YEAR = 1983, VOLUME = "A39", PAGES = "615-621",
- COMMENT = {Eight moment of magnitude of trigonometric structure factor.
-Used {REDUCE}.  Description of {REDUCE} in appendix.}}
-
-@TECHREPORT{Shtokhamer:75,
- AUTHOR = "R. Shtokhamer",
- TITLE = "Canonical Form of Polynomials in the Presence of
-Side Relations",
- INSTITUTION = "Technion",
- YEAR = 1975, NUMBER = "Technion-PH-76-25"}
-
-@TECHREPORT{Shtokhamer:77,
- AUTHOR = "R. Shtokhamer",
- TITLE = "The Use of {``LET''} Statements in Producing Short
-Comprehended Outputs",
- INSTITUTION = "Department of Physics, Technion-Israel
-Institute of Technology, Haifa, Israel",
- YEAR = 1977, NUMBER = "Technion-PH-77-36",
- ABSTRACT = {It is shown that an algebraic implementation of {"LET"}
-statements may be useful in producing comprehended outputs.
-The suggested algorithm is based on solving large set of
-linear equations over a field.}}
-
-@INPROCEEDINGS{Smit:79,
- AUTHOR = "J. Smit",
- TITLE = "New Recursive Minor Expansion Algorithms, A Presentation in
-a Comparative Context",
- BOOKTITLE = "Proc. {EUROSAM} 1979, Lecture Notes
-in Computer Science", YEAR = 1979, VOLUME = 72, PAGES = "74-87",
-PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{Smit:81,
- AUTHOR = "J. Smit and J. A. van Hulzen and B. J. A. Hulshof",
- TITLE = "{NETFORM} and Code Optimizer Manual",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1981, VOLUME = 15, NUMBER = 4, PAGES = "23-32",
- MONTH = "November"}
-
-@INPROCEEDINGS{Smit:82,
- AUTHOR = "J. Smit and J. A. van Hulzen",
- TITLE = "Symbolic Numeric Methods in Microwave Technology",
- BOOKTITLE = "Proc. {EUROCAM} 1982, Lecture Notes
-in Computer Science", YEAR = 1982, VOLUME = 144, PAGES = "281-288",
- PUBLISHER = "Springer-Verlag"}
-
-@INPROCEEDINGS{Smit:87,
- AUTHOR = "J. Smit and S. H Gerez and R. Mulder",
- TITLE = "Application of a Structured {LISP} System to Computer Algebra",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "149-160",
- PUBLISHER = "Springer-Verlag"}
-
-@TECHREPORT{Soderstrand:72,
- AUTHOR = "M. A. Soderstrand and D. C. Huey",
- TITLE = "Sensitivities of Fourth-Order Filters Obtained by a
-Low-Pass to Band-Pass Transformation",
- INSTITUTION = "University of California, Davis",
- YEAR = 1972, TYPE = "Report"}
-
-@INPROCEEDINGS{Soderstrand:72a,
- AUTHOR = "M. A. Soderstrand and S. K. Mitra",
- TITLE = "Computer-aided Sensitivity Analysis of Higher Filters",
- YEAR = 1972, MONTH = "July",
- BOOKTITLE = "Proc. Second Symposium on Network Theory,
-Herzegnovia, Yugoslavia"}
-
-@TECHREPORT{Soderstrand:74,
- AUTHOR = "M. A. Soderstrand and J. F. Lathrop",
- TITLE = "Two Computer Programs for the Sensitivity Analysis
-of Higher Order Filters",
- INSTITUTION = "Sandia Laboratories", YEAR = 1974,
- TYPE = "Report", NUMBER = "SLL-73-0225", MONTH = "January"}
-
-@ARTICLE{Soma:77,
- AUTHOR = "T. Soma",
- TITLE = "Relativistic Aberration Formulas for Combined
-Electric-Magnetic Focusing-Deflection System",
- JOURNAL = "Optik",
- YEAR = 1977, VOLUME = 49, PAGES = "255-262",
- COMMENT = {Existence of a vertical landing electron beam deflecting
-system free of all deflection induced aberrations is
-presented analytically.}}
-
-@INPROCEEDINGS{Soma:85,
- AUTHOR = "Takashi Soma",
- TITLE = "Recent Applications of {REDUCE} in {RIKEN}",
- YEAR = 1985,
- BOOKTITLE = "Proc. of the Second {RIKEN} International
-Symposium on Symbolic and Algebraic Computation by Computers",
- PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "181-182"}
-
-@INPROCEEDINGS{Spiridonova:87,
- AUTHOR = "M. Spiridonova",
- TITLE = "Some extensions and Applications of {REDUCE} System",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "136-137",
- PUBLISHER = "Springer-Verlag"}
-
-@TECHREPORT{Squire,
- AUTHOR = "W. Squire",
- TITLE = "Some Applications of Symbolic Matrix Inversion",
- INSTITUTION = "Dept. of Mechanical and Aerospace Engineering,
-West Virginia University"}
-
-@BOOK{Steeb:92b,
- AUTHOR = "Willi-Hans Steeb and Dirk Lewien",
- TITLE = "Algorithms and Computation with {REDUCE}",
- PUBLISHER = "BI-Wissenschaftsverlag, Mannheim", YEAR = 1992,
- ABSTRACT ={This book gives a collection of 75 standard methods
- in mathematics, physics and engineering together with their
- programs in {REDUCE} 3.4. Each item consists of a one page mathematical
- description and one page {REDUCE} algebraic source text (in most cases
- a few lines only). The book is an introduction by example
- to algebraic programming in {REDUCE} and a collection of
- ready to use solutions for many mathematical subtasks}}
-
-@BOOK{Steeb:92c,
- AUTHOR = "Willi-Hans Steeb",
- TITLE = "Chaos and Fractals: Algorithms and Computations",
- PUBLISHER = "BI-Wissenschaftsverlag, Mannheim",
- YEAR = 1992,
- COMMENT = "This book includes 26 Turbo C and C++, 47 Turbo PASCAL
-and 23 REDUCE programs"}
-
-@ARTICLE{Steeb:92d,
- AUTHOR = "W-H Steeb",
- TITLE = "Computer Algebra and Its Applications in Physics",
- JOURNAL = "International Journal of Modern Physics C",
- YEAR = 1992, VOLUME = 3, NUMBER = 6, PAGES = "1333-1350",
- COMMENT = {Computer algebra is a powerful tool in the study of a wide
-class of problems in mathematics, physics, and engineering.  The primary
-domain of computer algebra is the solution of large scale formal problems.
-We give an introduction and survey on computer algebra.  In particular we
-show with examples how problems in physics can be solved.  We also show
-with an example how object-oriented programming can be used in such
-problems.}}
-
-@ARTICLE{Steeb:93,
- AUTHOR = "W-H Steeb",
- TITLE = "Fermi Systems and Computer Algebra",
- JOURNAL = "International Journal of Modern Physics C",
- YEAR = 1993, VOLUME = 4, NUMBER = 4, PAGES = "841-846",
- COMMENT = {Computer algebra is a helpful tool in studying Fermi systems.
-We show how the anticommutation relations can be implemented with computer
-algebra.  Then we give an application to the Hubbard model.}}
-
-@BOOK{Steeb:93a,
- AUTHOR = "W.-H Steeb",
- TITLE = "Invertible Point Transformations and Nonlinear Differential
-Equations",
- PUBLISHER = "World Scientific Publishing",
- YEAR = 1993}
-
-@BOOK{Steeb:94,
- AUTHOR = "W.-H Steeb",
- TITLE = "Chaos und Quantenchaos in dynamischen Systemen",
- PUBLISHER = "Bi-Wissenschaftsverlag, Mannheim",
- YEAR = 1994}
-
-@BOOK{Steeb:94a,
- AUTHOR = "W.-H Steeb",
- TITLE = "Quantum Mechanics using Computer Algebra",
- PUBLISHER = "World Scientific Publishing, Singapore",
- YEAR = 1994}
-
-@ARTICLE{Steeb:94b,
- AUTHOR = "W-H Steeb",
- TITLE = "Applications of Computer Algebra in Quantum Groups",
- JOURNAL = "International Journal of Modern Physics C",
- YEAR = 1994, VOLUME = 6, PAGES = "701-706"}
-
-@ARTICLE{Steeb:94c,
- AUTHOR = "W-H Steeb",
- TITLE = "Extended {Lorenz} Models and Time Dependent First Integrals",
- JOURNAL = "Zeitschrift fuer Naturforschung",
- YEAR = 1994, VOLUME = "49a", PAGES = "751-753"}
-
-@ARTICLE{Steeb:95,
- AUTHOR = "W-H Steeb",
- TITLE = "{Bose-Fermi} Systems and Computer Algebra",
- JOURNAL = "Foundations of Physics Letters", YEAR = 1995}
-
-@ARTICLE{Steinberg:82,
- AUTHOR = "Stanly Steinberg",
- TITLE = "Mathematics and Symbol Manipulation",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1982, VOLUME = 16, NUMBER = 3, PAGES = "11-15", MONTH = "August"}
-
-@InProceedings{Steinberg:93,
-  author =      "S. Steinberg and R. Liska",
-  title =       "Stability Analysis and Quantifier Elimination",
-  booktitle =   "Proceedings of the 1993 International IMACS Symposium on
-                 Symbolic Computation",
-  year =        "1993",
-  editor =      "G. Jacob and N. E. Oussous and S. Steinberg",
-  pages =       "62-67",
-  organization ="IMACS",
-  publisher =   "Laboratoire d'Informatique Fondamentale de Lille, France",
-  comment =     {Stability of time-stepping numerical schemes for partial
-                 differential equations based on the {REDUCE} package FIDE
-                 and the SACLIB package QEPCAD.}
-}
-
-@ARTICLE{Steuerwald,
- AUTHOR = "J. Steuerwald and W. Kerner",
- TITLE = "A Contribution to the Efficient Solution of
-Extensive Symbolic Computations",
- JOURNAL = "Comp. Phys. Comm."}
-
-@ARTICLE{Stoutemyer:74,
- AUTHOR = "D. Stoutemyer",
- TITLE = "Automatic Error Analysis Using the Computer Symbolic
-Manipulation Language",
- JOURNAL = "TOMS 3",
- YEAR = 1977, VOLUME = 3, NUMBER = 1, PAGES = "26-43",
- MONTH = "March",
- ABSTRACT = {This paper shows how the inherent error and the fixed-point
-or floating-point roundoff of chopoff error of an expression can be
-determined automatically using a computer algebra language such as
-{REDUCE}.}}
-
-@TECHREPORT{Stoutemyer:75,
- AUTHOR = "David R. Stoutemyer",
- TITLE = "Symbolic Computer Solution of an Equation in Finite Terms",
- INSTITUTION = "Dept. of Comp. Science, Univ. of Utah",
- TYPE = "Report", YEAR = 1975, NUMBER = "UCP-33",
- ABSTRACT = {This report contains a program listing together with
-documentation, a demonstration, and discussion of a {REDUCE} program for the
-exact solution of an equation in finite terms.  Capable of treating certain
-equations involving elementary transcendental functions, radicals,
-and polynomials, the program incorporates several solution techniques
-not implemented in existing analogous programs written in other
-computer algebra languages.  The program is also capable of solving
-linear or linear fractional in the unknowns.  In this case it simply
-used the built-in matrix equation solver, but permitting input as
-lists of expressions rather than matrices, which is convenient for
-sparse or small linear systems.}}
-
-@ARTICLE{Stoutemyer:77,
- AUTHOR = "David R. Stoutemyer",
- TITLE = "Analytically Solving Integral Equations by Using Computer
-Algebra",
- JOURNAL = "TOMS",
- YEAR = 1977, VOLUME = 3, NUMBER = 2, PAGES = "128-146",
- MONTH = "June",
- ABSTRACT = {This report describes how a computer algebra language, such as
-{REDUCE}, may be used to automatically construct closed-form and series
-analytical solutions of integral equations.}}
-
-@ARTICLE{Stroscio:74,
- AUTHOR = "M. A. Stroscio and J. M. Holt",
- TITLE = "Radiative Corrections to the Decay Rate of Orthopositronium",
- JOURNAL = "Phys. Rev. A",
- YEAR = 1974, MONTH = "September", VOLUME = 10, PAGES = "749-755"}
-
-@ARTICLE{Stuart:88,
- AUTHOR = "Robin G. Stuart",
- TITLE = "Algebraic Reduction of one-loop {Feynman} Diagrams to
-Scalar Integrals",
- JOURNAL = "Comp. Phys. Commun.",
- YEAR = 1988, VOLUME = 48, NUMBER = 3, PAGES = "367-389", MONTH = "March"}
-
-@ARTICLE{Stuart:90,
- AUTHOR = "Robin G. Stuart and A. G{\'o}ngora-T",
- TITLE = "Algebraic Reduction of one-loop {Feynman} Diagrams to
-Scalar Integrals II",
- JOURNAL = "Comp. Phys. Commun.",
- YEAR = 1990, VOLUME = 56, NUMBER = 3, PAGES = "337-350", MONTH = "January"}
-
-@ARTICLE{Suppes:89,
- AUTHOR = "Patrick Suppes and Shuzo Takahashi",
- TITLE = "An Interactive Calculus Theorem-prover for Continuity
-Properties",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1989, VOLUME = 7, NUMBER = 6, PAGES = "573-590", MONTH = "June"}
-
-@ARTICLE{Surguladze:89,
- AUTHOR = "L.R. Surguladze and F.V. Tkachov",
- TITLE = "{LOOPS:} Procedures for Multiloop Calculations in Quantum Field
-Theory for the {REDUCE} System",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1989, VOLUME = 55, NUMBER = 2, PAGES = "205-215",
- MONTH = "September", PUBLISHER = "North Holland Publishing Company"}
-
-@INPROCEEDINGS{Surguladze:91,
- AUTHOR = "Levan R. Surguladze and Mark A. Samuel",
- TITLE = "Algebraic Perturbative Calculations in High Energy Physics
-Methods, algorithms, computer programs and physical applications",
- YEAR = 1991, MONTH = "July",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
- PAGES = "439-447",
- ABSTRACT = {The methods and algorithms for high order algebraic
-perturbative calculations in theoretical high energy physics are briefly
-reviewed.  The {SCHOONSCHIP} program {MINCER} and the {REDUCE} program
-{LOOPS} for analytical computation of arbitrary massless, one-, two-
-and three-loop Feynman diagrams of the propagator type are described.
-The version of the program {LOOPS} for personal computers and the extended
-version of the program {MINCER} for four-loop renormalization group
-calculations are presented.  The new program for algebraic perturbative
-calculations is also discussed.  This program is written on the new
-algebraic programming system {FORM}.  Some recent results of application
-to the high energy physics are given.}}
-
-@ARTICLE{Tallents:84,
- AUTHOR = "G. J. Tallents",
- TITLE = "The Relative Intensities of Hydrogen-Like Fine Structure",
- JOURNAL = "J. Phys. B",
- YEAR = 1984, VOLUME = 17, PAGES = "3677-3691",
- COMMENT = {{REDUCE} used to check a formula; also checked numerically.}}
-
-@InProceedings{Tao90,
-  author =      "Qingsheng Tao",
-  title =       "Symbolic and Algebraic manipulation for Formulae of
-                 Interpolation and Quadrature",
-  booktitle =   "Proceedings of the 1990 International Symposium on
-                 Symbolic and Algebraic Computation",
-  year =        "1990",
-  editor =      "S. Watanabe and Morio Nagata",
-  pages =       "306",
-  organization =        "ACM",
-  publisher =   "Addison-Wesley"
-}
-
-@TECHREPORT{Tasso:76,
- AUTHOR = "H. Tasso and J. Steuerwald",
- TITLE = "Subroutine for Series Solutions of Linear Differential Equations",
- INSTITUTION = "Max Planck Institut for Plasmaphysik",
- YEAR = 1976, NUMBER = "IPP 6/143"}
-
-@TECHREPORT{Thas:89,
- AUTHOR = "C. Thas",
- TITLE = "A collection of {REDUCE} and {MACSYMA} programs about college
-geometry.  Part 1",
- INSTITUTION = "State University of Gent",
- YEAR = 1989, NUMBER = 5, MONTH = "September"}
-
-@TECHREPORT{Thas:89a,
- AUTHOR = "C. Thas",
- TITLE = "A collection of {REDUCE} and {MACSYMA} programs about college
-geometry.  Part 2",
- INSTITUTION = "State University of Gent",
- YEAR = 1989, NUMBER = 5, MONTH = "September"}
-
-@INPROCEEDINGS{Todd:88,
- AUTHOR = "P. H. Todd and G. W. Cherry",
- TITLE = "Symbolic Analysis of Planar Drawings",
- BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
- YEAR = 1988, VOLUME = 358, PAGES = "344-355"}
-
-@ARTICLE{Toth:86,
- AUTHOR = "K. T{\'o}th and K. Szeg{\"o} and A. Margaritis",
- TITLE =  "Radiative Corrections for Semileptonic Decays of {Hyperons:
-`Model-Independent' Part}",
- JOURNAL = "Physical Review D", YEAR = 1986, VOLUME = 33, NUMBER = 11,
- PAGES = "3306-3315", MONTH ="June"}
-
-@INPROCEEDINGS{Tournier:79,
- AUTHOR = "Evelyne Tournier",
- TITLE = "An Algebraic Form of a Solution of a System
-of Linear Differential Equations with Constant Coefficients",
- BOOKTITLE = "Proc. {EUROSAM} 1979, Lecture Notes
-in Computer Science", YEAR = 1979, VOLUME = 72, PAGES = "153-163",
- PUBLISHER = "Springer-Verlag",
- ABSTRACT = {In this paper we describe an algorithm for finding an
-algebraic form for the solution of a system of linear differential
-equations with constant coefficients, using the properties of elementary
-divisors of a polynomial matrix.}}
-
-@PHDTHESIS{Tournier:87,
- AUTHOR = "Evelyne Tournier",
- TITLE = "Solutions Formelles D'Equations Differentielles,
-le Logiciel de Calcul Formel:  {DESIR} Etude Theorique
-et Realisation",
- SCHOOL = "L'Universit{\'e} Scientifique, Technologique et
-Medicale de Grenoble",
- YEAR = 1987, MONTH = "April"}
-
-@INPROCEEDINGS{Trenkov:91,
- AUTHOR = "I. Trenkov and M. Spiridonova and M. Daskalova",
- TITLE = "An Application of the {REDUCE} System for Solving a Mathematical
-Geodesy Problem",
- YEAR = 1991, MONTH = "July",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
- PAGES = "448-449"}
-
-@INPROCEEDINGS{Trotter:89,
- AUTHOR = "H. F. Trotter",
- TITLE = "Use of Symbolic Methods in Analyzing an Integral Operator",
- BOOKTITLE = "Proc. of Computers and Mathematics '89",
- EDITOR = "E. Kaltofen and S. M. Watt",
- YEAR = 1989, PAGES = "82-90", PUBLISHER = "Springer-Verlag, New York"}
-
-@ARTICLE{Tsai:65,
- AUTHOR = "Y. S. Tsai and A. C. Hearn",
- TITLE = "Differential Cross-Section for e+ + e- $\rightarrow$ {W+} +
-{W-} $\rightarrow$ e- + $\overline{\nu}_{e} + \mu + \nu_{\mu}$",
- JOURNAL = "Phys. Rev.",
- YEAR = 1965, VOLUME = 140, PAGES = "B721-B729"}
-
-@ARTICLE{Tsai:74,
- AUTHOR = "Y. S. Tsai",
- TITLE = "Pair Production and Bremsstrahlung of Charged Leptons",
- JOURNAL = "Rev. Mod. Phys.",
- YEAR = 1974, VOLUME = 46, PAGES = "815-851"}
-
-@ARTICLE{Ucoluk:82,
- AUTHOR = "G. {\"U}\c{c}oluk and A. Hacinliyan",
- TITLE = "A Proposal for Extensions to {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1982, VOLUME = 16, NUMBER = 2, PAGES = "4-14", MONTH = "May",
- ABSTRACT = {Three classes of extensions are proposed for {REDUCE}:  A
-facility  for evaluating arbitrary functions of matrices; a facility for
-grouping, modifying or restoring the status of various flags
-in {REDUCE}; further extensions and modifications for separating
-terms, coefficients of expressions, concatenation, and non-
-commuting algebra.}}
-
-@BOOK{Ueberberg:92,
- AUTHOR = "Johannes Ueberberg",
- TITLE = "Einf{\"u}hrung in die computeralgebra mit {REDUCE}",
- PUBLISHER = "BI-Wissenschaftsverlag, Mannheim",
- YEAR = 1992}
-
-@ARTICLE{Umeno:89,
- AUTHOR = "Takaji Umeno and Syuichi Yamashita and Osami Saito and
-Kenichi Abe",
- TITLE = "Symbolic Computation Application for the Design of Linear
-Multivariable Control Systems",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1989, VOLUME = 8, NUMBER = 6, PAGES = "581-588", MONTH = "December"}
-
-@INPROCEEDINGS{Urintsev:91,
- AUTHOR = "A.L. Urintsev and A.V. Samoilov",
- TITLE = "Complex Reduce-programs for analytic solution of some problems of
-beam transport systems",
- YEAR = 1991,
- BOOKTITLE = "In:  4th International Conference on Computer Algebra in
-Physical Research",
- EDITOR = "D.V. Shirkov and V.A. Rostovtsev and V.P. Gerdt",
- PUBLISHER = "World Scientific", ADDRESS = "Singapore, New Jersey, London,
-Hong Kong", PAGES = "438-442"}
-
-@ARTICLE{vandenHeuvel:86,
- AUTHOR = "Pim van den Heuvel",
- TITLE = "Adding Statements to {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1986, VOLUME = 20, NUMBER = "1 and 2", PAGES = "8-14",
- MONTH = "February and May"}
-
-@TECHREPORT{vandenHeuvel:86a,
- AUTHOR = "Pim van den Heuvel",
- TITLE = "Some Experiments in {REDUCE} Related to the
-Calculation of {Groebner} Bases",
- INSTITUTION = "Department of Computer Science, Twente
-University of Technology, The Netherlands",
- YEAR = 1986, MONTH = "June"}
-
-@INPROCEEDINGS{vandenHeuvel:87,
- AUTHOR = "P. van den Heuvel and J. A. van Hulzen and V. V. Goldman",
- TITLE = "Automatic Generation of {FORTRAN}-Coded {Jacobians} and
-{Hessians}",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "120-131",
- PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{vandenHeuvel:87a,
- AUTHOR = "P. van den Heuvel and B. J. A. Hulshof and J. A. van Hulzen",
- TITLE = "Some Simple Pretty-Print Facilities for {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1987, VOLUME = 21, NUMBER = 1, PAGES = "14-17", MONTH = "February"}
-
-@TECHREPORT{vanHeerwaarden,
- AUTHOR = "M. C. van Heerwaarden and J. A. van Hulzen",
- TITLE = "Pretty Print Facilities for {REDUCE}",
- INSTITUTION = "Department of Computer Science, University
-of Twente, The Netherlands",
- YEAR = 1988, TYPE = "Memorandum",
- NUMBER = "INF-88-36", MONTH = "August"}
-
-@ARTICLE{vanHulzen:80,
- AUTHOR = "J. A. van Hulzen",
- TITLE = "Computational Problems in Producing {Taylor} Coefficients
-for the Rotating Disk Problem",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1980, VOLUME = 14, NUMBER = 2, PAGES = "36-49", MONTH = "May"}
-
-@TECHREPORT{vanHulzen:81,
- AUTHOR = "J. A. van Hulzen",
- TITLE = "Breuer's Grow Factor Algorithm in Computer Algebra",
- INSTITUTION = "Department of Applied Mathematics, Twente University
-of Technology, The Netherlands",
- YEAR = 1981, TYPE = "Memorandum", NUMBER = 332, MONTH = "April",
- COMMENT = {A shorter version appears in: Proceedings SYMSAC 81
- (Paul S. Wang, ed.) ACM, August 1981.}}
-
-@ARTICLE{vanHulzen:82,
- AUTHOR = "J. A. van Hulzen and B. J. A. Hulshof",
- TITLE = "An Expression Analysis Package for {REDUCE}",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1982, VOLUME = 16, NUMBER = 4, PAGES = "32-44", MONTH = "November"}
-
-@INPROCEEDINGS{vanHulzen:82a,
- AUTHOR = "J. A. van Hulzen",
- TITLE = "Computer Algebra Systems Viewed by a Notorious User",
- BOOKTITLE = "Proc. {EUROCAM} 1982, Lecture Notes
-in Computer Science", YEAR = 1982, VOLUME = 144, PAGES = "166-180"}
-
-@INCOLLECTION{vanHulzen:83,
- AUTHOR = "J. A. van Hulzen and J. Calmet",
- TITLE = "Computer Algebra Systems",
- EDITOR = "B. Buchberger and G. E. Collins and R. Loos and R. Albrecht",
- BOOKTITLE = "Computer Algebra and Symbolic and Algebraic Computation",
- EDITION = "2nd", PUBLISHER = "Springer-Verlag", YEAR = 1983}
-
-@INPROCEEDINGS{vanHulzen:83a,
- AUTHOR = "J. A. van Hulzen",
- TITLE = "Code Optimization of Multivariate Polynomial Schemes:  A
-Pragmatic Approach",
- BOOKTITLE = "Proc. {EUROCAL} 1983, Lecture Notes
-in Computer Science", YEAR = 1983, VOLUME = 162, PAGES = "286-300",
- PUBLISHER = "Springer-Verlag"}
-
-@INPROCEEDINGS{vanHulzen:87,
- AUTHOR = "J. A. van Hulzen",
- TITLE = "Program Generation Aspects of the Symbolic-Numeric Interface",
- BOOKTITLE = "Proc. Third Intern. Conf. on Computer Algebra and its
-applications in Theor. Phys, 1985", YEAR = 1987, PAGES = "104-113",
- PUBLISHER = "{J.I.N.R., Dubna, USSR}"}
-
-@TECHREPORT{vanHulzen:88,
- AUTHOR = "J. A. van Hulzen",
- TITLE = "Formule Manipulatie m.b.v. {REDUCE} (in {Dutch})",
- INSTITUTION = "Department of Computer Science, Twente University
-of Technology, The Netherlands",
- YEAR = 1988, MONTH = "October"}
-
-@INPROCEEDINGS{vanHulzen:89,
- AUTHOR = "J. A. van Hulzen and B. J. A. Hulshof and B. L. Gates and
-M. C. Van Heerwaarden",
- TITLE = "A Code Optimization Package for {REDUCE}",
- BOOKTITLE = "Proc. of {ISSAC} '89", PUBLISHER = "{ACM} Press, New York",
- YEAR = 1989, PAGES = "163-170",
- COMMENT = {Lecture Notes.}}
-
-@TECHREPORT{vanHulzen:89a,
- AUTHOR = "J. A. van Hulzen",
- TITLE = "Computer Algebra and Numerical Mathematics:  The Odd Couple?",
- INSTITUTION = "Department of Computer Science, Twente University
-of Technology, The Netherlands",
- NUMBER = "Informatica 89-40",
- YEAR = 1989, MONTH = "June"}
-
-@TECHREPORT{VanProeyan:76,
- AUTHOR = "A. Van Proeyen",
- TITLE = "Quantum Gravity Corrections on the Anomalous
-Magnetic and Quadrupole Moments of a Spin-1 Particle",
- INSTITUTION = "Instituut voor Theor. Fys., Leuven",
- YEAR = 1976, MONTH = "October"}
-
-@TECHREPORT{VanProeyan:79,
- AUTHOR = "A. Van Proeyan",
- TITLE = "Gravitational Divergences of the Electromagnetic
-Interactions of Massive Vectorparticles",
- INSTITUTION = "Universiteit Leuven",
- YEAR = 1979, TYPE = "Preprint", NUMBER = "KUL-TF-79/032",
- MONTH = "October",
- ABSTRACT = {In a search for the explanation of the finite quantum
-gravity corrections to anomalous moments we examined a
-spontaneous broken 0(3) model with Yang-Mills particles
-and Higgs scalars coupled to gravitons.}}
-
-@INPROCEEDINGS{Vega:91,
- AUTHOR = "Laureano Gonz{\'a}lez Vega",
- TITLE = "Working with Real Algebraic Plane Curves in {REDUCE:} the
-{GCUR} package",
- YEAR = 1991, MONTH = "July",
- BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
-Algebraic Computation",
- EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
- PAGES = "397-402"}
-
-@TECHREPORT{Vinitsky:87,
- AUTHOR = "S. I. Vinitsky and V. A. Rostovtsev",
- TITLE = "A Use of {REDUCE} System in Problems of
-Hydrogen Atom in an Electric Field",
- INSTITUTION = "J.I.N.R., Dubna", TYPE = "Preprint",
- YEAR = 1987, NUMBER = "P11-87-303"}
-
-@ARTICLE{Viry:93,
- AUTHOR = "Guy Viry",
- TITLE = "Factorization of Multivariate Polynomials with Coefficients in
-$F_{p}$",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1993, VOLUME = 15, NUMBER = 4, PAGES = "371-391", MONTH = "November",
- COMMENT = {The ring of polynomials in $X,X_{1}, \1dots ,X_{m}$ are denoted
-by $F_{p}[X,X_{1}, \1dots ,X_{m}]$ in $F_{p}$, that is the field of
-integers defined modulo $p$. In the usual factorization algorithm defined
-by Wang, the given polynolmial $P$ is first factorized modulo $\Delta^{n}$,
-where $\Delta^{n}$ is an ideal.  This algorithm uses a generalization of
-Hensel's Lemma.  If there are no extraneous factors, then the factors
-defined modulo $\delta^[{n}$ correspond to the factors of $P$ in
-$F_{p}[X,X_{1}, \1dots ,X_{m}]$ or else the defined factors must be
-regrouped to find the factors of $P$ in $F_{p}[X,X_{1}, \1dots ,X_{m}]$.
-In this paper, a mapping that transforms the product of the factors into a
-sum is defined.  A theorem that determines whether a subproduct of the
-factors of $P$ corresponds to a factor of $P$ in $F_{p}[X,X_{1}, \1dots
-,X_{m}]$ is given.  Therefore the regrouping of the factors of $P$ reduces
-to solving a system of linear equations, as in the univariate case, with
-Berlekamp's algorithm.}}
-
-@ARTICLE{Voros:77,
- AUTHOR = "A. Voros",
- TITLE = "Asymptotic K-Expansions of Stationary Quantum States",
- JOURNAL = "Ann. Inst. H. Poincare",
- YEAR = 1977, VOLUME = "26A", PAGE = "343"}
-
-@TECHREPORT{Wanas,
- AUTHOR = "M. I. Wanas",
- TITLE = "The Third Face of Computer -- Computer Solution
-of Symbolic Problems",
- INSTITUTION = "Military Technical College, Cairo, Egypt",
- NUMBER = "CAP-3 837"}
-
-@INPROCEEDINGS{Wanas:85,
- AUTHOR = "M. I. Wanas",
- TITLE = "Manipulation of Parameters Indicating the
-Physical Significance of any Absolute Parallelism
-Space Using {REDUCE} 2",
- YEAR = 1985,
- BOOKTITLE = "Tenth International Congress for Statistics,
-Computer Science, Social and Demographic Research"}
-
-@INPROCEEDINGS{Wang:84,
- AUTHOR = "Paul S. Wang and T. Y. P. Chang and J. A. van Hulzen",
- TITLE = "Code Generation and Optimization for Finite Element Analysis",
- BOOKTITLE = "Proc. {EUROSAM} 1984, Lecture Notes
-in Computer Science", YEAR = 1984, VOLUME = 174, PAGES = "237-247",
- PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{Wang:93,
- AUTHOR = "Jian-Xiong Wang",
- TITLE = "Automatic calculation of {Feynman loop-diagrams}, I.  Generation
-of a simplified form of the amplitude",
- YEAR = 1993, VOLUME = 77, NUMBER = 2, PAGES = "263-285", MONTH = "October"}
- ABSTRACT = {In order to develop an automatic system to calculate loop
-diagrams in renormalizable theories, we present the first part of a
-complete system written in {REDUCE} and {RLISP}.  It can generate the tensor
-and gamma matrix basis which is able to cast the total amplitude into a
-simpler form with the help of gauge invariance and symmetry among identical
-particles.}
-
-@ARTICLE{Wassam:87,
- AUTHOR = "W. A. {Wassam, Jr.} and Go. Torres-Vega",
- TITLE = "Dual {Lanczos} Transformation Theory:  Closed Set of Algebraic
-Equations Connecting {Lanczos} Parameters with Moments in Moment
-Expansions of Time-Dependent Quantities",
- JOURNAL = "Chemical Phys. Lett.",
- YEAR = 1987, VOLUME = 134, NUMBER = 4, PAGES = "355-360",
- COMMENT = {"The utility of this set of equations is illustrated by using
-them with the aid of symbolic manipulation on a computer to construct a
-previously unknown exact continued fraction for the spectral density
-of the incoherent scattering function{\ldots}" The system used is {REDUCE}
-on a Burroughs.  Appear enthusiastic about the possibilities for
-computer algebra in related fields.}}
-
-@ARTICLE{Wassam:87a,
- AUTHOR = "W. A. {Wassam, Jr.} and Go. Torres-Vega and J. Neito-Frausto",
- TITLE = "Dual {Lanczos} Transformation Theory:  Exact Continued
-Fraction Expression for Resonant $\gamma$-ray Absorption Spectrum of a
-Harmonically Bound Atom Executing Classical Motion Described by
-{Smoluchowski} Dynamics",
- JOURNAL = "Chemical Phys. Lett.",
- YEAR = 1987, VOLUME = 136, NUMBER = 1, PAGES = "26-30",
- COMMENT = {"{\ldots}with the aid of symbolic manipulation techniques, we
-construct a previously unknown exact continued fraction for the resonance
-$\gamma$-ray absorption spectrum{\dots}"  The system used is {REDUCE}
-on a Burroughs.}}
-
-@TECHREPORT{Watanabe:85,
- AUTHOR = "Yoichi Watanabe",
- TITLE = "Symbolic Manipulation of Structure Functions
-in Availability Analysis",
- INSTITUTION = "Fusion Technology Institute, University of
-Wisconsin, Madison, Wisconsin",
- YEAR = 1985, NUMBER = "UWFDM-658", MONTH = "November"}
-
-@ARTICLE{Watanabe:76,
- AUTHOR = "Shunro Watanabe",
- TITLE = "Formula Manipulations Solving Linear Ordinary
-Differential Equations {II}",
- JOURNAL = "Publications of the Research Institute for
-Mathematical Sciences, Kyoto University",
- YEAR = 1976, VOLUME = 11, NUMBER = 2, PAGES = "297-337"}
-
-@ARTICLE{Watanabe:79,
- AUTHOR = "Shunro Watanabe",
- TITLE = "A Verification for Non-existence of Movable Branch Points of Six
-Painlev{\'e} Transcendents by Formula Manipulations",
- JOURNAL = "Tokyo Journal of Mathematics",
- YEAR = 1979, VOLUME = 2, NUMBER = 2, PAGES = "285-291"}
-
-@ARTICLE{Weber:79,
- AUTHOR = "Lawrence A. Weber and Gerhard Rayna",
- TITLE = "Problem \#11 Solved in {REDUCE:}  A Case Study in Program
-Translation",
- JOURNAL = "{SIGSAM} Bulletin",
- YEAR = 1979, VOLUME = 13, NUMBER = 4, PAGES = "21-24", MONTH = "November"}
-
-@ARTICLE{Wehner:86,
- AUTHOR = "M. F. Wehner and W. G. Wolfer",
- TITLE = "The Pressure of a Hard Sphere Fluid on a Curved Surface",
- JOURNAL = "J. Statistical Phys.",
- YEAR = 1986, VOLUME = 42, PAGES = "509-521",
- COMMENT = {Integral equation approach and perturbation expansions in
-{REDUCE}.  "Therefore, in order to avoid errors, the integrations have been
-done in closed form with the algebraic manipulation routine {REDUCE}."}}
-
-@InProceedings{Weispfenning:94,
-  author =       {Volker Weispfenning},
-  title =        {Quantifier elimination for real algebra -- the cubic case},
-  booktitle =    {Symbolic and Algebraic Computation},
-  editor =       {},
-  series =       {ISSAC},
-  year =         {1994},
-  organization = {SIGSAM},
-  publisher =    {ACM},
-  pages =        {258--263}
-}
-
-@INCOLLECTION{Winkelmann:89,
- AUTHOR = "Volker Winkelmann and Friedrich W. Hehl",
- TITLE = "{REDUCE} for Beginners. Six Lectures on the
-Application of Computer Algebra",
- EDITOR = "D. Stauffer and F. W. Hehl and V. Winkelmann and
-J. G. Zabolitzky",
- BOOKTITLE = "Computer Simulation and Computer Algebra.
-Lectures for Beginners",
- CHAPTER = 3, EDITION = "2nd", PUBLISHER = "Springer-Verlag",
- YEAR= 1989}
-
-@TECHREPORT{Winkler:88,
- AUTHOR = "F. Winkler and B. Kutzler and F. Lichtenberger",
- TITLE = "Computeralgebrasysteme (in {German})",
- INSTITUTION = "RISC - LINZ, Austria", TYPE = "Report",
- YEAR = 1988, NUMBER = "88-10"}
-
-@ARTICLE {Witham:77,
- AUTHOR = "C. R. Witham and S. Dubowsky",
- TITLE = "An Improved Symbolic Manipulation Technique for
-the Simulation of Nonlinear Dynamic Systems With Mixed
-Time-Varying and Constant Terms",
- JOURNAL = "Journal of Dynamic Systems, Measurement, and Control",
- YEAR = 1977, MONTH = "September", PAGES = "157-165",
- ABSTRACT = {The time domain behavior of nonlinear dynamic systems
-often is obtained by numerical integration on the digital
-computer.  These solutions are usually expensive and limit
-the scope of the dynamic study.  The proposed improved
-technique results in a substantial increase in the computational
-efficiency by using automatic symbolic manipulation to generate
-explicit equations of motion algebraically prior to numerical
-integration.}}
-
-@TECHREPORT{Wolf:95,
- AUTHOR = "Thomas Wolf",
- TITLE = "Programs for Applying Symmetries of PDEs",
- INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin",
- YEAR = 1995, TYPE = "Preprint", NUMBER = "SC 95-5", MONTH = "February",
- ABSTRACT = {In this paper the programs APPLYSYM, QUASILINPDE and DETRAFO
-are described which aim at the utilization of infinitesimal symmetries of
-differential equations.  The purpose of QUASILINPDE is the general solution
-of quasilinear PDEs.  This procedure is used by APPLYSYM for the
-application of point symmetries for either
-
-calculating similarity variables to perform a point transformation which
-lowers the order of an ODE or effectively reduces the number of explicitly
-occuring independent variables in a PDE(-system) or for
-
-generalizing given special solutions of ODEs/PDEs with new constant
-parameters.
-
-The program DETRAFO performs arbitrary point- and contact transformations
-of ODEs/PDEs and is applied if similarity and symmetry variables have been
-found.  The program APPLYSYM is used in connection with the program LIEPDE
-for formulating and solving the conditions for point- and contact
-symmetries which is described in [4].  The actual problem solving is done
-in all these programs through a call to the package CRACK for solving
-overdetermined PDE-systems.}}
-
-@ARTICLE{Wood:89,
- AUTHOR = "John C. Wood",
- TITLE = "Harmonic Two Spheres in the Unitary Group",
- YEAR = 1989,
- JOURNAL = "Proc. London Math. Soc.",
- VOLUME = 3, NUMBER = 58, PAGES = "608-624"}
-
-@TECHREPORT{Wright:84,
- AUTHOR = "F. J. Wright and G. Dangelmayr",
- TITLE = "Explicit Iterative Algorithms to Reduce a Univariate Catastrophe
-to Normal Form",
- INSTITUTION = "Universit{\"a}t T{\"u}bingen",
- YEAR = 1984}
-
-@TECHREPORT{Wulkow:90,
- AUTHOR = "Michael Wulkow and Peter Deuflhard",
- TITLE = "Towards an efficient computational treatment of heterogeneous
-polymer reactions",
- INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin",
- YEAR = 1990, TYPE = "Preprint", NUMBER = "SC 90-1", MONTH = "January"}
-
-@INPROCEEDINGS{Yamamoto:87,
- AUTHOR = "T. Yamamoto and Y. Aoki",
- TITLE = "{REDUCE} 3.2 on {iAPX 86/286}-based Personal Computers",
- BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
-in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "134-135",
- PUBLISHER = "Springer-Verlag"}
-
-@ARTICLE{Yamartino:91,
- AUTHOR = "Robert J. Yamartino and Richard Pavelle",
- TITLE = "An Application of Computer Algebra to a Problem in Stratified
-Fluid Flow",
- JOURNAL = "J. Symb. Comp.",
- YEAR = 1991, VOLUME = 12, NUMBER = 6, PAGES = "669-672", MONTH = "December",
- ABSTRACT = {The computationally tedious problem of considering trial Green's
-function solutions to the fourth-order partial differential equation for a
-stratified atmosphere flowing over a hill is approached using MACSYMA.
-Significance of the problem, solution methodologies and CPU time
-intercomparisons using various computer platforms and other algebra systems
-are discussed.}}
-
-@ARTICLE{Yannouleas:88,
- AUTHOR = "C. Yannouleas and J. M. Pacheco",
- TITLE = "An Algebraic Program for the States Associated with the
-${U(5)} \supset {O(5)} \supset {O(3)}$ Chain of Groups",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1988, VOLUME = 52, NUMBER = 1, PAGES = "85-92", MONTH = "December"}
-
-@ARTICLE{Yannouleas:89,
- AUTHOR = "C. Yannouleas and J. M. Pacheco",
- TITLE = "Algebraic Manipulation of the States Associated with the
-${U(5)} \supset {O(5)} \supset {O(3)}$ Chain of {groups:}
-Orthonormalization and Matrix Elements",
- JOURNAL = "Comp. Phys. Comm.",
- YEAR = 1989, VOLUME = 54, NUMBER = "2 and 3", PAGES = "315-328",
-MONTH = "June and July"}
-
-@ARTICLE{Zacrep:75,
- AUTHOR = "Douglas Zacrep and Bing-Lin Young",
- TITLE = "Trace and {Ward-Takahashi} Identity Anomalies
-in an {SU}(3) Current Model with Energy-Momentum Tensor",
- JOURNAL = "Phys. Rev. D",
- YEAR = 1975, VOLUME = 12, PAGES = "513-522"}
-
-@ARTICLE{Zahalak:87,
- AUTHOR = "G. I. Zahalak and P. R. Rao and S. P. Sutera",
- TITLE = "Large Deformations of a Cylindrical Liquid-Filled Membrane
-by a Viscous Shear Flow",
- JOURNAL = "J. Fluid Mech.",
- YEAR = 1987, VOLUME = 179, PAGES = "283-305",
- COMMENT = {Draws attention to the use of classical perturbation
-techniques combined with computer algebra as an alternative to
-numerical calculation.}}
-
-@ARTICLE{Zeng:84,
- AUTHOR = "{Wan-zhen} Zeng and {Bail-lin} Hao",
- TITLE = "Scaling Property of Period-n-Tupling
-Sequences in One-Dimensional Mappings",
- JOURNAL = "Commun. in Theor. Phys., Beijing, China",
- YEAR = 1984, VOLUME = 3, NUMBER = 3, PAGES = "283-295"}
-
-@ARTICLE{Zharkov:93,
- AUTHOR = "A. Yu. Zharkov",
- TITLE = "Computer Classification of the Integrable Coupled {Kdv}-like
-Systems with Unit Main Matrix",
- JOURNAL = "J. Symbolic Computation",
- YEAR = 1993, VOLUME = 15, NUMBER = 1, PAGES = "85-90", MONTH = "January",
- COMMENT = {The classification of 2-component systems of equations for
-the form $u^{i}_{t}=u^{i}_{xxx}+c_{ij}u^{i}u^{j}_{x}(i,j=1,2)$ which
-possess higher symmetries is given.  A new class of such integrable
-KdV-like systems is obtained.  All the computations have been done using
-the {REDUCE}computer algebra system.}}
-
-@InProceedings{Zharkov:93a,
-  author =      "A. Yu. Zharkov and Yu. A. Blinkov",
-  title =       "Involution Approach to Solving Systems of Algebraic
-Equations",
-  booktitle =   "Proceedings of the 1993 International IMACS Symposium on
-                 Symbolic Computation",
-  year =        "1993",
-  editor =      "G. Jacob and N. E. Oussous and S. Steinberg",
-  pages =       "11-16",
-  organization ="IMACS",
-  publisher =   "Laboratoire d'Informatique Fondamentale de Lille, France",
-
-  comment =     {An "involutive set" is a canonical basis of a 0-dim
-		 polynomial ideal based on Janet division and well suited for
-                 equation solving.  It can be transformed into a
-                 lexicographic Groebner basis by linear algebra tools.
-                 The algorithms for computing involutive sets has been
-		 developed using {REDUCE}.}
-}
-
-@TECHREPORT{Zhidkova:78,
- AUTHOR = "I. E. Zhidkova and I. P. Nedyalkov and V. A. Rostovtsev",
- TITLE = "On Applicability Limits of the Experimental Method
-for Investigating Strong Gravitational Fields",
- INSTITUTION = "J.I.N.R., Dubna",
- YEAR = 1978, NUMBER = "P2 - 11589",
- COMMENT = {Mechanical effects of tidal forces on the physical apparatus
-exploring strong gravitational fields are investigated.}}
-
+%                          REDUCE BIBLIOGRAPHY
+
+%                              Part 1:  A-E
+
+% Copyright (c) 1995 RAND.  All Rights Reserved.
+
+% Additions and corrections are solicited.  Please send them, in the
+% same format as these entries if possible, to reduce at rand.org.
+
+
+@ARTICLE{Abbott:85,
+ AUTHOR = "J. A. Abbott and R. J. Bradford and J. H. Davenport",
+ TITLE = "A Remark on Factorisation",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1985, VOLUME = 19, NUMBER = 2, PAGES = "31-33", MONTH = "May"}
+
+@INPROCEEDINGS{Abbott:86,
+ AUTHOR = "J. A. Abbott and R. J. Bradford and J. H. Davenport",
+ TITLE = "The {Bath} Algebraic Number Package",
+ BOOKTITLE = "Proc. of {SYMSAC} '86",
+ YEAR = 1986, PAGES = "250-253"}
+
+@INPROCEEDINGS{Abbott:87,
+ AUTHOR = "J. A. Abbott and J. H. Davenport",
+ TITLE = "Polynomial Factorization: An Exploration of {Lenstra's}
+Algorithm",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes in Computer Science",
+ YEAR = 1987, VOLUME = 378, PAGES = "391-402",
+ PUBLISHER = "Springer-Verlag"}
+
+@INPROCEEDINGS{Abbott:87a,
+ AUTHOR = "J. A. Abbott",
+ TITLE = "Integration: Solving the {Risch} Differential Equation",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "465-467",
+ PUBLISHER = "Springer-Verlag"}
+
+@PHDTHESIS{Abbott:88,
+ AUTHOR = "J. A. Abbott",
+ TITLE = "Factorisation of Polynomials over Algebraic Number Fields",
+ SCHOOL = "Univ. of Bath, England",
+ YEAR = 1988}
+
+@ARTICLE{Abbott:88a,
+ AUTHOR = "J. A. Abbott and J. H. Davenport",
+ TITLE = "A Remark on a Paper by {Wang}: Another Surprising Property of 42",
+ JOURNAL = "Math. Comp.",
+ YEAR = 1988, VOLUME = 51, PAGES = "837-839"}
+
+@INPROCEEDINGS{Abbott:89,
+ AUTHOR = "J. A. Abbott",
+ TITLE = "Recovery of Algebraic Numbers from their p-Adic Approximations",
+ BOOKTITLE = "Proc. of {ISSAC} '89", PUBLISHER = "{ACM} Press, New York",
+ YEAR = 1989, PAGES = "112-120"}
+
+@TECHREPORT{Abbott:89a,
+ AUTHOR = "J. A. Abbott and R. J. Bradford and J. H. Davenport",
+ TITLE = "A Remark on the Multiplication of Sparse Polynomials",
+ NUMBER = "TR 89-21", YEAR = 1989,
+ INSTITUTION = "School of Mathematical Sciences, University of Bath"}
+
+@INPROCEEDINGS{Abdali:88,
+ AUTHOR = "S. K. Abdali and D. S. Wise",
+ TITLE = "Experiments with Quadtree Representation of Matrices",
+ BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
+ YEAR = 1988, VOLUME = 358, PAGES = "96-108"}
+
+@ARTICLE{Abiezzi:83,
+ AUTHOR = "Salim S. {Abi-Ezzi}",
+ TITLE = "Clarification to the Symbolic Mode in {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1983, VOLUME = 17, NUMBER = "3 and 4", PAGES = "43-47",
+ MONTH = "August and November"}
+
+@INPROCEEDINGS{Abramov:91,
+ AUTHOR = "S. A. Abramov and K. Yu. Kvansenko",
+ TITLE = "Fast Algorithms to Search for the Rational Solutions of Linear
+Differential Equations with Polynomial Coefficients",
+ EDITOR = "Stephen M. Watt",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ PUBLISHER = "ACM Press", ADDRESS = "Maryland", YEAR = 1991,
+ PAGES = "267-270"}
+
+@TECHREPORT{Abramov:91a,
+ AUTHOR = "S. A. Abramov and K. Yu. Kvashenko",
+ TITLE = "Fast search of a certain type solutions of linear ordinary
+differential equations with polynomial coefficients",
+ INSTITUTION = "Computer Center of the USSR, Academy of Science, Moscow",
+ YEAR = 1991}
+
+@InProceedings{Adamchik90,
+  author =      "V. S. Adamchik and O. I. Marichev",
+  title =       "The Algorithm for calculating Integrals of
+                 Hypergeometric type functions and its realization in
+                 {REDUCE} System",
+  booktitle =   "Proceedings of the 1990 International Symposium on
+                 Symbolic and Algebraic Computation",
+  year =        "1990",
+  editor =      "S. Watanabe and Morio Nagata",
+  pages =       "212-224",
+  organization =        "ACM",
+  publisher =   "Addison-Wesley"
+}
+
+@ARTICLE{Adams:83,
+ AUTHOR = "K. J. Adams",
+ TITLE = "Analytic Estimates for the Dynamic Aperture of Nonlinear Lattices",
+ JOURNAL = "IEEE Trans. Nucl. Sci.",
+ YEAR = 1983, VOLUME = "NS-30", PAGES = "2436-2438",
+ COMMENT = {"For an accelerator lattice{\ldots}" {REDUCE} was used to obtain low
+order coefficients in the calculation of the amplitude.}}
+
+@ARTICLE{Adkins:83,
+ AUTHOR = "G. S. Adkins",
+ TITLE = "Analytic Evaluation of an {O}($\alpha$) Vertex Correction to the
+Rate of Orthopositronium",
+ JOURNAL = "Phys. Rev. A",
+ YEAR = 1983, VOLUME = 27,  PAGES = "530-532",
+ ABSTRACT = {The order-$\alpha$ correction to the lowest order
+orthopositronium decay rate due to the two outer-vertex graphs obtained in
+analytic form.}}
+
+@ARTICLE{Adkins:83a,
+ AUTHOR = "G. S. Adkins and  F. R. Brown",
+ TITLE = "Rate for Positronium Decay to Five Photons",
+ JOURNAL = "Phys. Rev. A",
+ YEAR = 1983, VOLUME = 28, PAGES = "1164-1165",
+ COMMENT = {{REDUCE} used to calculate trace of $\gamma$ matrices.  Large
+calculation.}}
+
+@ARTICLE{Adkins:85,
+ AUTHOR = "G. S. Adkins",
+ TITLE = "Inner-Vertex Contributions to the Decay Rate of Orthopositronium",
+ JOURNAL = "Phys. Rev. A",
+ YEAR = 1985, VOLUME = 31, PAGES = "1250-1252",
+ COMMENT = {{REDUCE} trace calculations.  "In this paper the order-$\alpha$
+contribution to the inner-vertex graphs to the decay rate of
+orthopositronium is obtained in analytic form."}}
+
+@ARTICLE{Aguilera-Navarro:87,
+ AUTHOR = "V. C. Aguilera-Navarro and  R. Guardiola and C. Keller and
+M. de Llano and M. Popovic and M. Fortes",
+ TITLE = "Van der {Waals} Perturbation Theory for Fermion and Boson
+Ground-State Matter",
+ JOURNAL = "Phys. Rev. A",
+ YEAR = 1987, VOLUME = 35, PAGES = "3901-3910",
+ COMMENT = {Uses computer algebra to rearrange ideal-gas-based low-density
+expansions; to them {REDUCE} or {MACSYMA} provide just the expertise they
+require to substitute forms into equations, and so makes their
+formulation possible.}}
+
+@TECHREPORT{Akselrod:90,
+ AUTHOR = "I.R. Akselrod and V.P. Gerdt and V.E. Kovtun and V.N. Robuk",
+ TITLE = "Construction of a {Lie} algebra by a subset of generators and
+commutation relations",
+ INSTITUTION = "J.I.N.R.", YEAR = 1990, TYPE = "Preprint",
+ NUMBER = "E5-90-508",
+ ABSTRACT = {The problem of constructing the quotient algebra for a free
+{Lie} algebra over an ideal given by a subset of generators and commutation
+relations is investigated.  The method proposed to solve this problem can be
+applied in particular for constructing a {L-A} pair for nonlinear evolution
+equations.  The algorithm is based on the concept of {Hall} basis for a
+free {Lie} algebra and is implemented in the computer algebra system
+{REDUCE}.}}
+
+@ARTICLE{Aldins:69,
+ AUTHOR = "J. Aldins and S. J. Brodsky and A. J. Dufner and
+T. Kinoshita",
+ TITLE = "Photon-Photon Scattering Contribution to the Sixth
+Order Magnetic Moments of the Muon and Electron",
+ JOURNAL = "Phys. Rev. Lett.",
+ YEAR = 1969, VOLUME = 23, PAGES = "441-443"}
+
+@TECHREPORT{Alekseev:86,
+ AUTHOR = "A. I. Alekseev and V. F. Edneral",
+ TITLE = "Tensor Structure of Axial Gauge Polarization Operator in the
+Infrared Region",
+ INSTITUTION = "IHEP", YEAR = 1986, TYPE = "Preprint",
+ NUMBER = "86-46"}
+
+@ARTICLE{Alekseev:87,
+ AUTHOR = "A. I. Alekseev and V. F. Edneral",
+ TITLE = "Tensor Structure of Gluon Polarization Operator in the
+Axial Gauge for Infra-Red Region",
+ JOURNAL = "Journal of Nuclear Physics",
+ YEAR = 1987, PAGES = "1105-1114"}
+
+@TECHREPORT{Alekseev:87a,
+ AUTHOR = "A. I. Alekseev and V. F. Edneral",
+ TITLE = "On Evaluation of {Feynman} Integrals in Axial Gauge",
+ INSTITUTION = "IHEP", YEAR = 1987, TYPE = "Preprint",
+ NUMBER = "87-118",
+ ABSTRACT = {The recurrent algorithm for axial gauge calculations of
+one-loop massless {Feynman} integrals in the n-dimensional
+momentum space is described.  The algorithm we suggest is
+realized on the basis of {REDUCE} system and presented as
+a procedure.  It is rather effective for cumbersome
+combinations of those integrals.}}
+
+@ARTICLE{Alfeld:82,
+ AUTHOR = "P. Alfeld",
+ TITLE = "Fixed Point Iteration with Inexact Function Values",
+ JOURNAL = "Math. Comp.",
+ YEAR = 1982, VOLUME = 38, PAGES = "87-98",
+ COMMENT = {Numerical analysis generating an improved iterative scheme.
+"The technical manipulations in this paper were carried out using the
+symbol manipulation language {REDUCE}."}}
+
+@TECHREPORT{Amirkhanov:87,
+ AUTHOR = "I. V. Amirkhanov and E. P. Zhidkov and I. E. Zhidkova",
+ TITLE = "The Conditions of Bounding of the Oscillation Amplitudes of
+Charge Particle within the Resonance Vicinity Investigations",
+ INSTITUTION = "J.I.N.R., Dubna", YEAR = 1987, NUMBER = "P11-87-452"}
+
+@INPROCEEDINGS{Amirkhanov:91,
+ AUTHOR = "I.V. Amirkhanov and E.P. Zhidkov and I.E. Zhidkova",
+ TITLE = "The Betatron Oscillations in the Vicinity of Nonlinear Resonance
+in Cyclic Accelerator Investigation",
+ EDITOR = "Stephen M. Watt",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ PUBLISHER = "ACM Press", ADDRESS = "Maryland", YEAR = 1991,
+ PAGES = "452-453"}
+
+@ARTICLE{Antweiler:89,
+ AUTHOR = "Werner Antweiler and Andreas Strotmann and Volker Winkelmann",
+ TITLE = "A {\TeX}-{REDUCE}-Interface",
+ JOURNAL = "SIGSAM Bulletin",
+ YEAR = 1989, VOLUME = 23,
+ MONTH = "February", PAGES = "26-33"}
+
+@ARTICLE{Appelquist:70,
+ AUTHOR = "T. W. Appelquist and S. J. Brodsky",
+ TITLE = "The Order $\alpha^{2}$ Electrodynamic Corrections to
+the {Lamb} Shift",
+ JOURNAL = "Phys. Rev. Letters",
+ YEAR = 1970, VOLUME = 24, PAGES = "562-565"}
+
+@TECHREPORT{Arbuzov:86,
+ AUTHOR = "B. A. Arbuzov and E. E. Boos and A. I. Davydychev",
+ TITLE = "Infrared Asymptotics of Gluonic {Green} Functions
+in Covariant Gauge",
+ INSTITUTION = "IHEP", YEAR = 1986, TYPE = "Preprint",
+ NUMBER = "86-123"}
+
+@TECHREPORT{Kendall:93,
+ AUTHOR = "Gerard Ben Arous and Michael Cranston and Wilfrid S. Kendall",
+ TITLE = "Coupling constructions for hypoelliptic diffusions:  Two
+examples",
+ INSTITUTION = "University of Warwick, Dept. of Statistics", YEAR = 1993,
+ MONTH = "October", TYPE = "Research Report", NUMBER = 261,
+ ABSTRACT = {Coupling constructions are given for two examples of
+hypoelliptic diffusions with smooth coefficients:  the two-dimensional
+diffusion formed by scalar Brownian motion and its time integral; and the
+three-dimensional diffusion formed by planar Brownian motion and its
+stochastic area.  In both cases it is shown that one can construct
+co-adapted copies of Brownian motion such that the corresponding copies of
+the diffusion will couple in finite time.  The first case uses stopping
+time arguments; the second is computationally more involved and the
+solution was found using a computer algebra implementation of stochastic
+calculus (though the final proof has been checked completely by hand).
+Questions are formulated about coupling problems for more general
+hypoelliptic diffusions with smooth coefficients.}}
+
+@ARTICLE{Aso:81,
+ AUTHOR = "T. Aso and T. Nonoyama and S. Kato",
+ TITLE = "Numerical Simulation of Semidiurnal Atmospheric Tides",
+ JOURNAL = "J. Geophysical R.",
+ YEAR = 1981, VOLUME = 86, NUMBER = 11, PAGES = "388-400",
+ COMMENT = {"Numerical modeling of the solar and lunar semidiurnal
+atmospheric tides has been performed by invoking a comprehensive approach that
+includes both algebraic manipulation and numerical solution of the
+primitive equation system."  Used {REDUCE} to overcome difficulties of
+complication and error.}}
+
+@ARTICLE{Atherton:73,
+ AUTHOR = "R. W. Atherton and G. M. Homsey",
+ TITLE = "Use of Symbolic Computation to Generate Evolution
+Equations and Asymptotic Solutions to Elliptic Equations",
+ JOURNAL = "Journ. Comp. Phys.",
+ YEAR = 1973, VOLUME = 1, PAGES = "45-59"}
+
+@ARTICLE{Aurenche:84,
+ AUTHOR = "P. Aurenche and A. Douir and R. Baier and M. Fontannaz and
+D. Schiff",
+ TITLE = "Photoproduction of Hadrons at Large Transverse Momentum in
+Second Order {QCD}",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1984, VOLUME = "135B", PAGES = "164-168",
+ COMMENT = {Uses {REDUCE} and {SCHOONSCHIP} in the extension of calculations
+to a higher order to keep pace with experimental results.}}
+
+@ARTICLE{Aurenche:84a,
+ AUTHOR = "P. Aurenche and A. Douir and R. Baier and M. Fontannaz and
+D. Schiff",
+ TITLE = "Prompt Photon Production at Large $p_{\tau}$ in {GCD} Beyond the
+Leading Order",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1984, VOLUME = "140B", PAGES = "87-92",
+ COMMENT = {Uses {REDUCE} and {SCHOONSCHIP}.}}
+
+@ARTICLE{Autin:89,
+ AUTHOR = "B. Autin and J. Bengtsson",
+ TITLE = "Symbolic Evaluation of Integrals Occurring in Accelerator
+Orbit Theory",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1989, VOLUME = 7, NUMBER = 2, PAGES = "183-187", MONTH = "February"}
+
+@ARTICLE{Baekler:84,
+ AUTHOR = "P. Baekler and F. W. Hehl",
+ TITLE = "A Charged {Taub-NUT} Metric with Torsion:  A New Axially
+Symmetric Solution of the {Poincar\'{e}} Gauge Field Theory",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1984, VOLUME = "100A", PAGES = "277-316"}
+
+@TECHREPORT{Baekler:84a,
+ AUTHOR = "Peter Baekler and Friedrich W. Hehl",
+ TITLE = "On the Dynamics of the Torsion of Spacetime:
+Exact Solutions in a Gauge Theoretical Model of Gravity",
+ INSTITUTION = "Department of Physics, University of California,
+Los Angeles", YEAR = 1984,
+ NUMBER = "UCLA/84/TEP/19", PAGE = "18", MONTH = "December"}
+
+@INPROCEEDINGS{Baekler:86,
+ AUTHOR = "P. Baekler and F. W. Hehl and E. W. Mielke",
+ TITLE = "Nonmetricity and Torsion:  Facts and Fancies in Gauge
+Approaches to Gravity",
+ EDITOR = "R. Ruffini",
+ BOOKTITLE = "Proc. 4th Marcel Grossmann Meeting on
+General Relativity", PUBLISHER = "North-Holland, Amsterdam",
+ YEAR = 1986, PAGES = "277-316"}
+
+@ARTICLE{Baekler:87,
+ AUTHOR = "P. Baekler and R. Hecht and F. W. Hehl and T. Shirafuji",
+ TITLE = "Mass and Spin of Exact Solutions of the {Poincar{\'e}} Gauge
+Theory",
+ JOURNAL = "Prog. Theor. Phys.",
+ YEAR = 1987, VOLUME = 78, PAGES = "16-21"}
+
+@ARTICLE{Baekler:87a,
+ AUTHOR = "P. Baekler and M. Guerses",
+ TITLE = "Exact Solutions of the {Poincar{\'e}} Gauge Theory from Its
+Linearized Field Equations",
+ JOURNAL = "Lett. Math. Phys.",
+ YEAR = 1987, VOLUME = 14, PAGES = "185-191"}
+
+@ARTICLE{Baekler:87b,
+ AUTHOR = "P. Baekler and E. W. Mielke and F. W. Hehl",
+ TITLE = "Kinky Torsion in a {Poincar{\'e}} Gauge Model of Gravity Coupled
+to a Massless Scalar Field",
+ JOURNAL = "Nuclear Phys.",
+ YEAR = 1987, VOLUME = "B288", PAGES = "800-812"}
+
+@ARTICLE{Baekler:88,
+ AUTHOR = "P. Baekler and M. Seitz and V. Winkelmann",
+ TITLE = "Cylindrically Symmetric Solutions of Self-Consistently
+Coupled {Dirac} Fields in Gauge Theories of Gravity",
+ JOURNAL = "Class. Quantum Grav.",
+ YEAR = 1988, VOLUME = 5, PAGES = "479-490"}
+
+@ARTICLE{Baekler:88a,
+ AUTHOR = "P. Baekler and M. Guerses and F. W. Hehl and J. D. McCrea",
+ TITLE = "The Exterior Gravitational Field of a Charged Spinning
+Source in the {Poincar{\'e}} Gauge Theory:  A {Kerr-Newman} Metric with
+Dynamic Torsion",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1988, VOLUME = "A128", PAGES = "245-250"}
+
+@ARTICLE{Baekler:88b,
+ AUTHOR = "P. Baekler and M. Guerses and F. W. Hehl",
+ TITLE = "A New Method to Solve the Field Equations of {Poincar{\'e}}
+Gauge Theories",
+ JOURNAL = "Class. Quantum Grav.",
+ YEAR = 1988}
+
+@TECHREPORT{Bahrdt:90,
+ AUTHOR = "J. Bahrdt and G. W{\"u}stefeld",
+ TITLE = "A New Tracking Routine for Particles in Undulator and
+Wiggler Fields",
+ INSTITUTION = "Technischer Bericht",
+ YEAR = 1990, TYPE = "Report", NUMBER = "BESSY TB Nr. 158",
+ MONTH = "October",
+ ABSTRACT = {In this report we present an approximated solution of the
+particle motion in wiggler and undulator fields by an algebraic mapping
+routine.  The solution is based on a series expansion up to the third
+order in the two transversal angle coordinates and, as a third variable,
+the bending radius of the particle orbit.  The wiggler and undulator fields
+are represented by an expansion as suggested by K. Halbach.
+
+The report consists of two parts.  In the first part we solve the
+equations of motion by an iteration procedure, which originally was also
+the first approach.  In the second part the solution is based on a Taylor
+series expansion.  Both approaches are equivalent.},
+ABSTRACT2 = {Beside the presentation of the solution, the main topics
+discussed in the two parts are the calculation speed and accuracy of the
+algebraic method in comparison to integration methods along undulator
+fields, as they are typically applied in lattice design codes.
+
+As a further result of the discussion we obtain a proper canonical mapping
+routine at least as accurate but faster than typical integration routines.}}
+
+@ARTICLE{Baier:81,
+ AUTHOR = {V. N. Baier and A. G. Grozin},
+ TITLE = {Inclusive quarkonium production in {$e^+ e^-$} annihilation},
+ JOURNAL = {Yad. Fiz. (Sov. J. Nucl. Phys.)},
+ YEAR = 1981, VOLUME = 33, NUMBER = 2, PAGES = {491-500}}
+
+@ARTICLE{Baier:85,
+ AUTHOR = {V. N. Baier and A. G. Grozin},
+ TITLE = {Gluonic contributions to the exclusive amplitudes},
+ JOURNAL = {Zeit. f\"ur Phys. C},
+ YEAR = 1985, VOLUME = 29, PAGES = {161-165}}
+
+@ARTICLE{Baier:90,
+ AUTHOR = {V. N. Baier and A. G. Grozin},
+ TITLE = {Decay {$B \to D l \bar\nu$} from {QCD} sum rules},
+ JOURNAL = {Zeit. f\"ur Phys. C},
+ YEAR = 1990, VOLUME = 47, PAGES = {669-675}}
+
+@TECHREPORT{Bajla:78,
+ AUTHOR = "I. Bajla and G. A. Ososkov and A. C. Hearn",
+ TITLE = "The Orthogonalization Program of Polynomials
+in Two Variables in {REDUCE}-2 Language",
+ INSTITUTION = "J.I.N.R., Dubna",
+ YEAR = 1978, TYPE = "Report", NUMBER = "P10-11944",
+ ABSTRACT = {The analytical algorithm for constructing orthogonal
+polynomials in two variables, based on the {Gram-Schmidt}
+orthogonalization method, is proposed.}}
+
+@INPROCEEDINGS{Balian:78,
+ AUTHOR = "R. Balian and G. Parisi and A. Voros",
+ TITLE = "Quartic Oscillator",
+ YEAR = 1978, MONTH = "May",
+ BOOKTITLE = "Proc. of the Colloq. on Mathematical Problems in {Feynman}
+Path Integrals, Marseille",
+ ABSTRACT = {On the example of the semi-classical expansion for the levels
+of the quartic oscillator -(d**2/dq**2)+q**4, we show how the complex WKB
+method provides information about the singularities of the Borel transform
+of the semi-classical series.}}
+
+@ARTICLE{Baker:81,
+ AUTHOR = "G. A. Baker and L. P. Benofy and M. Fortes and M. de Llano and
+S. M. Peltier and A. Plastino",
+ TITLE = "Hard-Core Square-Well Fermion",
+ JOURNAL = "Phys. Rev. A",
+ YEAR = 1982, VOLUME = 26, PAGES = "3575-3588",
+ COMMENT = {The mixed use of {FORTRAN} and {REDUCE}, various derivative were
+calculated algebraically, but the double series was evaluated numerically.}}
+
+@ARTICLE{Barbier:92,
+ AUTHOR = "Christine Barbier and Peter Bettess and Jacqueline A. Bettess",
+ TITLE = "Automatic Generation of Mapping Functions for Infinite Elements
+using {REDUCE}",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1992, VOLUME = 14, NUMBER = 5, PAGES = "523-534", MONTH = "November",
+ ABSTRACT = {Co continuous basis functions for use in the finite element
+method when the elements extend to infinity in one or more directions can be
+derived simply following the method of Zienkiewicz.  The numerical code
+for these functions can be generated automatically using computer algebra
+languages such as {REDUCE}.  This paper describes the method and explains
+how {REDUCE} is used to easily produce numerical code.}}
+
+@ARTICLE{Barfoot:86,
+ AUTHOR = "D. T. Barfoot and D. J. Broadhurst",
+ TITLE = "Investigation of a bound on the anomalous dimensions of four-quark
+operators",
+ JOURNAL = "Phys. Lett. B",
+ YEAR = 1986, VOLUME = 166, PAGES = "347-350"}
+
+@ARTICLE{Barfoot:87,
+ AUTHOR = "D. T. Barfoot and D. J. Broadhurst",
+ TITLE = "Finite field theories in three dimensions with and without
+supersymmetry",
+ JOURNAL = "Zeitschrift {f\"{u}r} Physik C",
+ YEAR = 1987, VOLUME = 33, PAGES = "391-395"}
+
+@ARTICLE{Barfoot:88,
+ AUTHOR = "D. T. Barfoot and D. J. Broadhurst",
+ TITLE = {$\mbox{Z}_2\times\mbox{S}_6$ symmetry of the two-loop diagram},
+ JOURNAL = "Zeitschrift {f\"{u}r} Physik C",
+ YEAR = 1988, VOLUME = 41, PAGES = "81-85"}
+
+@ARTICLE{Bark:78,
+ AUTHOR = "Fritz H. Bark and Herman Tinoco",
+ TITLE = "Stability of Plane {Poiseuille} Flow of a Dilute
+Suspension of Slender Fibres",
+ JOURNAL = "J. Fluid Mech.",
+ YEAR = 1978, VOLUME = 87, PAGES = "321-333",
+ ABSTRACT = {The linear hydrodynamic stability problem for plane {Poiseuille}
+flow of a dilute suspension of rigid fibers is solved
+numerically.  The constitutive equation given by {Batchelor}
+is used to model the rheological properties of the suspension.
+The resulting eigenvalue problem is shown to be singular.}}
+
+@ARTICLE{Barthes-Biesel:73,
+ AUTHOR = "D. Barthes-Biesel and A. Acrivos",
+ TITLE = "On Computer Generated Analytic Solutions to the
+Equations of Fluid Mechanics, The Case of Creeping Flows",
+ JOURNAL = "Journ. Comp. Phys.",
+ YEAR = 1973, VOLUME = 3, PAGES = "403-411"}
+
+@ARTICLE{Barton:72,
+ AUTHOR = "David Barton and Anthony C. Hearn",
+ TITLE = "Comment on Problem \#2 - The {Y(2n)} Functions",
+ JOURNAL = "SIGSAM Bulletin",
+ YEAR = 1972, VOLUME = 15,
+ ABSTRACT = {A compact program for the solution of {SIGSAM} Problem \#2
+is presented.}}
+
+@ARTICLE{Bateman:86,
+ AUTHOR = "G. Bateman and R. G. Storer",
+ TITLE = "Direct Determination of Axisymmetric Magnetohydrodynamic
+Equilibrium in {Hamada} Coordinates",
+ JOURNAL = "Journ. Comp. Phys.",
+ YEAR = 1986, VOLUME = 64, PAGES = "161-176",
+ COMMENT = {Plasma.  {"REDUCE} was used to analyse the general set of
+equations for large numbers of {Fourier} harmonics {\ldots}"}}
+
+@INPROCEEDINGS{Belkov:91,
+ AUTHOR = "Alexander A. Bel'Kov and Alexander V. Lanyov",
+ TITLE = "{REDUCE} Usage for Calculation of Low-Energy Process Amplitudes in
+Chiral {QCD} Model",
+ EDITOR = "Stephen M. Watt",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ PUBLISHER = "ACM Press", ADDRESS = "Maryland", YEAR = 1991,
+ PAGES = "454-455",
+ ABSTRACT = {We describe the extension of {REDUCE} capabilities for the
+calculations of strong and weak meson processes within the chiral
+Lagrangians with higher derivatives.  The main non-trivial difficulty is to
+obtain the process amplitude from the Lagrangian, describing these
+interactions.  Another one is to overcome some {REDUCE} deficiencies such
+as the lack of arguments in the matrix data type as well as of some
+physical operations with the particle operators.  This package of procedures
+allows one to claculate the amplitudes of the strong and weak processes by
+simple specifying the particles involved and their momenta.}}
+
+@TECHREPORT{Bennett:88,
+ AUTHOR = "J. P. Bennett and J. H. Davenport and H. M. Sauro",
+ TITLE = "Solution of Some Equations in Biochemistry",
+ INSTITUTION = "School of Mathematical Sciences, University of
+Bath, England", NUMBER = "88-12", YEAR = 1988}
+
+@ARTICLE{Bennett:93,
+ AUTHOR = "J. P. Bennett and M. Grinfeld and J. Hubble",
+ TITLE = "Computer Algebra Techniques in Affinity Binding Equations:
+the Dimer Case",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1993, VOLUME = 15, NUMBER = 1, PAGES = "79-83", MONTH = "January",
+ COMMENT = {In this note we apply computer algebra techniques to affinity
+binding equations.  We treat the situation in which the protein is
+dimeric and shows cooperative binding.  Special attention is paid to the
+case where more than one molecule of the immobilized ligand can be
+bound by the macromolecule.}}
+
+@ARTICLE{Berends:81,
+ AUTHOR = "A. Berends and R. Kleiss and P. de Causmaecher and T. T. Wu",
+ TITLE = "Single Bremsstrahlung Process in Gauge Theories",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1981, VOLUME = "103B", PAGES = "124-128",
+ COMMENT = {Used {REDUCE} to calculate 25 {Feynman} diagrams to produce
+theoretical results which could be checked against experiment.}}
+
+@TECHREPORT{Berkovich:89,
+ AUTHOR = "L.M. Berkovich and V.P. Gerdt and Z.T. Kostova and
+M.L. Nechaevsky",
+ TITLE = "Second Order Reducible Linear Differential Equations",
+ INSTITUTION = "J.I.N.R., Dubna", YEAR = 1989, TYPE = "Preprint",
+ NUMBER = "E5-89-141"}
+
+@TECHREPORT{Berkovich:90,
+ AUTHOR = "L.M. Berkovich and V.P. Gerdt and Z.T. Kostova and
+M.L. Nechaevsky",
+ TITLE = "Computer algebra generating related {2nd} order linear differential
+equation",
+ INSTITUTION = "J.I.N.R., Dubna", YEAR = 1990, TYPE = "Preprint",
+ NUMBER = "E5-90-509",
+ ABSTRACT = {An algorithm with its mathematical foundation concerning {2nd}
+order ordinary linear differential equations {(OLDE)} is described.  It
+allows one to generate related {four-parametric} families of {OLDE} with
+coefficients of preassigned (in the scope of the procedure) structures
+integrable in terms of a given (generating) equation.  The number of those
+families in each next generation grows according to geometric progression
+with ratio eight.  Several examples of both mathematical and physical
+significance illustrate the efficiency of the algorithm implemented in the
+{REDUCE} compute algebra system.}}
+
+@ARTICLE{Berman:63,
+ AUTHOR = "S. M. Berman and Y. S. Tsai",
+ TITLE = "Intermediate Boson Pair Production as a Means for
+Determining its Magnetic Moment",
+ JOURNAL = "Phys. Rev. Lett.",
+ YEAR = 1963, VOLUME = 11, PAGES = "483-487"}
+
+@INPROCEEDINGS{Berndt:91,
+ AUTHOR = "R. Berndt and A. Lock and G. Witte and Ch. W{\"o}ll",
+ TITLE = "Application of Computer Algebra to Surface Lattice Dynamics",
+ EDITOR = "Stephen M. Watt",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ PUBLISHER = "ACM Press", ADDRESS = "Maryland", YEAR = 1991,
+ PAGES = "433-438",
+ ABSTRACT = {Lattice dynamical calculations for surfaces and in particular
+for stepped and adsorbed covered surfaces are commonly hampered by the
+complexity of the dynamical matrix for these systems.  We propose the use
+of computer algebra programs to set up the dynamical matrix.  In the
+present implementation the dynamical matrix is calculated fully analytically
+within the framework of a force constant-model and partially analytically
+for other interaction models such as the shell model or the bond charge
+model.}}
+
+@ARTICLE{Bessis:85,
+ AUTHOR = "N. Bessis and G. Bessis and D. Roux",
+ TITLE = "Closed-Form Expressions for the {Dirac-Coulomb} Radial $r^{t}$
+Integrals",
+ JOURNAL = "Phys. Rev. A",
+ YEAR = 1985, VOLUME = 32, PAGES = "2044-2050",
+ COMMENT = {No direct algebraic manipluation, but the formula is stated to be
+well suited to evaluation by {REDUCE} or {MACSYMA}, and this is an
+advantage of their formula.}}
+
+@ARTICLE{Bilge:92,
+ AUTHOR = "Ay{\c{s}}e H{\"{u}}meyra Bilge",
+ TITLE = "A {REDUCE} program for the integration of differential
+polynomials",
+ JOURNAL = "Comp. Phys. Commun.",
+ YEAR = 1992, VOLUME = 71, NUMBER = 3, PAGES = "263-268",
+ MONTH = "September",
+ COMMENT = {A differential polynomial F[u] is a polynomial expression of the
+derivatives of the function u(x).  A {REDUCE} program for the integration
+of differential polynomials is given.  The program is tested on the
+computation of the conserved densities of polynomial evolution equations.
+Input and output from the test runs are included in the library files.}}
+
+@TECHREPORT{Billoire:78,
+ AUTHOR = "A. Billoire and R. Lacaze and A. Morel and H. Navelet",
+ TITLE = "The {OZI} Rule Violating Radiative Decays of the Heavy
+Pseudoscalars",
+ INSTITUTION = "{CEN}-Saclay", YEAR = 1978, TYPE = "Report",
+ NUMBER = "DpH-T 43/78",
+ COMMENT = {Submitted to Phys. Letters B.
+In lowest order {QCD} the rates for radiative transitions violating the {OZI}
+rule of heavy pseudoscalars are found to be extremely small.}}
+
+@ARTICLE{Biro:86,
+ AUTHOR = "T. S. Biro and J. Zimanyi and M. Zimanyi",
+ TITLE = "Hadrochemistry in Relativistic Mean Fields",
+ JOURNAL = "Physics Letters",
+ YEAR = 1986, VOLUME = "167B", NUMBER = 3, PAGES = "271-276",
+ MONTH = "February"}
+
+@ARTICLE{Biro:87,
+ AUTHOR = "T. S. Biro and K. Niita and A. L. de Paoli and W. Bauer
+and W. Cassing and U. Mosel",
+ TITLE = "Microscopic Theory of Photon Production in Proton-Nucleus
+and Nucleus-Nucleus Collisions",
+ JOURNAL = "Nuclear Physics",
+ YEAR = 1987, VOLUME = "475A", PAGES = "579-597", MONTH = "December"}
+
+@TECHREPORT{Birrell:77,
+ AUTHOR = "N. D. Birrell",
+ TITLE = "The Application of Adiabatic Regularization
+to Calculations of Cosmological Interest",
+ INSTITUTION = "Dept. Math, King's College, London",
+ YEAR = 1977}
+
+@ARTICLE{Biswas:75,
+ AUTHOR = "S. N. Biswas and S. R. Chaudhuri and K. S. Taank
+and J. A. Campbell",
+ TITLE = "Neutrino Production in Stellar Matter by Photons
+in a Renormalizable Scalar-Boson-Exchange Model of Weak
+Interactions",
+ JOURNAL = "Phys. Rev. D",
+ YEAR = 1975, VOLUME = 8, PAGES = "2523-2525"}
+
+@TECHREPORT{Bittencourt:90,
+ AUTHOR = "Guilherme Bittencourt and Jacques Calmet",
+ TITLE = "Integrating Computer Algebra and Knowledge Representation",
+ INSTITUTION = "Universit{\"a}t Karlsruhe Institut f{\"u}r
+Algorithmen und Kognitive Systeme", YEAR = 1990, TYPE = "Preprint"}
+
+@InProceedings{Blum:93,
+  author =      "W. Blum and V. Ganzha and W. Strampp",
+  title =       "An Introduction to ODE's by CAS",
+  booktitle =   "Proceedings of the 1993 International IMACS Symposium on
+                 Symbolic Computation",
+  year =        "1993",
+  editor =      "G. Jacob and N. E. Oussous and S. Steinberg",
+  pages =       "110-119",
+  organization ="IMACS",
+  publisher =   "Laboratoire d'Informatique Fondamentale de Lille, France",
+  comment =     {Use of {REDUCE} and MATHEMATICA for math education.}
+}
+
+@ARTICLE{Bocko:92,
+ AUTHOR = "J. Bocko",
+ TITLE = "{EQSHELL} - a {REDUCE-based} program for generation of equations
+of equilibrium for shell",
+ JOURNAL = "Comp. Phys. Commun.",
+ YEAR = 1992, VOLUME = 69, NUMBER = 1, PAGES = "215-222", MONTH = "February",
+ COMMENT = {EQSHELL is a REDUCE-based program which generates the equations
+of equilibrium for various shapes of shells.  This program also produces
+other important characteristics of the shell.}}
+
+@ARTICLE{Boege:86,
+ AUTHOR = "W. Boege and R. Gebauer and H. Kredel",
+ TITLE = "Some Examples for Solving Systems of Algebraic Equations
+by Calculating {Groebner} Bases",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1986, VOLUME = 2, NUMBER = 1, PAGES = "83-98", MONTH = "March"}
+
+@ARTICLE{Bogdanova:88,
+ AUTHOR = "N. Bogdanova and H. Hogreve",
+ TITLE = "A {REDUCE} Package for Exact {Coulomb} Interaction Matrix
+Elements",
+ JOURNAL = "Comp. Phys. Commun.",
+ YEAR = 1988, VOLUME = 48, NUMBER = 2, PAGES = "319-326", MONTH = "February"}
+
+@ARTICLE{Bordoni:81,
+ AUTHOR = "Luciana Bordoni and Attilio Colagrossi",
+ TITLE = "An Application of {REDUCE} to Industrial Mechanics",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1981, VOLUME = 15, NUMBER = 2, PAGES = "8-12", MONTH = "May"}
+
+@InProceedings{Borst:94,
+  author =       "W. N. Borst and V. V. Goldman and J. A. van Hulzen",
+  title =        {{GENTRAN} 90: a {REDUCE} package for the generation of
+		  {Fortran} 90 code},
+  booktitle =    {Symbolic and Algebraic Computation},
+  editor =       {},
+  series =       {ISSAC},
+  year =         {1994},
+  organization = {SIGSAM},
+  publisher =    {ACM},
+  pages =        {45--51},
+ ABSTRACT = {GENTRAN is a code GENerator and TRANslator running under REDUCE
+and MACSYMA.  It is a tool for generating Fortran 77, RATFOR or C programs
+from program specifications and symbolic expressions.  Its facilities
+include template processing, automatic segmentation of large expressions
+and a file handling mechanism.  GENTRAN can be used in combination with
+SCOPE 1.5, a Source Code Optimization PackagE for REDUCE.  We present an
+extension of the REDUCE version of GENTRAN, called GENTRAN 90.  It makes
+generation of Fortran 90 code possible.}}
+
+@INPROCEEDINGS{Bowyer:87,
+ AUTHOR = "A. Bowyer and J. H. Davenport and P. S. Milne and J. A. Padget
+and A. F. Wallis",
+ TITLE = "Applications of Computer Algebra in Solid Modelling",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "244-245",
+ PUBLISHER = "Springer-Verlag"}
+
+@TECHREPORT{Boyd:78,
+ AUTHOR = "John P. Boyd",
+ TITLE = "The Effects of Latitudinal Shear on Equatorial
+Waves, Part {I}:  Theory and Methods",
+ INSTITUTION = "Dept. of Atmos. and Oceanic Science, Univ.
+of Michigan",
+ YEAR = 1978, TYPE = "Preprint", MONTH = "January",
+ COMMENT = {To be published in Journal of The Atmospheric Sciences.
+By using the method of multiple scales in height and a
+variety of methods in latitude, analytic solutions for
+equatorial waves in combined vertical and horizontal shear
+are derived.}}
+
+@ARTICLE{Boyd:93,
+ AUTHOR = "John P. Boyd",
+ TITLE = "Chebyshev and {Legendre} Spectral Methods in Algebraic Manipulation
+Languages",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1993, MONTH = "October", VOLUME = 16, NUMBER = 4, PAGES = "377-399",
+ COMMENT = {In this tutorial, we show how to combine Galerkin and collocation
+methods with algebraic manipulation languages.  Because polynomial and
+trigonometric manipulations are a special strength of {REDUCE}, Maple, and
+other symbolic languages, it is easy to use Chebyshev and Legendre
+polynomials and Fourier series as the basis sets.  However, because the
+truncation is small and calculations are performed symbolically in rational
+arithmetic, many of the standard precepets for numerical use of spectral
+methods must be modified or reversed.  We offer many guidelines and
+suggestions.  Six examples programmed in {REDUCE}, and
+Maple---eigenproblems, bifurcations, and nonlinear diffusion--illustrate
+the possibilities.}}
+
+@INPROCEEDINGS{Brackx:87,
+ AUTHOR = "F. Brackx and H. Serras",
+ TITLE = "Boundary Value Problems for the {Laplacian} in {Euclidean} Space
+Solved by Symbolic Computation",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "208-215",
+ PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{Brackx:87a,
+ AUTHOR = "F. Brackx and D. Constales and R. Delanghe and H. Serras",
+ TITLE = "{Clifford} Algebra with {REDUCE}",
+ JOURNAL = "Rend. Circ. Mat. Palermo, Ser. II",
+ YEAR = 1987, VOLUME = 16, PAGES = "11-19"}
+
+@ARTICLE{Brackx:89,
+ AUTHOR = "F. Brackx and D. Constales and A. Ronveaux and H. Serras",
+ TITLE = "On the Harmonic and Monogenic Decomposition of Polynomials",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1989, VOLUME = 8, NUMBER = 3, PAGES = "297-304", MONTH = "September"}
+
+@BOOK{Brackx:92,
+ AUTHOR = "F. Brackx and D. Constales",
+ TITLE = "Computer Algebra with LISP and REDUCE",
+ PUBLISHER = "Kluwer Academic Publishers",
+ YEAR = 1992,
+ PREFACE = {This text is based upon a series of lectures on LISP and REDUCE
+  held at the Universities of Averio and Coimbra (Portugal), as part of the
+  European Community's ERASMUS Project, and at the University of Gent
+  (Belgium).  It has been adapted to the newest release of REDUCE, version
+  3.4}}
+
+@INPROCEEDINGS{Bradford:86,
+ AUTHOR = "R. J. Bradford and A. C. Hearn and J. A. Padget
+and E. Schr{\"u}fer",
+ TITLE = "Enlarging the {REDUCE} Domain of Computation",
+ BOOKTITLE = "Proc. of {SYMSAC} '86",
+ YEAR = 1986, PAGES = "100-106"}
+
+@INPROCEEDINGS{Bradford:88,
+ AUTHOR = "R. J. Bradford and J. H. Davenport",
+ TITLE = "Effective Tests for Cyclotomic Polynomials",
+ BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
+ YEAR = 1988, VOLUME = 358, PAGES = "244-251"}
+
+@InProceedings{Bradford90,
+  author =      "Russell Bradford",
+  title =       "A parallelization of the {Buchberger} Algorithm",
+  booktitle =   "Proceedings of the International Symposium on
+                 Symbolic and Algebraic Computation",
+  year =        "1990",
+  editor =      "S. Watanabe and Morio Nagata",
+  pages =       "296",
+  organization =        "ACM",
+  publisher =   "Addison-Wesley"
+}
+
+@ARTICLE{Broadhurst:83,
+ AUTHOR = "D. J. Broadhurst",
+ TITLE = "{Non-relativistic sum rules for $\mbox{QCD}_2$, {QED} and
+$\mbox{QCD}_4$}",
+ JOURNAL = "Phys. Lett. B",
+ YEAR = 1983, VOLUME = 123, PAGES = "251-254"}
+
+@ARTICLE{Broadhurst:84,
+ AUTHOR = "D. J. Broadhurst and S. C. Generalis",
+ TITLE = "Can mass singularities be minimally subtracted?",
+ JOURNAL = "Phys. Lett. B",
+ YEAR = 1984, VOLUME = 142, PAGES = "75-79"}
+
+@ARTICLE{Broadhurst:85,
+ AUTHOR = "D. J. Broadhurst and S. C. Generalis",
+ TITLE = "Dimension-8 contributions to light-quark {QCD} sum rules",
+ JOURNAL = "Phys. Lett. B",
+ YEAR = 1985, VOLUME = 165, PAGES = "175-180"}
+
+@ARTICLE{Broadhurst:85a,
+ AUTHOR = "D. J. Broadhurst",
+ TITLE = "Evaluation of a Class of {Feynman} Diagrams for all Numbers of
+Loops and Dimensions",
+ JOURNAL = "Phys. Lett. B",
+ YEAR = 1985, VOLUME = 164, PAGES = "356-360",
+ COMMENT = {Uses {REDUCE} to calculate explicitly the l-loop member of a
+class of massless, dimensionally regularized {Feynman} diagrams, in order to
+verify an explicit formula.}}
+
+@ARTICLE{Broadhurst:86,
+ AUTHOR = "D. J. Broadhurst and A. G. Grozin",
+ TITLE = "Exploiting the 1,440-fold symmetry of the master two-loop diagram",
+ JOURNAL = "Zeitschrift {f\"{u}r} Physik c",
+ YEAR = 1986, VOLUME = 32, PAGES = "249-253"}
+
+@ARTICLE{Broadhurst:87,
+ AUTHOR = "D. J. Broadhurst",
+ TITLE = "Two-loop negative-dimensional integration",
+ JOURNAL = "Phys. Lett. B",
+ YEAR = 1987, VOLUME = 197, PAGES = "179-182"}
+
+@ARTICLE{Broadhurst:90,
+  AUTHOR = "D. J. Broadhurst",
+ TITLE = "The master two-loop diagram with masses",
+ JOURNAL = "Zeitschrift {f\"{u}r} Physik C",
+ YEAR = 1990, VOLUME = 47, PAGES = "115-124"}
+
+@ARTICLE{Broadhurst:91,
+ AUTHOR = {D. J. Broadhurst and A. G. Grozin},
+ TITLE = {Two-loop renormalization of the effective field theory
+of a static quark},
+ JOURNAL = {Phys. Lett. B},
+ YEAR = 1991, VOLUME = 267, PAGES = {105-110}}
+
+@TECHREPORT{Broadhurst:91a,
+ AUTHOR = {D. J. Broadhurst and A. G. Grozin},
+ TITLE = {Operator product expansion in static-quark effective theory:
+large perturbative corrections},
+ INSTITUTION = {Open University, Milton Keynes MK7 6AA, England},
+ YEAR = 1991, NUMBER = {OUT-4102-31}}
+
+@ARTICLE{Broadhurst:91b,
+ AUTHOR = "D. J. Broadhurst and N. Gray and K. Schilcher",
+ TITLE = {Gauge-invariant on-shell ${Z}_2$ in {QED}, {QCD} and the effective
+field theory of a static quark},
+ JOURNAL = "Zeitschrift {f\"{u}r} Physik C",
+ YEAR = 1991, VOLUME = 52, PAGES = "111-122"}
+
+@ARTICLE{Broadhurst:92,
+ AUTHOR = {D. J. Broadhurst and A. G. Grozin},
+ TITLE = "Operator product expansion in static-quark effective field theory:
+Large perturbative correction",
+ JOURNAL = {Phys. Lett. B},
+ YEAR = 1992, VOLUME = 274, PAGES = {421- }}
+
+@ARTICLE{Broadhurst:92a,
+ AUTHOR = {D. J. Broadhurst},
+ TITLE = {Three-loop on-shell charge renormalization without integration:
+$\Lambda^{\overline{\rm MS}}_{\rm QED}$ to four loops},
+ JOURNAL = "Zeitschrift {f\"{u}r} Physik C",
+ YEAR = 1992, VOLUME = 54, PAGES = {599- }}
+
+@ARTICLE{Broadhurst:93,
+ AUTHOR = "D. J. Broadhurst",
+ TITLE = "Large {N} expansion of {QED}: asymptotic photon propagator and
+contributions to the muon anomaly, for any number of loops",
+ JOURNAL = "Zeitschrift {f\"{u}r} Physik C",
+ YEAR = 1993, VOLUME = 58, PAGES = {339-345}}
+
+@ARTICLE{Broadhurst:93a,
+ AUTHOR = "D. J. Broadhurst and J. Fleischer and O. V. Tarasov",
+ TITLE = "Two-loop two-point functions with masses:  asymptotic expansions
+and {Taylor} series, in any dimension",
+ JOURNAL = "Physics Letters", VOLUME = "B329", PAGES = {103-110}, YEAR = 1994,
+ ABSTRACT = {In all mass cases needed for quark and gluon self-energies,
+the two-loop master diagram is expanded at large and small $q^{2}$, in
+$d$ dimensions, using identities derived from integration by parts.
+Expansions are given, in terms of hypergeometric series, for all gluon
+diagrams and for all but one of the quark diagrams; expansions of the
+latter are obtained from differential equations.  Pad\'{e} approximants
+to truncations of the expansions are shown to be of great utility.  As an
+application, we obtain the two-loop photon self-energy, for all $d$, and
+achieve highly accelerated convergence of its expansions in powers of
+$q^{2}/m^{2}/q^{2}$, for $d=4$.}}
+
+@TECHREPORT{Broadhurst:94,
+ AUTHOR = {D. J. Broadhurst and P. A. Baikov and J. Fleischer and V. A.
+Smirnov},
+ TITLE = {Two-loop gluon-condensate contributions to heavy-quark
+current correlators: exact results and approximations},
+ INSTITUTION = {Open University, Milton Keynes MK7 6AA, England},
+ YEAR = 1994, NUMBER = {OUT-4102-49},
+ ABSTRACT = {The coefficient functions of the gluon condensate $\langle
+G^2\rangle$, in the correlators of heavy-quark vector, axial, scalar and
+pseudoscalar currents, are obtained analytically, to two loops, for all values
+of $z=q^2/4m^2$.  In the limiting cases $z\to0$, $z\to1$, and $z\to-\infty$,
+comparisons are made with previous partial results.  Approximation methods,
+based on these limiting cases, are critically assessed, with a view to
+three-loop work.  High accuracy is achieved using a few moments as input.
+A {\em single\/} moment, combined with only the {\em leading\/} threshold and
+asymptotic behaviours, gives the two-loop corrections to better than 1\% in
+the next 10 moments.  A two-loop fit to vector data yields
+$\langle\frac{\alpha_{\rm s}}{\pi}G^2\rangle\approx0.021$~GeV$^4$}}
+
+@ARTICLE{Brodsky:62,
+ AUTHOR = "S. J. Brodsky and A. C. Hearn and R. G. Parsons",
+ TITLE = "Determination of the Real Part of the {Compton} Amplitude
+at a Nucleon Resonance",
+ JOURNAL = "Phys. Rev.",
+ YEAR = 1962, VOLUME = 187, PAGES = "1899-1904"}
+
+@ARTICLE{Brodsky:67,
+ AUTHOR = "S. J. Brodsky and J. D. Sullivan",
+ TITLE = "W-Boson Contribution to the Anomalous Magnetic Moment of the
+Muon",
+ JOURNAL = "Phys. Rev.",
+ YEAR = 1967, VOLUME = 156, PAGES = "1644-1647"}
+
+@INPROCEEDINGS{Brodsky:69,
+ AUTHOR = "S. J. Brodsky",
+ TITLE = "Status of Quantum Electrodynamics",
+ YEAR = 1969,
+ BOOKTITLE = "Proc. International Symposium on
+Electron and Photon Interactions at High Energies, Liverpool,
+England"}
+
+@TECHREPORT{Brodsky:70,
+ AUTHOR = "S. J. Brodsky",
+ TITLE = "Quantum Electrodynamic Theory:  Its Relation to Precision Low
+Energy Experiments",
+ INSTITUTION = "SLAC",
+ YEAR = 1970, TYPE = "Report", NUMBER = "SLAC-PUB-795",
+ MONTH = "August"}
+
+@INPROCEEDINGS{Brodsky:71,
+ AUTHOR = "S. J. Brodsky",
+ TITLE = "Algebraic Computation Techniques in Quantum Electrodynamics",
+ YEAR = 1971, VOLUME = "II", PAGES = "IV-1 to IV-27",
+ BOOKTITLE = "Proc. {2nd} Computing Methods in Theoretical Physics,
+Marseilles"}
+
+@TECHREPORT{Brodsky:72,
+ AUTHOR = "S. J. Brodsky",
+ TITLE = "Atomic Physics and Quantum Electrodynamics in the Infinite
+Momentum Frame",
+ INSTITUTION = "SLAC", YEAR = 1972,
+ TYPE = "Report",
+ NUMBER = "SLAC-PUB-1118", MONTH = "August",
+ COMMENT = {Presented at the Third International Conference on Atomic
+Physics.}}
+
+@ARTICLE{Brodsky:72a,
+ AUTHOR = "S. J. Brodsky and J. F. Gunion and R. L. Jaffe",
+ TITLE = "Test for Fractionally Charged Partons from
+Deep-Inelastic Bremsstrahlung in the Scaling Region",
+ JOURNAL = "Phys. Rev. D",
+ YEAR = 1972, VOLUME = 6, PAGES = "2487-2494"}
+
+@ARTICLE{Brodsky:72b,
+ AUTHOR = "S. J. Brodsky and R. Roskies",
+ TITLE = "Quantum Electrodynamics and Renormalization Theory
+in The Infinite Momentum Frame",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1972, VOLUME = "41B", PAGES = "517-520"}
+
+@ARTICLE{Brodsky:73,
+ AUTHOR = "S. J. Brodsky and R. Roskies and R. Suaya",
+ TITLE = "Quantum Electrodynamics and Renormalization Theory in the
+Infinite-Momentum Frame",
+ JOURNAL = "Phys. Rev. D",
+ YEAR = 1973, VOLUME = 8, PAGES = "4574-4594"}
+
+@ARTICLE{Broughan:82,
+ AUTHOR = "K. A. Broughan",
+ TITLE = "{Grad-Fokker-Planck} Plasma Equations.  Part 1. {Collision}
+Moments",
+ JOURNAL = "J. Plasma Phys.",
+ YEAR = 1982, VOLUME = 27, PAGES = "437-452",
+ COMMENT = {{REDUCE} used in collaboration with hand calculation.  {REDUCE}
+did the substitutions, with hand integrations.  "Thirteen moments are taken
+of the collision term in Boltzmann-Fokker-Planck
+equation{\ldots}plasma{\ldots}"}}
+
+@ARTICLE{Broughan:91,
+ AUTHOR = "K. A. Broughan and G. Keady and T. D. Robb and M. G. Richardson
+and M. C. Dewar",
+ TITLE = "Some Symbolic Computing Links to the {NAG} Numeric Library",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1991, VOLUME = 25, NUMBER = 3, PAGES = "28-37", MONTH = "July"}
+
+@ARTICLE{Brown:79,
+ AUTHOR = "W. S. Brown and A. C. Hearn",
+ TITLE = "Applications of Symbolic Algebraic Computation",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1979, VOLUME = 17, PAGES = "207-215",
+ COMMENT = {This paper is a survey of applications of systems for symbolic
+algebraic computation.}}
+
+@ARTICLE{Bryan-Jones:87,
+ AUTHOR = "Jane Bryan-Jones",
+ TITLE = "A Tutorial in Computer Algebra for Statisticians",
+ JOURNAL = "The Professional Statistician",
+ YEAR = 1987, VOLUME = 6, NUMBER = 6, MONTH = "December",PAGES = "TBD"}
+
+@TECHREPORT{Burnel,
+ AUTHOR = "A. Burnel and H. Caprasse",
+ TITLE = "Locality in Class III Noncovariant Gauges",
+ INSTITUTION = "Physique Th{\'e}orique et Math{\'e}matique,
+Universit{\'e} de Li{\`e}ge",
+ ABSTRACT = {It is shown within a perturbative calculation of the gluon
+self-energy that, in the framework of a general formulation of linear gauges,
+axial gauges do not exhibit nonlocal counterterms.}}
+
+@TECHREPORT{Burnel:94,
+ AUTHOR = "A. Burnel and H. Caprasse and A. Dresse",
+ TITLE = "Computing the {BRST} operator",
+ INSTITUTION = "D{\'e}partement d'Astronomie et d'Astrophysique,
+Universit{\'e} de Li{\`e}ge", YEAR = 1994,
+ ABSTRACT = {It is shown that for a large class of non-holonomic quantum
+mechanical systems one can make the computation of {BRST} charge fully
+algorithmic.  Two computer algebra programs written in the language of
+{REDUCE} are described.  They are able to realize the complex calculations
+needed to determine the charge for general nonlinear algebras.  Some
+interesting specific solutions are discussed.}}
+
+@ARTICLE{Burnel:94a,
+ AUTHOR = "A. Burnel and H. Caprasse",
+ TITLE = "Computing the {BRST} Operator Used in Quantization of Gauge
+Theories",
+ JOURNAL = "International Journal of Modern Physics C",
+ YEAR = 1994, VOLUME = 5, NUMBER = 6, PAGES = "1035-1047",
+ COMMENTS = {It is shown that for a large class of non-holonomic quantum
+mechanical systems one can make the computation of BRST charge fully
+algorithmic.  Two computer algebra programs written in the language of REDUCE
+are described.  They are able to realize the complex calculations needed
+to determine the charge for general nonlinear algebras.  Some interesting
+specific solutions are discussed.}}
+
+@TECHREPORT{Calmet:72,
+ AUTHOR = "Jacques Calmet",
+ TITLE = "Further Evaluation of the Sixth Order Corrections to the
+Anomalous Magnetic Moment of the Electron",
+ INSTITUTION = "Department of Physics, University of Utah",
+ YEAR = 1972,
+ ABSTRACT = {We report on the contributions to the $\alpha^{3}$
+part of the anomalous magnetic moment of the electron from the
+seven so-called cross and ladder diagrams.}}
+
+@ARTICLE{Calmet:72a,
+ AUTHOR = "Jacques Calmet",
+ TITLE = "A {REDUCE} Approach to the Calculation of {Feynman} Diagrams",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1972, VOLUME = 4, PAGES = "199-204",
+ ABSTRACT = {A brief survey of two existing {REDUCE} programs (by
+Campbell-Hearn and by Calmet) dealing with algebraic computation of
+{Feynman} diagrams is given.  Work in progress on a more general approach
+to this problem is discussed.}}
+
+@ARTICLE{Calmet:74,
+ AUTHOR = "Jacques Calmet",
+ TITLE = "Computer Recognition of Divergences in {Feynman} Graphs",
+ JOURNAL = "SIGSAM Bulletin",
+ YEAR = 1974, VOLUME = 8, NUMBER = 3, PAGES = "74-75", MONTH = "August",
+ ABSTRACT = {A description of a program for the recognition of divergences
+in {Feynman} graphs is given.}}
+
+@INCOLLECTION{Calmet:83,
+ AUTHOR = "J. Calmet and J. A. van Hulzen",
+ TITLE = "Computer Algebra Applications",
+ EDITOR = "B. Buchberger and G. E. Collins and R. Loos and R. Albrecht",
+ BOOKTITLE = "Computer Algebra Symbolic and Algebraic Computation",
+ EDITION = "2nd", PUBLISHER = "Springer-Verlag", YEAR = 1983}
+
+@ARTICLE{Campbell:67,
+ AUTHOR = "J. A. Campbell",
+ TITLE = "Algebraic Computation of Radiative Corrections for
+Electron-Positron Scattering",
+ JOURNAL = "Nucl. Phys.",
+ YEAR = 1967, VOLUME = "B1", PAGES = "283-300"}
+
+@ARTICLE{Campbell:68,
+ AUTHOR = "J. A. Campbell",
+ TITLE = "Astrophysical Consequences of the Existence of Charged
+Intermediate Vector Bosons",
+ JOURNAL = "Aust. Journ. of Phys.",
+ YEAR = 1968, VOLUME = 21, PAGES = "139-148"}
+
+@ARTICLE{Campbell:70,
+ AUTHOR = "J. A. Campbell and A. C. Hearn",
+ TITLE = "Symbolic Analysis of {Feynman} Diagrams by Computer",
+ JOURNAL = "Journ. of Comp. Phys.",
+ YEAR = 1970, VOLUME = 5, PAGES = "280-327"}
+
+@ARTICLE{Campbell:70a,
+ AUTHOR = "J. A. Campbell and R. B. Clark and D. Horn",
+ TITLE = "Low-T Theorems for Charged-Pion Photoproduction",
+ JOURNAL = "Phys. Rev. D",
+ YEAR = 1970, VOLUME = 2, PAGES = "217-224"}
+
+@ARTICLE{Campbell:74,
+ AUTHOR = "J. A. Campbell",
+ TITLE = "Symbolic Computing and Its Relationship to Particle Physics",
+ JOURNAL = "Acta Physica Austriaca",
+ YEAR = 1974, VOLUME = "Suppl. XIII", PAGES = "595-647"}
+
+@ARTICLE{Campbell:87,
+ AUTHOR = "J. A. Campbell and P. O. Fr{\"o}man and E. Walles",
+ TITLE = "Explicit series formulae for the evaluation of integrals by the
+method of steepest descents",
+ JOURNAL = "Studies in Applied Mathematics",
+ YEAR = 1987, VOLUME = 77, PAGES = "151-172"}
+
+@TECHREPORT{Caprasse:84,
+ AUTHOR = "H. Caprasse",
+ TITLE = "Description et Utilisation d'Une Extension du Programme {REDUCE}",
+ INSTITUTION = "Physique Th{\'e}orique et Math{\'e}matique,
+Universit{\'e} de Li{\`e}ge", YEAR = 1984, MONTH = "October"}
+
+@ARTICLE{Caprasse:85,
+ AUTHOR = "H. Caprasse and M. Hans",
+ TITLE = "A New Use of Operators in the Algebraic Mode of {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1985, VOLUME = 19, NUMBER = 3, PAGES = "46-52", MONTH = "August"}
+
+@ARTICLE{Caprasse:86,
+ AUTHOR = "H. Caprasse",
+ TITLE = "Description of an Extension of the Matrix Package of {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1986, VOLUME = 20, NUMBER = 4, PAGES = "7-10", MONTH = "December"}
+
+@ARTICLE{Caprasse:86a,
+ AUTHOR = "H. Caprasse",
+ TITLE = "A Complete Simplification Package for the Absolute Value
+Function in {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1986, VOLUME = 20, NUMBER = "1 and 2", PAGES = "18-21",
+ MONTH = "February and May",
+ COMMENT = {Implementation for {REDUCE} 3.2 of the function {"ABS"}.}}
+
+@INPROCEEDINGS{Caprasse:88,
+ AUTHOR = "H. Caprasse and J. Demaret and E. Schruefer",
+ TITLE = "Can {EXCALC} be Used to Investigate {High-dimensional}
+Cosmological Models with {Non-Linear Lagrangians}?",
+ BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
+ YEAR = 1988, PAGES = "116-124"}
+
+@ARTICLE{Caprasse:89a,
+ AUTHOR = "H. Caprasse",
+ TITLE = "Les Th{\'e}ories des {Champs} dans le monde de {REDUCE}
+(in {French})",
+ JOURNAL = "{CALSYF} (to appear)",
+ YEAR = 1989}
+
+@ARTICLE{Caprasse:90,
+ AUTHOR = "H. Caprasse",
+ TITLE = "Renormalization Group, Function Iterations and Computer
+Algebra",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1990, VOLUME = 9, NUMBER = 1, PAGES = "61-72", MONTH = "January",
+ COMMENT = {Based on a renormalization group equation met in Quantum Field
+Theory, Continuous Iterations of a large class of functions are computed
+using {REDUCE}.}}
+
+@ARTICLE{Caprasse:91,
+ AUTHOR = "H. Caprasse and J. Demaret and K. Gatermann and H. Melenk",
+ TITLE = "Power-law type solutions of fourth-order gravity for
+multidimensional {Bianchi I} Universes",
+ JOURNAL = "International Journal of Modern Physics C",
+ YEAR = 1991, VOLUME = 2, NUMBER = 2, PAGES = "601-611",
+ COMMENT = {This paper is devoted to the application of computer algebra to
+the study of solutions of the field equations derived from a non-linear
+Lagrangian, as suggested by recently proposed unified theories.  More
+precisely, we restrict ourselves to the most general quadratic Lagrangian,
+i.e. containing quadratic contributions in the different curvature tensors
+exclusively.  The corresponding field equations are then fourth-order in the
+metric tensor components.  The cosmological models studied are the simplest
+ones in the class of spatially homogeneous but anisotropic models,
+i.e. Bianchi I models.  For these models, we consider only power-law
+type solutions of the field equations.  All the solutions of the associated
+system of algebraic equations are found, using computer algebra, from a
+search of its Groebner bases.  While, in space dimension d=3, the
+Einsteinian-Kasner metric is still the most general power-law type solution,
+for d>3, no solution, other than the Minkowski space-time, is common to the
+three systems of equations corresponding to the three contributions to the
+Lagrangian density.  In the case of a pure Riemann-squared contribution to the
+Lagrangian (suggested by a recent calculation of the effective action for
+the heterotic string), the possibility exists to realize a splitting of the
+d-dimensional space into a (d-3)-dimensional internal space and a physical
+3-dimensional space, the latter expanding in time as a power bigger than
+2 (about 4.5 when d=9).}}
+
+@ARTICLE{Carlson:80,
+ AUTHOR = "P. Carlson",
+ TITLE = "Coordinate Free Relativity",
+ JOURNAL = "J. Math. Phys.",
+ YEAR = 1980, VOLUME = 21, PAGES = "1149-1154",
+ COMMENT = {{REDUCE} programs for tetrad formulation of GR.}}
+
+@PHDTHESIS{Carroll:73,
+ AUTHOR = "R. Carroll",
+ TITLE = "The Anomalous Magnetic Moment of the Electron in the
+Mass Operator Formalism",
+ SCHOOL = "University of Michigan",
+ YEAR = 1973}
+
+@ARTICLE{Carroll:75,
+ AUTHOR = "R. Carroll",
+ TITLE = "Mass-Operator Calculation of the Electron g-Factor",
+ JOURNAL = "Phys. Rev. D",
+ YEAR = 1975, VOLUME = 8, PAGES = "2344-2354"}
+
+@TECHREPORT{Cejchan,
+ AUTHOR = "A. Cejchan and J. Nadrchal",
+ TITLE = "Application of {REDUCE}-2 and Analytic Integration
+Program in the Theoretical Solid State Physics",
+ INSTITUTION = "Institute of Physics, CSAV, Prague"}
+
+@INPROCEEDINGS{Chaffy:88,
+ AUTHOR = "C. Chaffy-Camus",
+ TITLE = "An Application of {REDUCE} to the Approximation of $f(x,y)$",
+ BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
+ YEAR = 1988, VOLUME = 358, PAGES = "73-84"}
+
+@ARTICLE{Chinnick:86,
+ AUTHOR = "K. Chinnick and C. Gibson and J. F. Griffiths and W. Kordylewski",
+ TITLE = "Isothermal Interpretations of Oscillatory Ignition During
+Hydrogen Oxidation in an Open System.  {I}.  {Analytical} Predictions and
+Experimental Measurements of Periodicity",
+ JOURNAL = "Proc. Royal Soc. Lond.",
+ YEAR =  1986, VOLUME = "A405", PAGES = "117-128",
+ COMMENT = {Used {REDUCE} to solve Jacobian, but answer too complicated to
+be of any use.}}
+
+@ARTICLE{Cline:90,
+ AUTHOR = "Terry Cline and Harold Abelson and Warren Harris",
+ TITLE = "Symbolic Computing in Engineering Design",
+ JOURNAL = "AI EDAM", YEAR = 1990, MONTH = "February"}
+
+@TECHREPORT{Cohen:76,
+ AUTHOR = "H. I. Cohen and O. Leringe and Y. Sundblad",
+ TITLE = "The Use of Algebraic Computing in General Relativity",
+ INSTITUTION = "The Royal Institute of Technology Department of Mechanics",
+ YEAR = 1976, NUMBER = "TRITA-MEK-76-02"}
+
+@TECHREPORT{Cohen:76a,
+ AUTHOR = "I. Cohen and F. Bark",
+ TITLE = "Perturbation Calculations for the Spin Up Problem Using {REDUCE}",
+ INSTITUTION = "The Royal Institute of Technology, Department
+of Mechanics",
+ YEAR = 1976, NUMBER = "TRITA-MEK-76-03"}
+
+@TECHREPORT{Cohen:77,
+ AUTHOR = "I. Cohen and S. Yu. Slavyanov",
+ TITLE = "Smooth Perturbations of the {Schr{\"o}dinger} Equation with a
+Linear Potential Related to the Charmonium Models",
+ INSTITUTION = "University of Stockholm Institute of Physics",
+ YEAR = 1977, TYPE = "USIP Report", NUMBER = "77-17"}
+
+@ARTICLE{Cohen:79,
+ AUTHOR = "J. P. Fitch and H. I. Cohen",
+ TITLE = "Using {CAMAL} for Algebraic Calculations in General Relativity",
+ JOURNAL = "General Relativity and Gravitation", VOLUME = 11, YEAR = 1979,
+ PAGES = "411-418"}
+
+@ARTICLE{Cohen:84,
+ AUTHOR = "H. I. Cohen and I. B. Frick and J. E. {\AA}man",
+ TITLE = "Algebraic Computing in General Relativity",
+ JOURNAL = "General Relativity and Gravitation, ed.",
+ YEAR = 1984, PAGES = "139-162",
+ COMMENT = {General relativity review.}}
+
+@INPROCEEDINGS{Cohen:89,
+ AUTHOR = "Joel S. Cohen",
+ TITLE = "The Effective Use of Computer Algebra Systems",
+ YEAR = 1989, PAGES = "677-698",
+ BOOKTITLE = "Transactions of the Sixth Army Conference on Applied
+Mathematics and Computing",
+ COMMENT = {Review of author's experience with four computer algebra
+systems.}}
+
+@ARTICLE{Connor:84,
+ AUTHOR = "J. N. L. Connor and P. R. Curtis and D. Farrelly",
+ TITLE = "The Uniform Asymptotic Swallowtail Approximation:  Practical
+Methods for Oscillating Integrals with Four Coalescing Saddle Points",
+ JOURNAL = "J. Phys. A",
+ YEAR = 1984, VOLUME = 17, PAGES = "283-310",
+ COMMENT = {Used {REDUCE} and {SCHOONSCHIP} for some algebraic
+manipulations, and then checked the results with {MACSYMA}; this is the most
+distrustful reference we have found.}}
+
+@ARTICLE{Connor:84a,
+ AUTHOR = "J. N. L. Connor and P. R. Curtis and C. J. Edge and A. Lagan{`a}",
+ TITLE = "The Uniform Asymptotic Swallowtail Approximation:  Application
+to the Collinear $H+F_{2}$",
+ JOURNAL = "J. Chem. Phys.", YEAR = 1984, VOLUME = 80, NUMBER = 3,
+ PAGES = "1362-1363", MONTH = "February"}
+
+@ARTICLE{Conwell:84,
+ AUTHOR = "P. R. Conwell and P. W. Barber and C. K. Rushworth",
+ TITLE = "Resonant Spectra of Dielectric Sphere",
+ JOURNAL = "J. Opt. Soc. Am. A",
+ YEAR = 1984, VOLUME = 1, PAGES = "62-67",
+ COMMENT = {{REDUCE} used to confirm independently convergence and accuracy
+of {Numerical Bessel} function routine, expanding series by {REDUCE} and
+using bigfloats.  Described as slow but worthwhile.}}
+
+@INPROCEEDINGS{Cowan:79,
+ AUTHOR = "Richard M. Cowan and Martin L. Griss",
+ TITLE = "Hashing -- The Key to Rapid Pattern Matching",
+ BOOKTITLE = "Proc. {EUROSAM} 1979, Lecture Notes
+in Computer Science", YEAR = 1979, VOLUME = 72, PAGES = "266-278",
+ PUBLISHER = "Springer-Verlag"}
+
+@BOOK{Cox:92,
+ AUTHOR = "D. Cox and J. Little and D. O'Shea",
+ TITLE = "deals, Varieties and Algorithms:
+   An Introduction of Computational Algebraic Geometry 
+   and Commutative Algebra",
+ PUBLISHER = "Springer-Verlag",
+ YEAR = 1992,
+ COMMENTS = {The appendix contains a discussion of the Groebner basis
+     package for REDUCE},
+ ABSTRACT = {This book is an introduction to algebraic geometry and 
+commutative algebra aimed primarily at undergraduates. It emphasizes 
+applications and the computational and algorithmic aspects of the 
+subject.  Less abstract than other texts, and with prerequisites 
+(a course in linear algebra and any course discussing how to do 
+simple proofs), the text is also ideal for computer scientists as
+well as mathematicians interested in the subject.  The exposition
+assumes that students have access to a computer algebra system such 
+as Maple, REDUCE or Mathematica, but assumes no prior experience 
+with a computer.
+
+Table of Contents: Geometry, Algebra and Algorithms; Groebner Bases;
+Elimination Theory; The Algebra-Geometry Dictionary; Polynomial and 
+Rational Functions on a Variety; Robotics and Automatic Geometric 
+Theorem Proving; Invariant Theory of Finite Groups; Projective 
+Algebraic Geometry; The Dimension of a Variety; Appendices on Some 
+Concepts From Algebra, Pseudocode, Computer Algebra Systems, and 
+Independent Projects.}}
+
+@ARTICLE{Cung:75,
+ AUTHOR = "V. K. Cung",
+ TITLE = "Differential Cross Section of e+ + e- to e+ + $\mu-$ +
+$\bar{\nu}_\mu$ + $\bar{\nu}_e$",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1975, VOLUME = "55B", PAGES = "67-70"}
+
+@TECHREPORT{Darbaidze:86,
+ AUTHOR = "Ya. Z. Darbaidze",
+ TITLE = "A Gluon Bremsstrahlung in Supersymmetry {QCD}",
+ INSTITUTION = "JINR", YEAR = 1986, TYPE = "Preprint",
+ NUMBER = "P2-86-825"}
+
+@ARTICLE{Darbaidze:86a,
+ AUTHOR = "J. Z. Darbaidze and V. A. Matveev and
+Z. V. Merebashvili and L. A. Slepchenko",
+ TITLE = "Gluon Bremsstrahlung in Supersymmetric {QCD}",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1986, VOLUME = "B177", PAGE = "188"}
+
+@TECHREPORT{Darbaidze:88,
+ AUTHOR = "Ya. Z. Darbaidze and Z.V. Merebashvili and V.A. Rostovtsev",
+ TITLE = "Some Computer Realizations of the {REDUCE-3} Calculations for
+Exclusive Processes",
+ INSTITUTION = "JINR", YEAR = 1988, TYPE = "Preprint",
+ NUMBER = "P2-88-769"}
+
+@TECHREPORT{Darbaidze:89,
+ AUTHOR = "Ya. Z. Darbaidze and V.A. Rostovtsev",
+ TITLE = "Analysis of the Differential Equations for the Exclusive Processes
+and Explanation for the {``Mystery''} of the {Gamma-Distribution}",
+ INSTITUTION = "JINR", YEAR = 1989, TYPE = "Preprint",
+ NUMBER = "E2-89-286"}
+
+@INPROCEEDINGS{Dautcourt:79,
+ AUTHOR = "G. Dautcourt",
+ TITLE = "Application of {REDUCE} to Algebraic Computations in General
+Relativity and Astrophysics",
+ YEAR = 1979, MONTH = "September",
+ BOOKTITLE = "Proc. of the Workshop in Symbolic Computation, Dubna,
+{U.S.S.R.}",
+ COMMENT = {Reports the use of the system {REDUCE} 2 for general relativistic
+calculations.}}
+
+@TECHREPORT{Dautcourt:80,
+ AUTHOR = "G. Dautcourt and K. P. Jann",
+ TITLE = "A Program Package in {REDUCE} 2 for Algebraic Computations in
+General Relativity",
+ YEAR = 1980,
+ INSTITUTION = "Zentralinstitut fuer Astrophysik der
+Akademie der Wissenschaften"}
+
+@ARTICLE{Dautcourt:81,
+ AUTHOR = "G. Dautcourt and K. P. Jann and E. Riemer and M. Riemer",
+ TITLE = "User's Guide to {REDUCE} Subroutines For Algebraic
+Computations in General Relativity",
+ JOURNAL = "Astron. Nachr.",
+ YEAR = 1981, VOLUME = 302, PAGES = "1-13"}
+
+@ARTICLE{Dautcourt:83,
+ AUTHOR = "G. Dautcourt",
+ TITLE = "The Cosmological Problem as an Initial Value Problem on the
+Observer's Past Light Cone:  Geometry",
+ JOURNAL = "J. Phys. A",
+ YEAR = 1983, VOLUME = 16, PAGES = "3507-3528",
+ COMMENT = {Checked calculations with {REDUCE}, mainly {Riemann} tensor in
+null coordinates.}}
+
+@ARTICLE{Davenport:81,
+ AUTHOR = "James Harold Davenport",
+ TITLE = "On the Integration of Algebraic Functions",
+ JOURNAL = "Lecture Notes in Computer Science",
+ PUBLISHER = "Springer-Verlag",
+ YEAR = 1981, VOLUME = 102, PAGES = "1-197"}
+
+@ARTICLE{Davenport:82,
+ AUTHOR = "James H. Davenport",
+ TITLE = "Fast {REDUCE:}  The {trade-off} between efficiency and
+generality",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1982, VOLUME = 16, NUMBER = 1, PAGES = "8-11", MONTH = "February"}
+
+@ARTICLE{Davenport:82a,
+ AUTHOR = "James H. Davenport",
+ TITLE = "What do we want from a {high-level} language?",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1982, VOLUME = 16, NUMBER = 4, PAGES = "6-9", MONTH = "November"}
+
+@INPROCEEDINGS{Davenport:85,
+ AUTHOR = "James Davenport and Julian Padget",
+ TITLE = "{HEUGCD:}  How Elementary Upperbounds Generate Cheaper Data",
+ BOOKTITLE = "Proc. {EUROCAL} 1985, Lecture Notes
+in Computer Science", YEAR = 1985, VOLUME = 204, PAGES = "18-28",
+ PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{Davenport:88,
+ AUTHOR = "J. H. Davenport",
+ TITLE = "The World of Computer Algebra",
+ JOURNAL = "New Scientist",
+ YEAR = 1988, MONTH = "September", VOLUME = 1629, PAGES = "71-72"}
+
+@BOOK{Davenport:88a,
+ AUTHOR = "J. H. Davenport and Y. Siret and E. Tournier",
+ TITLE = "Computer Algebra, Systems and Algorithms for Algebraic Computation",
+ PUBLISHER = "Academic Press", EDITION = "2nd", YEAR = 1993}
+
+@BOOK{Davenport:88b,
+ AUTHOR = "J. H. Davenport and Y. Siret and E. Tournier",
+ TITLE = "Calcul Formel (in French)",
+ PUBLISHER = "Masson", EDITION = "2nd", YEAR = 1993}
+
+@BOOK{Davenport:88c,
+ AUTHOR = "J. H. Davenport and Y. Siret and E. Tournier",
+ TITLE = "Kompyuter Algebra (in Russian)",
+ PUBLISHER = "MIR", EDITION = "1st", YEAR = 1991}
+
+@TECHREPORT{Della-Dora:81,
+ AUTHOR = "J. Della Dora and E. Tournier",
+ TITLE = "Solutions Formelles D'Equations Differentielles au Voisinage de
+Points Singuliers Reguliers",
+ INSTITUTION = "Centre National de la Recherche Scientifique",
+ YEAR = 1981, TYPE = "Report", NUMBER = 239}
+
+@INPROCEEDINGS{Della-Dora:84,
+ AUTHOR = "J. Della Dora and E. Tournier",
+ TITLE = "Homogeneous Linear Difference Equation {(Frobenius-Boole Method)}",
+ BOOKTITLE = "Proc. {EUROSAM} 1984, Lecture Notes
+in Computer Science", YEAR = 1984, VOLUME = 174, PAGES = "2-12",
+ PUBLISHER = "Springer-Verlag"}
+
+@TECHREPORT{Della-Dora:85,
+ AUTHOR = "Jean Della-Dora and Claire Dicrescenzo and Dominique Duval",
+ TITLE = "About a New Method for Computing in Algebraic Number Fields",
+ INSTITUTION = "Universit{\'e} de Grenoble, Institut Fourier,
+France", YEAR = 1985, MONTH = "November"}
+
+@ARTICLE{Demaret:89,
+ AUTHOR = "J. Demaret and H. Caprasse and A. Moussiaux and Ph. Tombal and
+D. Papadopoulos",
+ TITLE = "{Ten-dimensional Lovelock-type Space-Times}",
+ JOURNAL = "{To appear} Phys. Rev. D",
+ YEAR = 1989, MONTH = "July"}
+
+@ARTICLE{DeMenna:87,
+ AUTHOR = "L. De Menna and G. Miano and G. Rubinacci",
+ TITLE = "Volterra's Series Solutions of Free Boundary Plasma Equilibria",
+ JOURNAL = "Phys. Fluids",
+ YEAR = 1987, VOLUME = 30, PAGES = "409-416",
+ COMMENT = {Magnetohydrodynamics.  "We have carried out the computations up
+to the fourth order, (the fourth order has been obtained by means of the
+symbolic program {REDUCE}").}}
+
+@ARTICLE{Demichev:85,
+ AUTHOR = "A. P. Demichev and A. Ya. Rodionov",
+ TITLE = "A {REDUCE} Program for the Calculation of Geometrical
+Characteristics of Compactified Multidimensional {Riemannian} Space",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1985, VOLUME = 38, PAGES = "441-448",
+ COMMENT = {Covariant theories in N dimensional ($N \geq 4$) space-time.
+{REDUCE} programs to calculate {Ricci, Einstein and Yang-Mills} curvature
+and energy-momentum tensor.}}
+
+@TECHREPORT{Demichev:86,
+ AUTHOR = "A. P. Demichev and A. Ya. Rodionov",
+ TITLE = "Freund-{Rubin} Type Solutions for Different Compactifications of
+the Eleven-Dimensional Space",
+ INSTITUTION = "Institute for High Energy Physics", YEAR = 1986,
+ TYPE = "Preprint", NUMBER = "86-85",
+ ABSTRACT = {The results of calculating geometrical characteristics of
+seven-dimensional quotient spaces are represented.  These
+quantities are necessary for the construction of compactifying
+solutions of the eleven-dimensional supergravity.}}
+
+@ARTICLE{deRop:88,
+ AUTHOR = "Y. de Rop and J. Demaret",
+ TITLE = "Using {EXCALC} to Study Nondiagonal Multidimensional
+Spatially Homogeneous Cosmologies",
+ JOURNAL = "Gen. Rel. Grav.",
+ YEAR = 1988, VOLUME = 20, PAGES = "1127-1139"}
+
+@TECHREPORT{DeVos:89,
+ AUTHOR = "Alexis De Vos",
+ TITLE = "The use of {Reduce} in solar energy conversion theory",
+ INSTITUTION = "State University of Gent, {CAGe} Computer Algebra
+Group", YEAR = 1989, TYPE = "Reports of the {CAGe} Project",
+NUMBER = 4, MONTH = "August"}
+
+@TECHREPORT{DeVos:93,
+ AUTHOR = "Alexis De Vos",
+ TITLE = "Carnot engines, {Gr{\"o}bner} bases and all the winds on the Earth",
+ INSTITUTION = "University of Gent, {CAGe} Computer Algebra Group",
+ YEAR = 1993, TYPE = "The {CAGe} Reports", NUMBER = 9, MONTH = "March",
+ ABSTRACT = {In the present paper, we determine which part of the solar
+energy incident on a planet can be converted into mechanical work.  The
+planet is assumed to be spherical and not rotating around an axis.  From
+numerical calculations, we find that at the most 9.64% of the absorbed
+solar energy can be converted into work.  But can we find an analytical
+expression for this fundamental number?  We try this challenge with the
+REDUCE procedures for manipulation of polynomials.}}
+
+@INPROCEEDINGS{Dewar:89,
+ AUTHOR = "M. C. Dewar",
+ TITLE = "{IRENA --} An Integrated Symbolic and Numerical Computation
+Environment",
+ BOOKTITLE = "Proc. of {ISSAC} '89", PUBLISHER = "{ACM} Press, New York",
+ YEAR = 1989, PAGES = "171-179"}
+
+@ARTICLE{Dhar:85,
+ AUTHOR = "D. Dhar and J-M. Maillard",
+ TITLE = "Susceptibility of the Checkerboard {Ising} Model",
+ JOURNAL = "J. Phys. A",
+ YEAR = 1985, VOLUME = 18, PAGES = "L383-L388",
+ COMMENT = {Used {REDUCE} for tedious algebra, and got a simple answer.
+statistical mechanics(?). "At the disorder variety, the n-point correlation
+functions of the checkerboard Potts model has a simple causal
+structure.  An exact expression for the susceptibility in the Ising
+case is obtained."}}
+
+@TECHREPORT{Dicrescenzo:85,
+ AUTHOR = "Claire Dicrescenzo",
+ TITLE = "Algebraic Computation on Algebraic Numbers",
+ INSTITUTION = "Institut Fourier, Laboratoire de
+Math{\'e}matiques, France", YEAR = 1985, MONTH = "December",
+ COMMENT = {Examples are given of a new method, implemented on {REDUCE},
+for computing algebraically on algebraic numbers.}}
+
+@TECHREPORT{Diver,
+ AUTHOR = "D. A. Diver and E. Q. Laing and C. C. Sellar",
+ TITLE = "Waves in a Cold Plasma with a Spatially Rotating Magnetic Field",
+ YEAR = 1988,
+ INSTITUTION = "Department of Physics and Astronomy, University of
+Glasgow, Plasma Physics Group", TYPE = "Report", NUMBER = "GU TPA 88/12-1",
+ COMMENT = {"{\ldots}The algebraic manipulation system {REDUCE} was used in
+constructing the following tensor definitions which allows us to make fewer
+approximations than other authors."}}
+
+@INPROCEEDINGS{Diver:86,
+ AUTHOR = "D. A. Diver and E. W. Laing",
+ TITLE = "Proc. 8th {Europhysics} Conference on
+Computational Physics",
+ YEAR = 1986,
+ BOOKTITLE = "Computing in Plasma Physics"}
+
+@INPROCEEDINGS{Diver:88,
+ AUTHOR = "D. A. Diver and E. W. Laing",
+ BOOKTITLE = "Proc. {XV} {European} Conference on Controlled
+Fusion and Plasma Heating",
+ YEAR = 1988}
+
+@TECHREPORT{Diver:88a,
+ AUTHOR = "D. A. Diver and E. W. Laing",
+ TITLE = "Alfven Resonance Absorption in a Magnetofluid",
+ YEAR = 1988, TYPE = "Report",
+ INSTITUTION = "Department of Physics and Astronomy, University of
+Glasgow, Plasma Physics Group",
+ NUMBER = "GUTPA 88/04-01", MONTH = "July",
+ COMMENT = {Presented at 15th {UK} Plasma Physics Conference, {UMIST}.}}
+
+@ARTICLE{Diver:91,
+ AUTHOR = "D. A. Diver",
+ TITLE = "Modelling Waves with Computer Algebra",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1991, VOLUME = 11, NUMBER = 3, PAGES = "275-289", MONTH = "March",
+ ABSTRACT = {A sophisticated model for linear waves in an inhomogeneous
+plasma is tackled completely using the computer algebra system {REDUCE}.
+The algebra code mirrors the mathematics, and is structured in a simple
+and straightforward manner.  In so doing, the solution technique is made
+obvious, and the overall philosophy of the approach is intuitive to the
+{non-specialist} computer algebra user.}}
+
+@TECHREPORT{Dorfi:85,
+ AUTHOR = "E. A. Dorfi and L. O'C. Drury",
+ TITLE = "Simple Adaptive Grids for {1D} Initial Value Problems",
+ INSTITUTION = "Max-Plack-Institut fuer Kernphysik, Heidelberg,
+West Germany", YEAR = 1985,
+ NUMBER = "MPI H-1985-V21"}
+
+@ARTICLE{Dorizzi:86,
+ AUTHOR = "B. Dorizzi and B. Grammaticos and J. Hietarinta and A. Ramani
+and F. Schwarz",
+ TITLE = "New integrable three dimensional quartic potentials",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1986, VOLUME = "116A", PAGES = "432-436",
+ COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
+
+@TECHREPORT{dosSantos:85,
+ AUTHOR = "R. P. dos Santos and P. P. Srivastava",
+ TITLE = "Two-loop Effective Potential for {Wess-Zumino} Model using
+Superfields",
+ INSTITUTION = "International Centre for Theoretical Physics",
+ YEAR = 1985, NUMBER = "IC/85/205", MONTH = "October",
+ ABSTRACT = {For the case of several interacting chiral superfields the
+propagators for the unconstrained superfield potentials in the 'shifted'
+theory, where the supersymmetry is explicitly broken, are derived in a
+compact form.  They are used to compute one-loop effective potential in
+the general case, while a superfield calculation of renormalized effective
+potential to two loops for the Wess-Zumino model is performed.}}
+
+@ARTICLE{dosSantos:87,
+ AUTHOR = "Renato P. dos Santos",
+ TITLE = "Using {REDUCE} in Supersymmetry",
+ JOURNAL = "J. Symb. Comp.",
+ YEAR = 1989, VOLUME = 7, PAGES = "523-525"}
+
+@PHDTHESIS{dosSantos:87a,
+ AUTHOR = "R. P. dos Santos",
+ TITLE = "O M{\'e}todo de Supercampos para o C{\'a}lculo de Potencial
+Efetivo em Modelos com Supercampos Quirais: Os Modelos de Wess e
+Zumino e de O'Raifeartaigh",
+ SCHOOL = "Centro Brasileiro de Pesquisas F{\'i}sicas",
+ YEAR = 1987,
+ COMMENT = {{(In Portuguese)} Using the method of {Superfields}, the
+effective potential for supersymmetric models of {Wess-Zumino} and of
+{O'Raifeartaigh} is evaluated up to two-loop order. The spontaneous
+supersymmetry breaking is discussed.  {REDUCE} plays very important
+role in evaluation of the {Feynman} superdiagrams and in
+renormalization.}}
+
+@TECHREPORT{dosSantos:88a,
+ AUTHOR = "Renato P. dos Santos",
+ TITLE = "Introdu\c{c}\~{a}o ao Sistema {REDUCE} de C\'{a}lculo
+Alg\'{e}brico",
+ INSTITUTION = "CBPF, Rio de Janeiro, Brazil",
+ YEAR = 1988, NUMBER = "CBPF-NT-001/88",
+ COMMENT = {{(In Portuguese)} Lecture notes of a course on {REDUCE}.}}
+
+@ARTICLE{dosSantos:90,
+ AUTHOR = "R. P. dos Santos and W. L. Roque",
+ TITLE = "On the Design of an Expert Help System for Computer Algebra
+Systems",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1990, VOLUME = 24, NUMBER = 4, PAGES = "22-25", MONTH = "October"}
+
+@InProceedings{Dresse:93,
+  author =      "A. Dresse",
+  title =       "Treatment of Dummy Variables and {BRST} Theory in Computer
+		 Algebra",
+  booktitle =   "Proceedings of the 1993 International IMACS Symposium on
+                 Symbolic Computation",
+  year =        "1993",
+  editor =      "G. Jacob and N. E. Oussous and S. Steinberg",
+  pages =       "110-119",
+  organization ="IMACS",
+  publisher =   "Laboratoire d'Informatique Fondamentale de Lille, France",
+  comment =     {A canonical form algorithm for quantities with locally scoped
+                 variables (e.g. Summation convention, tensor products) is
+                 developed in a {REDUCE} package.}
+}
+
+@ARTICLE{Drska:90,
+ AUTHOR = "Ladislav Drska and Richard Liska and Milan Sinor",
+ TITLE = "Two practical packages for computational physics{-GCPM, RLFI}",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1990, VOLUME = 61, NUMBER = "1-2", MONTH = "November",
+ PAGES = "225-230",
+ ABSTRACT = {Two handy computer-program packages for technical support of
+the work in two different branches of the computational physics are reported:
+(1) A general package for the symbolic and numerical transformation of
+expressions from one system of units to another.  (2) A package allowing
+high-quality two-dimensional output of mathematical formulas from the
+computer-algebra system {REDUCE}.}}
+
+@ARTICLE{Dubowsky:75,
+ AUTHOR = "S. Dubowsky and J. L. Grant",
+ TITLE = "Application of Symbolic Manipulation to Time
+Domain Analysis of Nonlinear Dynamic Systems",
+ JOURNAL = "Journ. of Dynamic Systems, Measurement, and Control",
+ YEAR = 1975, VOLUME = "75-Aut-J"}
+
+@ARTICLE{Dudley:89,
+ AUTHOR = "M. L. Dudley and R. W. James",
+ TITLE = "{Computer-aided} Derivation of Spherical Harmonic Spectral Equations
+in Astrogeophyics",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1989, VOLUME = 8, NUMBER = 4, PAGES = "423-427", MONTH = "October"}
+
+@ARTICLE{Dufner:69,
+ AUTHOR = "A. M. Dufner and Y. S. Tsai",
+ TITLE = "Phenomenological Analysis of the $\gamma$NN* Form Factors",
+ JOURNAL = "Phys. Rev.",
+ YEAR = 1969, VOLUME = 168, PAGES = "1801-1809"}
+
+@INPROCEEDINGS{Dulyan:87,
+ AUTHOR = "L. S. Dulyan",
+ TITLE = "The Calculation of {QCD} Triangular {Feynman} Graphs in the
+External Gluonic Field Using {REDUCE}-2 System",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "172-173",
+ PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{Duncan:86,
+ AUTHOR = "Anthony Duncan and Ralph Roskies",
+ TITLE = "Representations of Unusual Mathematical Structures in Scientific
+Applications of Symbolic Computation",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1986, VOLUME = 2, NUMBER = 2, PAGES = "201-206", MONTH = "June",
+ ABSTRACT = {We present examples of techniques we have used to apply {REDUCE}
+to problems in particle physics which have mathematical structures unknown to
+{REDUCE}.}}
+
+@PHDTHESIS{Duval:87,
+ AUTHOR = "Dominique Duval",
+ TITLE = "Diverses questions relatives au Calcul Formel
+Avec des Nombres Alg{\'e}briques",
+ SCHOOL = "L'Universit{\'e} Scientifique, Technologique
+et M{\'e}dicale de Grenoble", YEAR = 1987}
+
+@InProceedings{Dyer:94,
+  author =       {Charles C. Dyer},
+  title =        {An Application of Symbolic Computation in the
+		  Physical Sciences},
+  booktitle =    {Symbolic and Algebraic Computation},
+  editor =       {},
+  series =       {ISSAC},
+  year =         {1994},
+  organization = {SIGSAM},
+  publisher =    {ACM},
+  pages =        {181--186}
+}
+
+@ARTICLE{Earles:70,
+ AUTHOR = "D. Earles",
+ TITLE = "A Measurement of the Electron-Production of Muon Pairs",
+ JOURNAL = "Phys. Rev. Lett.",
+ YEAR = 1970, VOLUME = 25, PAGES = "129-133"}
+
+@ARTICLE{Eastwood:87,
+ AUTHOR = "James W. Eastwood",
+ TITLE = "Orthovec:  A {REDUCE} Program for {3-D} Vector Analysis
+in Orthogonal Curvilinear Coordinates",
+ JOURNAL = "Comp. Phys. Commun.",
+ YEAR = 1987, VOLUME = 47, NUMBER = 1, PAGES = "139-147", MONTH = "October"}
+
+@TECHREPORT{Eastwood:87a,
+ AUTHOR = "James W. Eastwood and Christopher J. H. Watson",
+ TITLE = "An Analytic Theory of {Wave-Current} Interactions",
+ INSTITUTION = "Culham Laboratory, Theory and Optics Division",
+ YEAR = 1987, NUMBER = "Plasma Physics Note 87/7", MONTH = "February",
+ ABSTRACT = {This report presents results of the Department of Energy
+contract to obtain high order analytic solutions to nonlinear hydrodynamic
+equation describing steady periodic waves propagating in sheared currents.
+The purpose of this work is to provide working formulae for computing
+combined wave and current loadings in the design of offshore structures.
+Using the {REDUCE} algebra package, we have identified minor typographical
+errors in the published fifth coefficients for uniform currents given by
+{Fenton [2]} and by Skjelbreia and {Hendrickson [5]}.  We have demonstrated
+the equivalence of corrected forms of these expressions to fifth order, and
+extended Fenton's expansion to seventh order.  We present a new fifth order
+theory for bilinear current profiles. {FORTRAN} software for the seven order
+uniform current and fifth order bilinear current theories are given.}}
+
+@ARTICLE{Eastwood:91,
+ AUTHOR = "James W. Eastwood",
+ TITLE = "{ORTHOVEC:} version 2 of the {REDUCE} program for {3-D} vector
+analysis in orthogonal curvilinear coordinates",
+ JOURNAL = "Comp. Phys. Commun.",
+ YEAR = 1991, VOLUME = 64, NUMBER = 1, PAGES = "121-122", MONTH = "April"}
+
+@TECHREPORT{Edelen:81,
+ AUTHOR = "Dominic G. B. Edelen",
+ TITLE = "Programs for Calculation of Isovector Fields in the
+{REDUCE}-2 Environment",
+ INSTITUTION = "Center for the Application of Mathematics,
+Lehigh University", YEAR = 1981, NUMBER = "TBD", MONTH = "August"}
+
+@ARTICLE{Edelen:82,
+ AUTHOR = "D. G. B. Edelen",
+ TITLE = "Isovector Fields for Problems in the Mechanics of Solids and
+Fluids",
+ JOURNAL = "Int. Journ. Eng. Sci.",
+ YEAR = 1982, VOLUME = 20, PAGES = "803-815",
+ COMMENT = {Prolongation methods as a {REDUCE} package for this, available
+from Center for Applications of Mathematics, Lehigh Univ., Bethlehem, PA
+18015.  Applications to mechanics of solids and fluids.}}
+
+@BOOK{Edneral:89,
+ AUTHOR = "Viktor F. Edneral and Aleksandr P. Kryukov and
+Anatolii Ia. Rodionov",
+ TITLE = "The language of the analytic computer program {REDUCE}",
+ PUBLISHER = "Moscow, {Izd-vo}, Moskovskogo {un-ta}", YEAR = 1989,
+ COMMENT = {This monograph -- first in The Soviet Union with a systematic
+treatment of the analytical computer (program) {REDUCE}.}}
+
+@ARTICLE{Eisenberger:90,
+ AUTHOR = "Moshe Eisenberger",
+ TITLE = "Application of Symbolic Algebra to the Analysis of Plates
+on Variable Elastic Foundation",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1990, VOLUME = 9, NUMBER = 2, PAGES = "207-213", MONTH = "February"}
+
+@TECHREPORT{Eissfeller:86,
+ AUTHOR = "Bernd Ei{\ss}feller and G{\"u}nter W. Hein",
+ TITLE = "A Contribution to {3D-Operational} Geodesy",
+ INSTITUTION = "Universit{\"a}rer Studiengang Vermessungswesen
+and Universit{\"a}t der Bundeswehr M{\"u}nchen",
+ YEAR = 1986, NUMBER = "Heft 17", MONTH = "December"}
+
+@PHDTHESIS{Eitelbach:73,
+ AUTHOR = "D. L. Eitelbach",
+ TITLE = "Automatic Analysis of Problems in Elementary Mechanics",
+ SCHOOL = "University of Illinois",
+ YEAR = 1973}
+
+@ARTICLE{Eleuterio:82,
+ AUTHOR = "S. M. Eleut{\'e}rio and R. V. Mendes",
+ TITLE = "Note on Equivalence and Singularities:  An Application of
+Computer Algebra",
+ JOURNAL = "Journ. Comp. Phys.",
+ YEAR = 1982, VOLUME = 48, PAGES = "150-156",
+ COMMENT = {{GR} equivalence, commenting on \AAman & Karlhede.}}
+
+@ARTICLE{Eliseev:85,
+ AUTHOR = "V. P. Eliseev and R. N. Fedorova and V. V. Kornyak",
+ TITLE = "A {REDUCE} Program for Determining Point and Contact {Lie}
+Symmetries of Differential Equations",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1985, VOLUME = 36, PAGES = "383-389",
+ ABSTRACT = {A universal {REDUCE} program for obtaining the systems of
+determining equations of the Lie algebra of point and contact
+symmetries is proposed.}}
+
+@ARTICLE{Elishakoff:87,
+ AUTHOR = "Isaac Elishakoff and Joseph Hollkamp",
+ TITLE = "Computerized Symbolic Solution for a Nonconservative
+System in Which Instability Occurs by Flutter in One Range
+of a Parameter and by Divergence in Another",
+ JOURNAL = "Comp. Methods in Applied Mechanics and Engineering",
+ YEAR = 1987, VOLUME = 62, PAGES = "27-46",
+ COMMENT = {"{\ldots}the problem is solved by the {Galerkin} method in
+conjunction with computerized symbolic algebra".  The system used is {REDUCE}.
+"It carries out algebraic operations irrespective of their complexity".
+Includes snatches of code and algebraic answers.  Mainly
+differentiation and substitution, plus a little integration.  The
+coefficients get rather large (18 digits or so).}}
+
+@ARTICLE{Elishakoff:87a,
+ AUTHOR = "Isaac Elishakoff and Brian Couch",
+ TITLE = "Application of Symbolic Algebra to the Instability of a
+Nonconservative System",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1987, VOLUME = 4, NUMBER = 3, PAGES = "391-396", MONTH = "December"}
+
+@ARTICLE{Esteban:90,
+ AUTHOR = "E.P. Esteban and E. Ramos",
+ TITLE = "Algebraic computing and the {Newman-Penrose} formalism",
+ JOURNAL = "Computers in Physics",
+ YEAR = 1990, PAGES = "285-290", MONTH = "May/June"}
+
+%                          REDUCE BIBLIOGRAPHY
+
+%                              Part 2:  F-H
+
+% Copyright (c) 1995 RAND.  All Rights Reserved.
+
+% Additions and corrections are solicited.  Please send them, in the
+% same format as these entries if possible, to reduce at rand.org.
+
+
+@ARTICLE{Falck:89,
+ AUTHOR = "N. K. Falck and D. Graudenz and G. Kramer",
+ TITLE = "Cross section for {five-parton} production in $e^{+} e^{-}$
+annihilation",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1989, VOLUME = 56, PAGES = "181-198", NUMBER = 2, MONTH = "December"}
+
+@ARTICLE{Fazio:84,
+ AUTHOR = "P. M. Fazio and G. E. Copeland",
+ TITLE = "Cooper-Type Minima in Multipole Cross Sections of Atomic Hydrogen",
+ JOURNAL = "Phys. Rev. Lett.",
+ YEAR = 1984, VOLUME = 53, NUMBER = "2", MONTH = "July"}
+
+@INPROCEEDINGS{Fedorova:87,
+ AUTHOR = "R. N. Fedorova and V. P. Gerdt and N. N. Govorun
+and V. P. Shirikov",
+ TITLE = "Computer Algebra in Physical Research of {Joint Institute}
+for {Nuclear Research}",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "1-10",
+ PUBLISHER = "Springer-Verlag"}
+
+@INPROCEEDINGS{Fedorova:87a,
+ AUTHOR = "R. N. Fedorova and V. V. Kornyak",
+ TITLE = "Computer Algebra Application for Determining Local Symmetries
+of Differential Equations",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "174-175",
+ PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{Feldmar:86,
+ AUTHOR = "E. Feldmar and K. S. K{\"o}lbig",
+ TITLE = "{REDUCE} Procedures for the Manipulation of Generalized
+Power Series",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1986, VOLUME = 39, PAGES = "267-284"}
+
+@ARTICLE{Feuillebois:84,
+ AUTHOR = "F. Feuillebois",
+ TITLE = "Sedimentation in a Dispersion with Vertical Inhomogenieties",
+ JOURNAL = "Journ. Fluid Mech.",
+ YEAR = 1984, VOLUME = 139, PAGES = "145-171",
+ COMMENT = {Uses {REDUCE} and {INT} to evaluate some integrals in the
+expansion of 1/s, a small quantity.}}
+
+@ARTICLE{Fitch:73,
+ AUTHOR = "John Fitch",
+ TITLE = "Problems \#3 and \#4 in {REDUCE} and {MACSYMA}",
+ JOURNAL = "SIGSAM Bulletin",
+ YEAR = 1973, PAGES = "10-11",
+ ABSTRACT = {The algebra systems {REDUCE} and {MACSYMA} are used to solve
+{SIGSAM} Problem \#3, the Reversion of a Double Series, and {SIGSAM}
+Problem \#4, the Lie Transform Solution of the Harmonic Oscillator.}}
+
+@INPROCEEDINGS{Fitch:81,
+ AUTHOR = "J. P. Fitch",
+ TITLE = "User-based Integration Software",
+ BOOKTITLE = "Proc. 1981 {ACM} Symposium on Symbolic
+and Algebraic Computation",
+ YEAR = 1981, PAGES = "245-248"}
+
+@INPROCEEDINGS{Fitch:83,
+ AUTHOR = "J. P. Fitch",
+ TITLE = "Implementing {REDUCE} on a Microprocessor",
+ BOOKTITLE = "Proc. {EUROCAL} 1983, Lecture Notes
+in Computer Science", YEAR = 1983, VOLUME = 162, PAGES = "128-136",
+ PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{Fitch:85,
+ AUTHOR = "J. P. Fitch",
+ TITLE = "Solving Algebraic Problems with {REDUCE}",
+ JOURNAL = "J. of Symbolic Computation",
+ YEAR = 1985, VOLUME = 1, NUMBER = 2, PAGES = "211-227", MONTH = "June"}
+
+@INPROCEEDINGS{Fitch:85a,
+ AUTHOR = "J. P. Fitch",
+ TITLE = "Applying Computer Algebra",
+ BOOKTITLE = "International Conference on Computer Algebra and its
+Application in Theory",
+ YEAR = 1985, PAGES = "262-275"}
+
+@INPROCEEDINGS{Fitch:87,
+ AUTHOR = "J. P. Fitch",
+ TITLE = "Utilisation du Calcul Formel",
+ BOOKTITLE = "Calcul Formel et Automatique",
+ EDITOR = "P. Chenin", PUBLISHER = "Editions du {CNRS}",
+ YEAR = 1987, PAGES = "119-136"}
+
+@INPROCEEDINGS{Fitch:87a,
+ AUTHOR = "J. P. Fitch and R. G. Hall",
+ TITLE = "Symbolic Computation and the Finite Element Method",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "95-96",
+ PUBLISHER = "Springer-Verlag"}
+
+@INPROCEEDINGS{Fitch:89,
+ AUTHOR = "J. P. Fitch",
+ TITLE = "Can {REDUCE} be run in parallel?",
+ BOOKTITLE = "Proc. of {ISSAC} '89", PUBLISHER = "{ACM} Press, New York",
+ YEAR = 1989, PAGES = "155-162"}
+
+@ARTICLE{Fitch:89a,
+ AUTHOR = "J. Fitch",
+ TITLE = "Compiling for Parallelism",
+ JOURNAL = "Computer Algebra and Parallelism", EDITOR = "J. Della Dora
+and J. Fitch",
+ YEAR = 1989, PAGES = "19-31", PUBLISHER = "Academic Press, London"}
+
+@InProceedings{Fitch90,
+  author =      "J. P. Fitch",
+  title =       "A delivery system for {REDUCE}",
+  booktitle =   "Proceedings of the International Symposium on
+                 Symbolic and Algebraic Computation",
+  year =        "1990",
+  editor =      "S. Watanabe and Morio Nagata",
+  pages =       "76-81",
+  organization =        "ACM",
+  publisher =   "Addison-Wesley"
+}
+
+@ARTICLE{Fitch:90a,
+ AUTHOR = "John Fitch",
+ TITLE = "The symbolic-numeric interface",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1990, VOLUME = 61, NUMBER = "1-2", MONTH = "November",
+ PAGES = "22-33",
+ ABSTRACT = {Algebraic computation can be of great assistance in the
+preparation of numerical programs.  The paper considers some of these,
+from simple to complex, and describes work currently in progress to produce
+a true integrated symbolic-numeric computing system.}}
+
+@ARTICLE{Fitch:93,
+ AUTHOR = "John Fitch",
+ TITLE = "Mathematics goes automatic",
+ JOURNAL = "Physics world",
+ YEAR = 1993, VOLUME = 6, NUMBER = 6, MONTH = "June", PAGES = "48-52",
+ COMMENT = {Computer algebra enhances the productivity of any scientist or
+engineer by increasing efficiency and doing away with tedious operations}}
+
+@TECHREPORT{Flatau:86,
+ AUTHOR = "Piotr J. Flatau and John P. Boyd and William R. Cotton",
+ TITLE = "Symbolic Algebra in Applied Mathematics and Geophysical
+Fluid Dynamics - {REDUCE} Examples",
+ INSTITUTION = "Dept. of Atmospheric and Oceanic Science, University
+of Michigan, and Dept. of Atmospheric Science, Colorado State
+University", YEAR = 1986}
+
+@TECHREPORT{Flath:86,
+ AUTHOR = "Dan Flath",
+ TITLE = "Remarks on Tensor Operators",
+ INSTITUTION = "National University of Singapore, Department
+of Mathematics", TYPE = "Research Report",
+ YEAR = 1986, NUMBER = 266, MONTH = "July"}
+
+@ARTICLE{Fleischer:71,
+ AUTHOR = "J. Fleischer",
+ TITLE = "Partial Wave Analysis of Nucleon-Nucleon {Bethe}-{Salpeter}
+Equation on the Computer",
+ JOURNAL = "Journ. of Comp. Phys.",
+ YEAR = 1971, VOLUME = 12, PAGES = "112-123"}
+
+@ARTICLE{Fleischer:73,
+ AUTHOR = "J. Fleischer and J. L. Gammel and M. T. Menzel",
+ TITLE = "Matrix {Pad\'e} Approximants for the {1SO}- and
+{3PO}- Partial Waves in Nucleon-Nucleon Scattering",
+ JOURNAL = "Phys. Rev. D",
+ YEAR = 1973, VOLUME = 8, PAGES = "1545-1552"}
+
+@ARTICLE{Fleischer:75,
+ AUTHOR = "J. Fleischer and J. A. Tjon",
+ TITLE = "Bethe-{Salpeter} Equation for {J}=0 Nucleon-Nucleon
+Scattering with One-Boson Exchange",
+ JOURNAL = "Nuclear Physics",
+ YEAR = 1975, VOLUME = "B84", PAGES = "375-396"}
+
+@ARTICLE{Fogelholm:82,
+ AUTHOR = "Rabbe Fogelholm and Inge B. Frick",
+ TITLE = "Standard {LISP} for the {VAX:}  A Provisional Implementation",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1982, VOLUME = 16, NUMBER = 4, PAGES = "10-12", MONTH = "November"}
+
+@ARTICLE{Foster:89,
+ AUTHOR = "Kenneth R. Foster and Haim H. Bau",
+ TITLE = "Symbolic Manipulation Programs for the Personal Computer",
+ JOURNAL = "Science",
+ YEAR = 1989, VOLUME = 243, PAGES = "679-243", MONTH = "February",
+ COMMENT = {Reviews several algebra programs that run on small machines.
+doesn't rate the {PC} version of {REDUCE} very highly because of the small
+workspace.}}
+
+@ARTICLE{Fox:71,
+ AUTHOR = "J. A. Fox",
+ TITLE = "Recalculation of the Crossed Graph Contribution
+to the 4th Order {Lamb} Shift",
+ JOURNAL = "Phys. Rev. D",
+ YEAR = 1971, VOLUME = 3, PAGES = "3228-3230"}
+
+@ARTICLE{Fox:74,
+ AUTHOR = "John A. Fox and Anthony C. Hearn",
+ TITLE = "Analytic Computation of Some Integrals in Fourth Order
+Quantum Electrodynamics",
+ JOURNAL = "Journ. Comp. Phys.",
+ YEAR = 1974, VOLUME = 14, PAGES = "301-317",
+ ABSTRACT = {A program for the analytic evaluation of some parametric
+integrals which occur in fourth order {QED} calculations is described.}}
+
+@ARTICLE{Franceschetti:85,
+ AUTHOR = "G. Franceschetti and I. Pinto",
+ TITLE = "Nonlinear Propagation and Scattering:  Analytical Solution and
+Symbolic Code Implementation",
+ JOURNAL = "J. Opt. Soc. Am. A",
+ YEAR = 1985, VOLUME = 2, PAGES = "997-1006",
+ COMMENT = {Volterra series using {REDUCE}.  Perturbation expansions.}}
+
+@INPROCEEDINGS{Freire:88,
+ AUTHOR = "E. Freire and E. Gamero and E. Ponce and L. G. Franquelo",
+ TITLE = "An Algorithm for Symbolic Computation of Center Manifolds",
+ BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
+ YEAR = 1988, VOLUME = 358, PAGES = "218-230"}
+
+@INPROCEEDINGS{Freire:89,
+ AUTHOR = "E. Freire and E. Gamero and E. Ponce",
+ TITLE = "An Algorithm for Symbolic Computation of {Hopf} Bifurcation",
+ BOOKTITLE = "Proc. Computers and Mathematics '89",
+ EDITOR = "E. Kaltofen and S. M. Watt",
+ YEAR = 1989, PAGES = "109-118", PUBLISHER = "Springer-Verlag, New York"}
+
+@TECHREPORT{Frick:82,
+ AUTHOR = "I. G. Frick and R. Fogelholm",
+ TITLE = "An Implementation of {Standard} {Lisp} Built on Top of {Franz Lisp}",
+ INSTITUTION = "University of Stockholm, Institute of
+Physics", YEAR = 1982, TYPE = "Report", MONTH = "April",
+ COMMENT = {A Standard {LISP} system has been built for the {VAX-11}
+large-address-space computer by embedding the required function
+definitions in the available Franz Lisp system for {VAX/UNIX}.}}
+
+@ARTICLE{Fujimoto:84,
+ AUTHOR = "Y. Fujimoto and T. Garavaglia",
+ TITLE = "Phase Diagrams in {Scalar QED}",
+ JOURNAL = "Physics Letters",
+ YEAR = 1984, VOLUME = "148B", NUMBER = "1,2,3", PAGES = "220-224",
+ MONTH = "November"}
+
+@ARTICLE{Fuzio:85,
+ AUTHOR = "P. M. Fuzio and G. E. Copeland",
+ TITLE = "Partial Radiative-Recombination Cross Sections for Excited
+States of Hydrogen",
+ JOURNAL = "Phys. Rev. A",
+ YEAR = 1985, VOLUME = 31, NUMBER = 1, PAGES = "187-195",
+ ABSTRACT = {The squares of the dipole and quadrupole matrix elements for the
+free-to-bond transitions of hydrogen uptp high bound states are
+derived in closed analytic form using a method suitable for computer
+algebra.}}
+
+@TECHREPORT{Gaemers,
+ AUTHOR = "K. J. F. Gaemers and R. Gastmans and F. M. Renard",
+ TITLE = "Neutrino Counting in e+ e- Collisions",
+ INSTITUTION = "NIKHEF-H, Amsterdam", TYPE = "Preprint",
+ ABSTRACT = {The possibility of counting the number of neutrino types
+in e+ e- $\rightarrow$ gamma nu nubar is re-examined by taking into
+account effects of the Z-pole.}}
+
+@TECHREPORT{Gaemers:78,
+ AUTHOR = "K. J. F. Gaemers and G. J. Gounaris",
+ TITLE = "Polarization Amplitudes For e+e- $\rightarrow$ W+W-
+$\rightarrow$ ZZ",
+ INSTITUTION = "CERN", YEAR = 1978, TYPE = "Preprint",
+ NUMBER = "TH.2548-CERN", MONTH = "August",
+ ABSTRACT = {The main purpose of this work is to study the three weak boson
+vertex.  We give explicit formulae for all polarization amplitudes of
+the processes e+e- $\rightarrow$ W+W- and e+e- $\rightarrow$ ZZ, with
+arbitrary couplings between the various intermediate vector bosons.}}
+
+@INPROCEEDINGS{Ganzha:89,
+ AUTHOR = "V. Ganzha and R. Liska",
+ TITLE = "Application of the {REDUCE} Computer Algebra System to Stability
+Analysis of Difference Schemes",
+ BOOKTITLE = "Proc. Computers and Mathematics '89",
+ EDITOR = "E. Kaltofen and S. M. Watt",
+ YEAR = 1989, PAGES = "119-129", PUBLISHER = "Springer-Verlag, New York"}
+
+@InProceedings{Ganzha90,
+  author =      "Victor G. Ganzha and Michail Yu. Shaskov",
+  title =       "Local Approximation Study of Difference Operators by
+                 means of {REDUCE} System",
+  booktitle =   "Proceedings of the International Symposium on
+                 Symbolic and Algebraic Computation",
+  year =        "1990",
+  editor =      "S. Watanabe and Morio Nagata",
+  pages =       "185-192",
+  organization =        "ACM",
+  publisher =   "Addison-Wesley"
+}
+
+@InProceedings{Ganzha90a,
+  author =      "V. G. Ganzha and S. V. Meleshko and V. P. Shelest",
+  title =       "Application of {REDUCE} System for Analyzing
+                 Consistency of Systems of {P.D.E.'s}",
+  booktitle =   "Proceedings of the International Symposium on
+                 Symbolic and Algebraic Computation",
+  year =        "1990",
+  editor =      "S. Watanabe and Morio Nagata",
+  pages =       "301",
+  organization =        "ACM",
+  publisher =   "Addison-Wesley"
+}
+
+@INPROCEEDINGS{Ganzha:91,
+ AUTHOR = "V.G. Ganzha and B. Yu. Scobelev and E.V. Vorozhtsov",
+ TITLE = "Stability Analysis of Difference Schemes by the Catastrophe
+Theory Methods and by Means of Computer Algebra",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ EDITOR = "Stephen M. Watt",
+ PUBLISHER = "ACM Press", ADDRESS = "Maryland", PAGES = "427-428",
+ YEAR = 1991}
+
+@InProceedings{Ganzha:94,
+  author =       "V. G. Ganzha and E. V. Vorozhtsov and J. Boers and
+		  J. A. van Hulzen",
+  title =        {Symbolic-Numeric Stability Investigations of {Jameson's}
+		  Schemes for Thin-layer {Navier-Stokes} Equations},
+  booktitle =    {Symbolic and Algebraic Computation},
+  editor =       {},
+  series =       {ISSAC},
+  year =         {1994},
+  organization = {SIGSAM},
+  publisher =    {ACM},
+  pages =        {234--241}
+}
+
+@TECHREPORT{Garavaglia,
+ AUTHOR = "Theodore Garavaglia",
+ TITLE = "Polarized Electron Scattering on Spin Zero and Polarized Spin
+$\frac{1}{2}$ Targets:  Deep Inelastic Scattering, Elastic Electron-muon
+Scattering, and Elastic Electron-Nucleon Scattering",
+ INSTITUTION = "Inst. Teich. Bhaile Atha Cliath, Eire", TYPE = "Preprint",
+ ABSTRACT = {A covariant formulation is developed and used to derive
+cross-sections for the analysis of experiments in which
+polarized electrons(muons) are scattered from spin zero and
+from polarized spin 1/2 targets.}}
+
+@ARTICLE{Garavaglia:80,
+ AUTHOR = "T. Garavaglia",
+ TITLE = "A Covariant Formulation for Polarized Electron (Muon)
+Scattering on Spin-Zero and Polarized Spin-$\frac{1}{2}$ Targets",
+ JOURNAL = "Il Nuovo Cimento",
+ YEAR = 1980, VOLUME = "56A", PAGES = "121-128",
+ COMMENT = {{REDUCE} used in quantum mechanics.}}
+
+@ARTICLE{Garavaglia:84,
+ AUTHOR = "Theodore Garavaglia",
+ TITLE = "{Dirac-} and {Majorana-neutrino-mass} effects in
+{neutrino-electron} elastic scattering",
+ JOURNAL = "Physical Review {D}",
+ YEAR = 1984, VOLUME = 29, NUMBER = 3, PAGES = "387-392", MONTH = "February"}
+
+@ARTICLE{Garcia:86,
+ AUTHOR = "Arnaldo Garcia and Paulo Viana",
+ TITLE = "Weierstrass Points on Certain Non-Classical Curves",
+ JOURNAL = "Arch. Math.",
+ YEAR = 1986, VOLUME = 46, PAGES = "315-322"}
+
+@ARTICLE{Garrad:86,
+ AUTHOR = "A. D. Garrad and D. C. Quarton",
+ TITLE = "Symbolic Computing as a Tool in Wind Turbine Dynamics",
+ JOURNAL = "Journ. of Sound and Vibration",
+ YEAR = 1986, VOLUME = 109, NUMBER = 1, PAGES = "65-78",
+ COMMENT = {{REDUCE} as a tool in turbine design, in particular present a
+program for part of a stability analysis for a turbine tower.}}
+
+@ARTICLE{Gastmans:79,
+ AUTHOR = "R. Gastmans and A. van Proeyen and P. Verbaeten",
+ TITLE = "Symbolic Evaluations of Dimensionally Regularized {Feynman}
+Diagrams",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1979, VOLUME = 18, PAGES = "201-203",
+ ABSTRACT = {A modification of the symbolic and algebraic manipulation
+program {REDUCE} is reported which allows the treatment of vector and gamma
+algebra in an arbitrary number of dimensions.}}
+
+@TECHREPORT{Gatermann:90,
+ AUTHOR = "Karin Gatermann",
+ TITLE = "Gruppentheoretische {Konstruktion} von symmetrischen
+{Kubaturformeln}",
+ INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin",
+ YEAR = 1990, TYPE = "Preprint", NUMBER = "TR 90-1", MONTH = "January"}
+
+@InProceedings{Gatermann90a,
+  author =      "Karin Gatermann",
+  title =       "Symbolic solution of polynomial equation systems with
+                 symmetry",
+  booktitle =   "Proceedings of the 1990 International Symposium on
+                 Symbolic and Algebraic Computation",
+  year =        "1990",
+  editor =      "S. Watanabe and Morio Nagata",
+  pages =       "112-119",
+  organization =        "ACM",
+  publisher =   "Addison-Wesley"
+}
+
+@ARTICLE{Gatermann:91,
+ AUTHOR = "Karin Gatermann and Andreas Hohmann",
+ TITLE = "Symbolic Exploitation of Symmetry in Numerical Pathfollowing",
+ JOURNAL = "IMPACT of Computing in Science and Engineering",
+ YEAR = 1991, MONTH = "December", VOLUME = 3, NUMBER = 4,
+ PAGES = "330-365",
+ ABSTRACT = {{Parameter-dependent} systems of nonlinear equations with
+symmetry are treated by a combination of symbolic and numerical computations.
+In the symbolic part of the algorithm the complete analysis of the symmetry
+occurs, and it is here where symmetrical normal forms, symmetry reduced
+systems, and block diagonal Jacobians are computed.  Given a particular
+problem, the symbolic algorithm can create and compute through the list of
+possible bifurcations thereby forming a {so-called} tree of decisions
+correlated to the different types of symmetry breaking bifurcation points.
+The remaining part of the algorithm deals with the numerical pathfollowing
+based on the implicit reparametrisation as suggested and worked out by
+{Deuflhard/Fiedler/Kunkel}.  The symmetry preserving bifurcation points are
+computed using recently developed augmented systems incorporating the use
+of symmetry.}}
+
+@INPROCEEDINGS{Gatermann:91a,
+ AUTHOR = "Karin Gatermann",
+ TITLE = "Mixed symbolic-numeric solution of symmetrical nonlinear systems",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ EDITOR = "Stephen M. Watt",
+ ORGANIZATION =        "ACM",
+ PUBLISHER = "ACM Press", ADDRESS = "Maryland", PAGES = "431-432",
+ YEAR = 1991,
+ ABSTRACT = {The mixed symbolic-numeric algorithm {SYMCON} for the fully
+automatical treatment of equivariant systems is presented. The global
+aspects of the theory of Vanderbauwhede for these systems are viewed with
+regard to the full bifurcation scenario containing solution paths with
+different isotropy groups and symmetry preserving and symmetry breaking
+bifurcation points.  The advanced exploitation of symmetry in the numerical
+computations causes an comprehensive symmetry analysis and complicated
+organization of numerical work which is done by the symbolic part of the
+algorithm.}}
+
+@TECHREPORT{Gatermann:91b,
+ AUTHOR = "Karin Gatermann and Andreas Hohmann",
+ TITLE = "Hexagonal Lattice Dome--Illustration of a Nontrivial Bifurcation
+Problem",
+ INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
+ YEAR = 1991, MONTH = "July", TYPE = "Preprint", NUMBER = "SC-91-8"}
+ ABSTRACT = {The deformation of a hexagonal lattice dome under an external
+load is an example of a parameter dependent system which is equivariant
+under the symmetry group of a regular hexagon.  In this paper the mixed
+symbolic-numerical algorithm SYMCON is applied to analyze its steady state
+solutions automatically showing their different symmetry and stability
+properties.}}
+
+@TECHREPORT{Gatermann:92,
+ AUTHOR = "Karin Gatermann",
+ TITLE = "Computation of Bifurcation Graphs",
+ INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
+ YEAR = 1992, MONTH = "June", TYPE = "Preprint", NUMBER = "SC-92-13"}
+ ABSTRACT = {The numerical treatment of equivariant parameter-dependent
+nonlinear equation systems, and even more its automation requires the
+intensive use of group theory.  This paper illustrates the group theoretic
+computations which are done in the preparation of the numerical computations.
+The bifurcation graph which gives the bifurcation subgroups is determined
+from the interrelationship of the irreducible representations of a group
+and its subgroups.  The Jacobian is transformed to block diagonal
+structure using a modification of the transformation which transforms to
+block diagonal structure with respect to a supergroup.  The principle of
+conjugacy is used everywhere to make symbolic and numerical computations
+even more efficient.  Finally, when the symmetry reduced problems and
+blocks of Jacobian matrices are evaluated numerically, the fact that the
+given representation is a quasi-permutation representation is exploited
+automatically.}}
+
+@TECHREPORT{Gatermann:93,
+ AUTHOR = "Karin Gatermann and Bodo Werner",
+ TITLE = "Group Theoretical Mode Interactions with Different Symmetries",
+ INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
+ YEAR = 1993, MONTH = "January", TYPE = "Preprint", NUMBER = "SC-93-3"}
+ ABSTRACT = {In two-parameter systems two symmetry breaking bifurcation
+points of different types coalesce generically within one point.  This causes
+secondary bifurcation points to exit.  The aim of this paper is to
+understand this phenomenon with group theory and the innerconnectivity of
+irreducible representations of supergroup and subgroups.  Colored pictures
+of examples are included.}}
+
+@TECHREPORT{Gatermann:93a,
+ AUTHOR = "Karin Gatermann and Bodo Werner",
+ TITLE = "Secondary {Hopf} bifurcation caused by steady-state steady-state
+mode interaction",
+ INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
+ YEAR = 1993, MONTH = "July", TYPE = "Preprint", NUMBER = "SC-93-16",
+ ABSTRACT = {In two-parameter systems with symmetry two steady state
+bifurcation points of different symmetry types coalesce generically within
+one point.  Under certain group theoretic conditions involving the action
+of the symmetry group on the kernels, we show that secondary Hopf
+bifurcation is borne by the mode interaction.  We explain this phenomenon
+by using linear representation theory.  For motivation an example with
+$D_{3}$-symmetry is investigated where the main properties causing the Hopf
+bifurcation are summarized.}}
+
+@TECHREPORT{Gatermann:94,
+ AUTHOR = "Karin Gatermann",
+ TITLE = "Semi-invariants, equivariants and algorithms",
+ INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
+ YEAR = 1994, MONTH = "May", TYPE = "Preprint", NUMBER = "SC-94-11",
+ ABSTRACT = {The results from invariant theory and the results for semi-
+invariants and equivariants are summarized in a way suitable for the
+combination with G{r\"o}bner basis computation.  An algorithm for the
+determination of fundamental equivariants using projections and a
+Poinca\'{r}e series is described.  Secondly, an algorithm is given for the
+representation of an equivariant in terms  of the fundamental equivariants.
+Several ways for the exact determination of zeros of equivariant systems
+are discussed.}}
+
+@TECHREPORT{Gatermann:95,
+ AUTHOR = "Karin Gatermann and Reiner Lauterbach",
+ TITLE = "Automatic classification of normal forms",
+ INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
+ YEAR = 1995, MONTH = "February", TYPE = "Preprint", NUMBER = "SC-95-3",
+ ABSTRACT = {The aim of this paper is to demonstrate a specific application
+of Computer Algebra to bifurcation theory with symmetry.  The
+classification of different bifurcation phenomena in case of several
+parameters is automated, based on a classification of G{r\"o}bner bases of
+possible tangent spaces.  The computations are performed in new coordinates
+of fundamental invariants and fundamental equivariants, with the induced
+weighted ordering.  In order to justify the approach the theory of
+intrinsic modules is applied.  Results for the groups $D_{3},Z_{2}$, and
+$Z_{2} x Z_{2}$ demonstrate that the algorithm works independent of the
+group and that new results are obtained.}}
+
+@INPROCEEDINGS{Gates:85,
+ AUTHOR = "Barbara L. Gates and J. A. van Hulzen",
+ TITLE = "Automatic Generation of Optimized Programs",
+ BOOKTITLE = "Proc. {EUROCAL} '85", YEAR = 1985,
+ MONTH = "April"}
+
+@ARTICLE{Gates:85a,
+ AUTHOR = "Barbara L. Gates",
+ TITLE = "Gentran:  An Automatic Code Generation Facility
+for {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1985, VOLUME = 19, NUMBER = 3, PAGES = "24-42", MONTH = "August"}
+
+@TECHREPORT{Gates:85b,
+ AUTHOR = "Barbara L. Gates",
+ TITLE = "Gentran User's Manual - {REDUCE} Version",
+ INSTITUTION = "Twente University of Technology, Department of
+Computer Science, The Netherlands", TYPE = "Memorandum",
+ YEAR = 1985, NUMBER = "INF-85-11", MONTH = "June"}
+
+@TECHREPORT{Gates:85c,
+ AUTHOR = "Barbara L. Gates",
+ TITLE = "Gentran Design and Implementation, {REDUCE} Version",
+ INSTITUTION = "Twente University of Technology, Department of Computer
+Science, The Netherlands", YEAR = 1985, TYPE = "Memorandum",
+ NUMBER = "INF-85-12", MONTH = "August"}
+
+@INPROCEEDINGS{Gates:86,
+ AUTHOR = "Barbara L. Gates",
+ TITLE = "A Numerical Code Generation Facility for {REDUCE}",
+ BOOKTITLE = "Proc. {SYMSAC} '86",
+ YEAR = 1986, PAGES = "94-99", MONTH = "July"}
+
+@TECHREPORT{Gebauer:85,
+ AUTHOR = "R{\"u}diger Gebauer and H. Michael M{\"o}ller",
+ TITLE = "A Fast Variant of {Buchberger's} Algorithm",
+ INSTITUTION = "Universit{\"a}t Heidelberg and
+Fernuniversit{\"a}t {Hagen}", YEAR = 1985, MONTH = "October"}
+
+@ARTICLE{Gebauer:88,
+ AUTHOR = "R{\"u}diger Gebauer and H. Michael M{\"o}ller",
+ TITLE = "On an Installation of {Buchberger's} Algorithm",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1988, VOLUME = 6, NUMBER = "2 and 3", PAGES = "275-286"}
+
+@ARTICLE{Generalis:84,
+ AUTHOR = "S. C. Generalis and D. J. Broadhurst",
+ TITLE = "The heavy-quark expansion and {QCD} sum rules for light quarks",
+ JOURNAL = "Physics Lett. B",
+ YEAR = 1984, VOLUME = 139, PAGES = "85-89"}
+
+@ARTICLE{George:68,
+ AUTHOR = "D. J. George",
+ TITLE = "A Covariant Theory of the Disintegration of the
+Deuteron by Pions and Photons at High Energy",
+ JOURNAL = "Phys. Rev.",
+ YEAR = 1968, VOLUME = 167, PAGES = "1357-1364"}
+
+@ARTICLE{Gerdt:80,
+ AUTHOR = "V. P. Gerdt",
+ TITLE = "Analytical Calculations in High Energy Physics by Computer",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1980, VOLUME = 20, PAGES = "85-90",
+ COMMENT = {A review, comparing {SCHOONSCHIP, ASHMEDAI and REDUCE-2}.}}
+
+@ARTICLE{Gerdt:80a,
+ AUTHOR = "V. P. Gerdt and O. V. Tarasov and D. V. Shirkov",
+ TITLE = "Analytical Calculations on Digital Computers for Applications
+in Physics and Mathematics",
+ JOURNAL = "Sov. Phys. USP",
+ YEAR = 1980, VOLUME = 23, PAGES = "59-77",
+ COMMENT = {General review of applications in many languages.}}
+
+@TECHREPORT{Gerdt:80b,
+ AUTHOR = "V. P. Gerdt",
+ TITLE = "On Global Structure of the General Solution of the
+{Chew-Low} Equations",
+ INSTITUTION = "J.I.N.R., Dubna",
+ YEAR = 1980, TYPE = "Preprint", NUMBER = "P2-80-436"}
+
+@ARTICLE{Gerdt:85,
+ AUTHOR = "V. P. Gerdt and A. B. Shvachka and A. Yu. Zharkov",
+ TITLE = "Computer Algebra Application for Classification of
+Integrable Non-Linear Evolution Equations",
+ JOURNAL = "J. Symb. Comp.",
+ YEAR = 1985, VOLUME = 1, PAGES = "101-107"}
+
+@TECHREPORT{Gerdt:85a,
+ AUTHOR = "V. P. Gerdt and N. A. Kostov and P. P. Raychev
+and R. P. Roussev",
+ TITLE = "Calculation of the Matrix Elements of the
+{Hamiltonian} of the Interacting Vector Boson Model Using
+Computer Algebra - Basic Concepts of the Interacting Vector
+Boson Model and Matrix Elements of the {SU(3)-Quadrupole}
+Operator",
+ INSTITUTION = "Institute for Nuclear Research and Nuclear
+Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria",
+ YEAR = 1985, NUMBER = "E4-85-262"}
+
+@TECHREPORT{Gerdt:85b,
+ AUTHOR = "V. P. Gerdt and N. A. Kostov and P. P. Raychev",
+ TITLE = "Calculation of the Matrix Elements of the
+{Hamiltonian} of the Interacting Vector Boson Model Using
+Computer Algebra - Matrix Elements of the {Hamiltonian} and
+Some {U(6)-Clebsch-Gordon} Coefficients",
+ INSTITUTION = "Institute for Nuclear Research and Nuclear
+Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria",
+ YEAR = 1985, NUMBER = "E4-85-263"}
+
+@TECHREPORT{Gerdt:85c,
+ AUTHOR = "V. P. Gerdt and N. A. Kostov and P. P. Raychev
+and R. P. Roussev",
+ TITLE = "Calculation of the Matrix Elements of the
+{Hamiltonian} of the Interacting Vector Boson Model
+Using Computer Algebra - Matrix Elements of the {Hamiltonian} -
+Analytical Results",
+ INSTITUTION = "Institute for Nuclear Research and Nuclear
+Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria",
+ YEAR = 1985, NUMBER = "E4-85-264"}
+
+@TECHREPORT{Gerdt:86,
+ AUTHOR = "V. P. Gerdt and M. G. Meshcheryakov and D. V. Shirkov",
+ TITLE = "Computers in Theoretical Physics",
+ INSTITUTION = "J.I.N.R., Dubna",
+ YEAR = 1986, NUMBER = "P2-86-848",
+ ABSTRACT = {The paper is written on the basis of the report presented by
+two authors ({M.G. Meshcheryakov} and {D.V. Shirkov}) at the 60th session
+of the JINR Scientific Council, June 5, 1986.  It reviews the usage of
+computer mathematics in theoretical and mathematical investigations
+carried out in the Joint Institute.  Recommendations are given on further
+development of the JINR Computer Center in accordance with the program of
+theoretical researches in nearest Five-Year Plan.}}
+
+@INPROCEEDINGS{Gerdt:87,
+ AUTHOR = "V. P. Gerdt and A. B. Shabat and S. I. Svinolupov
+and A. Yu. Zharkov",
+ TITLE = "Computer Algebra Application for Investigating
+Integrability of Nonlinear Evolution Systems",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "81-92",
+ PUBLISHER = "Springer-Verlag"}
+
+@INPROCEEDINGS{Gerdt:87a,
+ AUTHOR = "V. P. Gerdt and N. A. Kostov and Z. T. Kostova",
+ TITLE = "Computer Algebra and Computation of {Puiseux} Expansions of
+Algebraic Functions",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "206-207",
+ PUBLISHER = "Springer-Verlag"}
+
+@INPROCEEDINGS{Gerdt:89,
+ AUTHOR = "V. P. Gerdt and N. A. Kostov",
+ TITLE = "Computer Algebra in the theory of Ordinary Differential Equations
+of Halphen type",
+ BOOKTITLE = "Proc. Computers and Mathematics '89",
+ EDITOR = "E. Kaltofen and S. M. Watt",
+ YEAR = 1989, PAGES = "279-288", PUBLISHER = "Springer-Verlag, New York"}
+
+@TECHREPORT{Gerdt:89a,
+ AUTHOR = "V. P. Gerdt and Z. T. Kostova and N. A. Kostov and I. P. Yudin",
+ TITLE = "Algebraic-Numeric Calculations of Proton Trajectories in Bending
+Magnets of Synchrotron Accelerator",
+ INSTITUTION = "J.I.N.R., Dubna",
+ YEAR = 1989, TYPE = "Preprint", NUMBER = "E11-89-755",
+ ABSTRACT = {We study a solution of nonlinear differential equation of the
+second degree which describes the trajectories of the charged particles in
+the fully inhomogeneous field of cyclic accelerator.  We give the clear
+mathematical statement of the problem and algorithm of solving it.  We
+realize this algorithm on the Computer Algebra System {REDUCE 3.2}.  Our
+algorithm is based both on the existence of exact solution in terms of
+hyperelliptic integral and on the existence of power series solution of
+specific inversion problem.  We use the known {REDUCE} procedures of
+operation on generalized power series.  Using the {FORTRAN} code we give the
+numerical analysis of these series in the close relation to the concrete
+physical situation.  We apply our results to the beam dynamics modeling
+of the protons in the bending magnets in synchrotron accelerator.}}
+
+@TECHREPORT{Gerdt:89b,
+ AUTHOR = "V. P. Gerdt and A. Yu. Zharkov",
+ TITLE = "Solving the Polynomial System Arising in Classification of
+Integrable Coupled {KdV-like} Systems",
+ INSTITUTION = "J.I.N.R., Dubna",
+ YEAR = 1989, TYPE = "Preprint", NUMBER = "P5-89-231",
+ ABSTRACT = {A system of algebraic equations which follows from the
+necessary integrability conditions for the {ten-parametric} family of
+coupled {KdV-like} nonlinear evolution systems is considered.  The method
+for solving this system based on the structure of the canonical local
+conservation laws densities is described.  Computer algebra system
+{REDUCE} was used to find all the solutions.  As a result we obtain the
+complete list of integrable coupled {KdV-like} systems.}}
+
+@InProceedings{Gerdt90,
+  author =      "V. P. Gerdt and A. Yu. Zharkov",
+  title =       "Computer Generation of Necessary Integrability
+                 Conditions for Polynomial-Nonlinear Evolution Systems",
+  booktitle =   "Proceedings of the International Symposium on
+                 Symbolic and Algebraic Computation",
+  year =        "1990",
+  editor =      "S. Watanabe and Morio Nagata",
+  pages =       "250-254",
+  organization =        "ACM",
+  publisher =   "Addison-Wesley"
+}
+
+@InProceedings{Gerdt90a,
+  author =      "Vladimar P. Gerdt and Nikolai V. Khutornoy and Alexey
+                 Yu. Zharkov",
+  title =       "Solving Algebraic Systems which arise as Necessary
+                 Integrability Conditions for Polynomial-Nonlinear
+                 evolution Equations",
+  booktitle =   "Proceedings of the International Symposium on
+                 Symbolic and Algebraic Computation",
+  year =        "1990",
+  editor =      "S. Watanabe and Morio Nagata",
+  pages =       "299",
+  organization =        "ACM",
+  publisher =   "Addison-Wesley"
+}
+
+@ARTICLE{Gerdt:90b,
+ AUTHOR = "V. P. Gerdt and A. Yu. Zharkov",
+ TITLE = "Computer Classification of Integrable Coupled {KdV-Like} Systems",
+ JOURNAL = "J. Symb. Comp.",
+ YEAR = 1990, VOLUME = 10, PAGES = "203-207",
+ ABSTRACT = {The foundations of the symmetry approach to the classification
+problem of integrable {non-linear} evolution systems are briefly described.
+Within the framework of the symmetry approach the {ten-parametric} family
+of the third order {non-linear} evolution coupled {KdV-like} systems is
+investigated.  The necessary integrability conditions lead to an
+{over-determined} {non-linear} algebraic system.  To solve that system an
+effective method based on its structure has been used.  This allows us
+to obtain the complete list of integrable systems of a given type. All
+computation has been completed on the basis of computer algebra systems
+{FORMAC} and {REDUCE}.}}
+
+@INPROCEEDINGS{Gerdt:90c,
+ AUTHOR = "V. P. Gerdt and N. A. Kostov and A. Yu. Zharkov",
+ TITLE = "Nonlinear Evolution Equations and Solving Algebraic Systems:
+The Importance of Computer Algebra",
+ YEAR = 1990,
+ BOOKTITLE = "International Conference on Solitons and Its Applications",
+ PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "120-128"}
+ ABSTRACT = {In the present paper we study the application of computer
+algebra to solve the nonlinear polynomial systems which arise in
+investigation of nonlinear evolution equations.  We consider several
+systems which are obtained in classification of integrable nonlinear
+evolution equations with uniform rank.  Other polynomial systems are related
+with the finding of algebraic curves for finite-gap elliptic potentials of
+{Lame} type and generalizations.  All systems under consideration are
+solved using the method based on construction of the {Groebner} basis for
+corresponding polynomial ideals.  The computations have been carried out
+using computer algebra systems.}}
+
+@INPROCEEDINGS{Gerdt:91,
+ AUTHOR = "V. P. Gerdt and A. Yu. Zharkov",
+ TITLE = "Lie-{B{\"a}cklund} Symmetries of Coupled Nonlinear
+{Schr{\"o}dinger} Equations",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ EDITOR = "Stephen M. Watt",
+ PUBLISHER = "ACM Press", ADDRESS = "Maryland", PAGES = "313-314",
+ YEAR = 1991}
+
+@TECHREPORT{Gerdt:91a,
+ AUTHOR = "V. P. Gerdt and P. Tiller",
+ TITLE = "A {Reduce} Program for Symbolic Computation of {Puiseux}
+Expansions",
+ INSTITUTION = "J.I.N.R., Dubna",
+ YEAR = 1991, TYPE = "Preprint", NUMBER = "E5-91-401"}
+ ABSTRACT = {The program is described for computation of Puiseux expansions
+of alebraic functions.  The Newton polygon method is used for construction
+of initial coefficients of all the Puiseux series at the given point.  The
+program is written in computer algebra language Reduce.  Some illustrative
+examples are given.}}
+
+@TECHREPORT{Gerdt:91b,
+ AUTHOR = "V. P. Gerdt",
+ TITLE = "Computer Algebra Tools for Higher Symmetry Analysis of Nonlinear
+Evolution Equations",
+ INSTITUTION = "J.I.N.R., Dubna",
+ YEAR = 1991, TYPE = "Preprint", NUMBER = "E5-91-402"}
+ ABSTRACT = {This paper presents a computer-aided approach and a software
+package for symbolic algebraic computation to solve the problem of
+verifying the existence of the canonical Lie-B{\"a}cklund symmetries
+for multicomponent quasilinear evolution equations with polynomial-
+nonlinearity and computing a given order symmetry if any.  In the presence
+of arbitrary numerical parameters the problem is reduced to investigation
+and solving of nonlinear algebraic equations in those parameters.  It is
+remarkable that in all the known cases these algebraic equations are
+completely solvable by the Gr{\"o}bner basis technique implemented as a part
+of the software package.}}
+
+@InProceedings{Gerdt:93,
+  author =      "V. Gerdt",
+  title =       "Homogeneity of Integrability Conditions for Multiparametric
+                 Families of Polynomial-Nonlinear Evolution Equations",
+  booktitle =   "Proceedings of the 1993 International IMACS Symposium on
+                 Symbolic Computation",
+  year =        "1993",
+  editor =      "G. Jacob and N. E. Oussous and S. Steinberg",
+  pages =       "181-186",
+  organization ="IMACS",
+  publisher =   "Laboratoire d'Informatique Fondamentale de Lille, France",
+  comment =     {A canonical form algorithm for quantities with locally scoped
+                 variables (e.g. Summation convention, tensor products) is
+                 developed in a {REDUCE} package.}
+}
+
+@ARTICLE{Gervois:74,
+ AUTHOR = "A Gervois and Y. Pomeau",
+ TITLE = "Logarithmic Divergence in the Virial Expansion
+of Transport Coefficients of Hard Spheres",
+ JOURNAL = "Phys. Rev. A",
+ YEAR = 1974, VOLUME = 9, PAGES = "2196-2213"}
+
+@TECHREPORT{Gladd:82,
+ AUTHOR = "N. T. Gladd",
+ TITLE = "Computational Aspects of Research on the
+Relativistic {Whistler} Instability",
+ INSTITUTION = "Jaycor", YEAR = 1982,
+ NUMBER = "J530-82-020", MONTH = "June"}
+
+@INPROCEEDINGS{Gladkih:83,
+ AUTHOR = "I. Gladkih and E. Lovas",
+ TITLE = "On the Application of Computer Algebra Languages in the {Central
+Research Institute for Physics}",
+ BOOKTITLE = "Proceedings of the International Conference on Systems and
+Techniques of Analytical Computing and Their Applications in Theoretical
+Physics, {D11-83-511, Dubna}", YEAR = 1983}
+
+@INPROCEEDINGS{Gladkih:84,
+ AUTHOR = "I. Gladkih and M. Zimanyi",
+ TITLE  = "Comparison of systems for Symbolic Computing in use in the
+{Central Research Institute for Physics} (in {Russian})",
+ BOOKTITLE = "Proceedings of the International Conference on {Computer-Based}
+Scientific Research, Plovdiv", YEAR =  1984}
+
+@ARTICLE{Goldman:89,
+ AUTHOR = "V. V. Goldman and J. A. van Hulzen",
+ TITLE = "Automatic Code Vectorization of Arithmetic Expressions by
+Bottom-Up Structure Recognition",
+ JOURNAL = "Computer Algebra and Parallelism", EDITOR = "J. Della Dora
+and J. Fitch",
+ YEAR = 1989, PAGES = "119-132", PUBLISHER = "Academic Press, London"}
+
+@INPROCEEDINGS{Golley,
+ AUTHOR = "Bruce W. Golley and Joseph Petrolito",
+ TITLE = "An Alternative Finite Strip Technique for the Static Analysis of
+Single-Span, Multi-Span and Continuous Plates",
+ YEAR = 1982,
+ BOOKTITLE = "Proc. International Conference on
+Finite Element Methods"}
+
+@ARTICLE{Good:75,
+ AUTHOR = "D. Good and R. L. London and W. W. Bledsoe",
+ TITLE = "An Interactive Program Verification System",
+ JOURNAL = "Sigplan Notices",
+ YEAR = 1975, VOLUME = 10, NUMBER = 6, PAGES = "482-492"}
+
+@ARTICLE{Goto:77,
+ AUTHOR = "E. Goto and T. Soma",
+ TITLE = "{MOL} (Moving Objective Lens) Formulation of
+Deflective Aberration Free System",
+ JOURNAL = "Optik",
+ YEAR = 1977, VOLUME = 48, PAGES = "255-270"}
+
+@INPROCEEDINGS{Goto:78,
+ AUTHOR = "E. Goto and T. Soma",
+ TITLE = "Electron Beam Lithography for Advanced {LSI} Fabrication",
+ YEAR = 1978, PAGES = "1223-1228",
+ BOOKTITLE = "Proc. 1978 National Computer Conference,
+{AFIPS} Press, New Jersey"}
+
+@ARTICLE{Gould:84,
+ AUTHOR = "H. W. Gould and M. E. Mays",
+ TITLE = "Series Expansions of Means",
+ JOURNAL = "Journ. of Mathematical Analysis and Applications",
+ YEAR = 1984, VOLUME = 101, NUMBER = 2, PAGES = "611-621",
+ MONTH = "July"}
+
+@ARTICLE{Graebe:93,
+ AUTHOR = "Hans-Gert Gr{\"a}be",
+ TITLE = "On Lucky Primes",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1993, VOLUME = 15, NUMBER = 2, PAGES = "199-209", MONTH = "February",
+ COMMENT = {Winkler (1988) and Pauer (1992) present algorithms for a Hensel
+lifting of a modular Gr{\"o}bner basis over lucky primes to a rational
+one.  They have to solve a linear system with modular polynomial entries
+that requires another (modular) Gr{\"o}ner basis computation.
+After an extension of luckiness to arbitrary (commutative noetherian) base
+rings we show in this paper that for a homogeneous polynomial ideal I one
+lift not only only its Gr{\"o}bner basis but also a homogeneous basis of
+its syzygy module.  The same result holds for arbitrary ideals and
+liftings from Z/p to Q.  Moreover the same lifting can be obtained from a
+true Gro{\"o}bner trace by linear algebra over Q only.  Parallel modular
+techniques allow to find such a true Gro{\"o}bner and a lucky prime with
+high probability.
+All these results generalize in an obvious way to homogeneous modules
+generated by the rows of matrices with polynomial entries.  Since
+luckiness can be weakened to a condition that transfers from I to higher
+syzygy modules the lifting theorem generalizes to a lifting theorem for
+the resolution of I.}}
+
+@PHDTHESIS{Gragert:81,
+ AUTHOR = "Peter Gragert",
+ TITLE = "Symbolic Computations in Prolongation Theory",
+ SCHOOL = "Twente University of Technology, The Netherlands",
+ YEAR = 1981}
+
+@BOOK{Grammaticos,
+ AUTHOR = "B. Grammaticos and A. Voros",
+ TITLE = "Semi-Classical Approximations for Nuclear
+{Hamiltonians}:  {II}. {Spin-dependent} Potentials",
+ ABSTRACT = {A systematic semi-classical expansion procedure for physical
+quantities in nuclei, based on the Thomas-Fermi approximation
+to the Hartree-Fock equations and constructed in a previous
+work, is extended here to the realistic case where the
+effective one-body {Hamiltonian} for nucleons contains
+spin-dependent terms.}}
+
+@TECHREPORT{Grammaticos:78,
+ AUTHOR = "B. Grammaticos and A. Voros",
+ TITLE = "Semi-classical Approximations for Nuclear
+{Hamiltonians} {I}. {Spin-independent} Potentials",
+ INSTITUTION = "CEN, Saclay", YEAR = 1978, TYPE = "Preprint",
+ NUMBER = "DPh-T/78-75", MONTH = "August",
+ COMMENT = {Submitted to Annals of Physics},
+ ABSTRACT = {A systematic procedure for calculating semi-classical
+expansions of physically interesting quantities is presented.}}
+
+@ARTICLE{Grammaticos:85,
+ AUTHOR = "B. Grammaticos and B. Dorizzi and A. Ramani and J. Hietarinta",
+ TITLE = "Extending integrable {Hamiltonian} systems from 2 to {N}
+dimensions",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1985, VOLUME = "109A", PAGES = "81-84",
+ COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
+
+@ARTICLE{Gray:90,
+ AUTHOR = "N. Gray and D. J. Broadhurst and W. Grafe and K. Schilcher",
+ TITLE = {Three-loop relation of quark $\overline{\rm MS}$ and pole masses},
+ JOURNAL = "Zeitschrift {f\"{u}r} Physik C",
+ YEAR = 1990, VOLUME = 48, PAGES = "673-679"}}
+
+@ARTICLE{Greenland:84,
+ AUTHOR = "P. T. Greenland",
+ TITLE = "Comparison Between Phase Diffusion and Random Telegraph Signal
+Models of Laser Bandwidth",
+ JOURNAL = "Journ. Phys. B",
+ YEAR = 1984, VOLUME = 17, PAGES = "1919-1925",
+ COMMENT = {{REDUCE} calculation of correlation matrix for molecular physics.
+Tedious, but simple result.}}
+
+@ARTICLE{Grimm,
+ AUTHOR = "R. Grimm and H. K{\"u}hnelt",
+ TITLE = "Using {REDUCE} in Problems of Supersymmetry and Supergravity",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1980, VOLUME = 20, PAGES = "77",
+ COMMENT = {Describes how {REDUCE} may be used with advantage in tedious
+calculations of supersymmetry and supergravity.}}
+
+@INPROCEEDINGS{Griss:74,
+ AUTHOR = "M. L. Griss",
+ TITLE = "The Algebraic Solution of Large Sparse Systems of Linear
+Equations Using {REDUCE} 2",
+ YEAR = 1974, PAGES = "105-111",
+ BOOKTITLE = "Proc. ACM 74",
+ ABSTRACT = {This paper discusses some of the problems encountered during the
+solution of a large system of sparse linear equations with algebraic
+coefficients, using {REDUCE} 2.}}
+
+@ARTICLE{Griss:74a,
+ AUTHOR = "M. L. Griss",
+ TITLE = "The Algebraic Solution of Sparse Linear Systems Via Minor
+Expansion",
+ JOURNAL = "ACM TOMS 2",
+ YEAR = 1976, PAGES = "31-49",
+ ABSTRACT = {An improved algorithm for computing the determinants of a (large)
+sparse matrix of polynomials is described.}}
+
+@INPROCEEDINGS{Griss:75,
+ AUTHOR = "Martin L. Griss",
+ TITLE = "The {REDUCE} System for Computer Algebra",
+ BOOKTITLE = "Proc. ACM 75",
+ YEAR = 1975, PAGES = "4-5",
+ ABSTRACT = {A brief description of {REDUCE} is presented.}}
+
+@INPROCEEDINGS{Griss:76,
+ AUTHOR = "Martin L. Griss",
+ TITLE = "The Definition and Use of Data-Structures in {REDUCE}",
+ BOOKTITLE = "Proc. SYMSAC 76",
+ YEAR = 1976, PAGES = "53-59",
+ ABSTRACT = {This paper gives a brief description and motivation of the mode
+analyzing and data-structuring extensions to the algebraic language
+{REDUCE}.}}
+
+@INPROCEEDINGS{Griss:76a,
+ AUTHOR = "Martin L. Griss",
+ TITLE = "An Efficient Sparse Minor Expansion Algorithm",
+ BOOKTITLE = "Proc. ACM 76",
+ YEAR = 1976, PAGES = "429-434",
+ ABSTRACT = {An improved algorithm for computing the minors of a (large)
+sparse matrix of polynomials is described, with emphasis on efficiency and
+optimal ordering.  A possible application to polynomial resultant
+computation is discussed.}}
+
+@INPROCEEDINGS{Griss:77,
+ AUTHOR = "Martin L. Griss",
+ TITLE = "Efficient Expression Evaluation in Sparse Minor
+Expansion, Using Hashing and Deferred Evaluation",
+ YEAR = 1977, PAGES = "169-172",
+ BOOKTITLE = "Proc. 10th Hawaii International Conference on
+Systems Sciences, Western Periodicals, Calif.",
+ ABSTRACT = {Efficient computation of the determinant of a matrix with
+symbolic entries using minor expansion requires careful control of expression
+evaluation.  The use of hashing and deferred evaluation to avoid
+excess computation is explored.}}
+
+@ARTICLE{Griss:77a,
+ AUTHOR = "M. L. Griss",
+ TITLE = "Efficient Recursive Minor Expansion",
+ JOURNAL = "ACM TOMS",
+ YEAR = 1977,
+ ABSTRACT = {The use of a "memo" facility to develop an efficient recursive
+minor expansion algorithm (RMEM) is discussed.  The method is simple and
+efficient, and can be implemented as an interesting non-trivial
+recursive procedure.  The method is particularly attractive for
+sparse symbolic matrices, and can also be used to enhance other
+minor expansion methods developed for sparse symbolic matrices.}}
+
+@ARTICLE{Griss:78,
+ AUTHOR = "Martin L. Griss",
+ TITLE = "Using an Efficient Sparse Minor Expansion Algorithm to Compute
+Polynomial Subresultants and the Greatest Common Denominator",
+ JOURNAL = "IEEE Trans on Computers",
+ YEAR = 1978, VOLUME = "C-27", NUMBER = 10, PAGES = "945-950",
+ ABSTRACT = {In this paper, the use of an efficient sparse minor expansion
+method to directly compute the subresultants needed for the {GCD} of two
+polynomials is described.  The sparse minor expansion method (applied
+either to Sylvester's or Bezout's matrix) naturally computes the
+coefficients of the subresultants in the order corresponding to
+a {PRS}, avoiding wasteful recomputation as much as possible.  It is
+suggested that this is an efficient method to compute the Resultant
+and {GCD} of Sparse Polynomials.}}
+
+@INPROCEEDINGS{Griss:78a,
+ AUTHOR = "Martin L. Griss and Robert R. Kessler",
+ TITLE = "{REDUCE}/1700:  A Micro-coded Algebra System",
+ YEAR = 1978, VOLUME = 11, PAGES = "130-138",
+ BOOKTITLE = "Proc. Micro, {IEEE}",
+ ABSTRACT = {In this paper, we report on the status of an ongoing project
+aimed at producing a micro-coded Algebra machine.}}
+
+@ARTICLE{Griss:79,
+ AUTHOR = "Martin L. Griss and Anthony C. Hearn",
+ TITLE = "Portable {LISP} Compiler",
+ JOURNAL = "Software - Practice and Experience", VOLUME = 11,
+ PAGES = "541-605", YEAR = 1979,
+ ABSTRACT = {This paper describes the development of a portable {LISP}
+compiler in the sense that only Standard {LISP} functions are used in its
+definition and the output is a sequence of standard macro calls
+easily implementable on current computers.}}
+
+@TECHREPORT{Griss:79a,
+ AUTHOR = "Martin L. Griss and Robert R. Kessler",
+ TITLE = "A Micro-programmed Implementation of {Standard} {LISP} and
+{REDUCE} on the {Burroughs B1700/B1800} Computer",
+ INSTITUTION = "University of Utah", YEAR = 1979, TYPE = "Report",
+ MONTH = "February",
+ ABSTRACT = {This paper describes the implementation of a microcoded {LISP}
+"machine" (the MTLISP) for the Burroughs B1700/B1800 computers.
+This interpreter supports a complete Standard {LISP} and {REDUCE}
+Algebra system, as well as a variety of experimental {LISP-like}
+systems.}}
+
+@INPROCEEDINGS{Grozin:83,
+ AUTHOR={A. G. Grozin},
+ TITLE={Calculation of one-loop diagrams of {$1 \to 2$} decays with {REDUCE}},
+ BOOKTITLE={Proc. Int. Conf. on Computer Algebra in Theoretical Physics,
+Dubna},
+ YEAR = 1983, PAGES = {226-231},
+  COMMENT = {To appear in Phys. Lett. B}}
+
+@TECHREPORT{Grozin:88,
+ AUTHOR = "A. G. Grozin",
+ TITLE = "Solving Physical Problems with {REDUCE.}  {1. REDUCE}
+Language {2. Classical} Nonlinear Oscillator",
+ INSTITUTION = "Institute of Nuclear Physics 630090, Novosibirsk,
+{USSR}", YEAR = 1988, TYPE = "Preprint", NUMBER = "88-115",
+ ABSTRACT = {This preprint is the first part of the problem book on using
+{REDUCE} in physics.  It contains many examples useful for the
+construction of programs for solving physical problems of very
+different nature.  This part contains examples illustrating {REDUCE}
+language (sect. 1) and the problem of classical nonlinear
+oscillator (sect. 2).  To be published (with additions) as a book with
+"Nauka" publishers, Moscow.}}
+
+@TECHREPORT{Grozin:88a,
+ AUTHOR = "A. G. Grozin",
+ TITLE = "Solving Physical Problems with {REDUCE.}  {3. Nonlinear}
+Water Waves {4. Calculation} of the Curvature Tensor {5. Angular}
+Momentum Addition",
+ INSTITUTION = "Institute of Nuclear Physics 630090, Novosibirsk,
+{USSR}", YEAR = 1988, TYPE = "Preprint", NUMBER = "88-136",
+ ABSTRACT = {This preprint is the second part of the problem book on using
+{REDUCE} in physics.  It contains many examples useful for the construction of
+programs for solving physical problems of very different nature.  This
+part contains the problem of nonlinear water waves (sect. 3), the
+calculation of the curvature tensor (sect. 4) and angular momentum
+addition (sect. 5).}}
+
+@TECHREPORT{Grozin:88b,
+ AUTHOR = "A. G. Grozin",
+ TITLE = "Solving Physical Problems with {REDUCE.}  {6. Quantum}
+Nonlinear Oscillator {7. Rotator} in a Weak Field {8. Radiative}
+Transitions in Charmonium",
+ INSTITUTION = "Institute of Nuclear Physics 630090, Novosibirsk,
+{USSR}", YEAR = 1988, TYPE = "Preprint", NUMBER = "88-140",
+ ABSTRACT = {This preprint is the last part of the problem book on using
+{REDUCE} in physics.  It contains many examples useful for the construction of
+programs for solving physical problems of very different nature.  This
+part contains the problem of quantum nonlinear oscillator (sect. 6),
+rotator in a weak field (sect. 7) and radiative transitions in
+charmonium (sect. 8).}}
+
+@TECHREPORT{Grozin:90,
+ AUTHOR = {A. G. Grozin},
+ TITLE = {{REDUCE} in elementary particle physics. {Introduction}},
+ INSTITUTION = {Institute of Nuclear Physics, Novosibirsk},
+ YEAR = 1990, NUMBER = {INP 90-42},
+ COMMENT = {These 5 preprints together with the previous 3 will be published
+as a book "Solving physical problems with REDUCE"}}
+
+@TECHREPORT{Grozin:90a,
+ AUTHOR = {A. G. Grozin},
+ TITLE = {{REDUCE} in elementary particle physics. {Quantum electrodynamics}},
+ INSTITUTION = {Institute of Nuclear Physics, Novosibirsk},
+ YEAR = 1990, NUMBER = {INP 90-71}}
+
+@TECHREPORT{Grozin:90b,
+ AUTHOR = {A. G. Grozin},
+ TITLE = {{REDUCE} in elementary particle physics. {Quantum chromodynamics}},
+ INSTITUTION = {Institute of Nuclear Physics, Novosibirsk},
+ YEAR = 1990, NUMBER = {INP 90-62}}
+
+@TECHREPORT{Grozin:91,
+ AUTHOR = {A. G. Grozin},
+ TITLE = {{REDUCE} in elementary particle physics. {Weak interactions}},
+ INSTITUTION = {Institute of Nuclear Physics, Novosibirsk},
+ YEAR = 1991, NUMBER = {INP 91-56}}
+
+@TECHREPORT{Grozin:91a,
+ AUTHOR = {A. G. Grozin},
+ TITLE = {{REDUCE} in elementary particle physics. {Radiative corrections}},
+ INSTITUTION = {Institute of Nuclear Physics, Novosibirsk},
+ YEAR = 1991, NUMBER = {INP 91-46}}
+
+@ARTICLE{Gunion:72,
+ AUTHOR = "J. F. Gunion and S. J. Brodsky and R. Blankenbecler",
+ TITLE = "Composite Theory of Large Angle Scattering and New
+Tests of Parton Concepts",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1972, VOLUME = "39B", PAGES = "649-653"}
+
+@TECHREPORT{Gunion:73,
+ AUTHOR = "J. F. Gunion and S. J. Brodsky and R. Blankenbecler",
+ TITLE = "Large Angle Scattering and the Interchange Force",
+ INSTITUTION = "SLAC",
+ YEAR = 1973, TYPE = "Report", NUMBER = "SLAC-PUB-1183"}
+
+@ARTICLE{Gunion:85,
+ AUTHOR = "J. F. Gunion and Z. Kunszt",
+ TITLE = "Improved Analytic Techniques for Tree Graph Calculations and
+the $g g q {\bar q} l {\bar l}$ subprocess",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1985, VOLUME = "161B", PAGES = "333-340"}
+
+@ARTICLE{Hadinger:87,
+ AUTHOR = "G. Hadinger and Y. S. Tergimen",
+ TITLE = "Recurrence Relations for the {Dunham} Coefficients and Analytic
+Expressions of the Diagonal Radial Matrix Elements for an Anharmonic
+Oscillator",
+ JOURNAL = "Journ. Chem. Phys.",
+ YEAR = 1987, VOLUME = 87, NUMBER = 4, PAGES = "2143-2150",
+ COMMENT = {"As an illustrative application, all the set of $Y_{n}$
+coefficients previously published are found again by using the
+computer algebraic manipulation language {REDUCE}.  A number of diagonal
+matrix elements of {CO, HBr and HCl} have been symbolically computed and
+compared with previous available results."  Their method depends on
+some algebraic manipulation, and the main point is that automation
+gives a simpler formulation of the problem.}}
+
+@ARTICLE{Handy:87,
+ AUTHOR = "N. C. Handy",
+ TITLE = "The Derivation of Vibration-Rotation Kinetic Energy Operators,
+in Internal Coordinates",
+ JOURNAL = "Mol. Phys.",
+ YEAR = 1987, VOLUME = 61, PAGES = "207-223",
+ COMMENT = {{REDUCE USED} to produce a straightforward method for the
+derivation of kinetic energy operators in molecular vibration-rotation.  He
+notes in the introduction "The purpose of this paper is to derive a simple and
+straightforward procedure for which it is possible to make the
+computer do all the hard work.  After many years of investigating this
+problem, this author believes that this must be the reliable way to
+proceed."}}
+
+@PHDTHESIS{Harper:87,
+ AUTHOR = "David Harper",
+ TITLE = "Dynamics of the Outer Satellites of Saturn",
+ SCHOOL = "Univ. of Liverpool, England",
+ YEAR = 1987}
+
+@TECHREPORT{Harper:89,
+ AUTHOR = "David Harper and Chris Wooff and David Hodgkinson",
+ TITLE = "A Guide to Computer Algebra Systems",
+ INSTITUTION = "Computer Laboratory, The University of Liverpool,
+Liverpool, England", YEAR = 1989, MONTH = "September", TYPE = "Report"}
+
+@ARTICLE{Harper:89a,
+ AUTHOR = "David Harper",
+ TITLE = "{Vector33:}  A {REDUCE} Program for Vector Algebra and Calculus
+in Orthogonal Curvilinear Coordinates",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1989, VOLUME = 54, NUMBER = "2 and 3", PAGES = "295-305",
+ MONTH = "June and July"}
+
+@ARTICLE{Harrington:77,
+ AUTHOR = "Steven J. Harrington",
+ TITLE = "A Symbolic Limit Evaluation Program in {REDUCE}",
+ YEAR = 1977,
+ ABSTRACT = {A program for the automatic evaluation of algebraic
+limits, implemented in {MODE-REDUCE}, is described.  The program
+incorporates many of the techniques previously employed, including
+the top-down recursive evaluation, power series expansion, and
+L'Hopital's rule.  It also introduces the concept of a special
+algebraic form for limits.}}
+
+@ARTICLE{Harrington:77a,
+ AUTHOR = "S. J. Harrington",
+ TITLE = "{REDUCE} Solution to Problem \#8",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = "1977 and 1978", VOLUME = "11 and 12", NUMBER = "4 and 1",
+ PAGES = "7-8", MONTH = "November and February"}
+
+@ARTICLE{Harrington:79,
+ AUTHOR = "Steven J. Harrington",
+ TITLE = "A New Symbolic Integration System in {REDUCE}",
+ JOURNAL = "Comp. Journ.",
+ YEAR = 1979, VOLUME = 22, NUMBER = 2, PAGE = "127-131",
+ ABSTRACT = {A new integration system, employing both algorithmic and
+pattern match integration schemes is presented.  The organization of the
+system differs from that of earlier programs in its emphasis on the
+algorithmic approach to integration, its modularity, and its ease of
+revision.  The new {Norman-Risch} algorithm and its implementation at the
+University of Cambridge are employed, supplemented by a powerful
+collection of simplification and transformation rules.  The facility for
+user defined integrals and functions is also included.  The program is
+both fast and powerful, and can be easily modified to incorporate
+anticipated developments in symbolic integration.}}
+
+@ARTICLE{Harrington:79a,
+ AUTHOR = "Steven J. Harrington",
+ TITLE = "A Symbolic Limit Evaluation Program in {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1979, VOLUME = 13, NUMBER = 1, PAGES = "27-31", MONTH = "February"}
+
+@ARTICLE{Hartley:91,
+ AUTHOR = "David Hartley and Robin W. Tucker",
+ TITLE = "A Constructive Implementation of the {Cartan-K{\"a}hler} Theory
+of Exterior Differential Systems",
+ JOURNAL = "J. Symb. Comp.",
+ YEAR = 1991, VOLUME = 12, NUMBER = 6, PAGES = "655-667",
+ MONTH = "December",
+ ABSTRACT = {An efficient algorithm for the construction of a regular chain
+of involutive integral elements for a general exterior differential system
+is presented.  It is based upon the existence theorems of the
+{Cartan-}K{"\a}hler theory, and may be used to analyse partial differential
+equations by formulating them as exterior differential systems.}}
+
+@ARTICLE{Hasenfratz:80,
+ AUTHOR = "Anna Hasenfratz and Peter Hasenfratz",
+ TITLE = "The Connection Between the Parameters of Lattice and
+Continuum {QCD}",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1980, VOLUME = "93B", NUMBER = "1,2", PAGES = "165-169",
+ MONTH = "June"}
+
+@INPROCEEDINGS{Hearn:68,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "{REDUCE}: A User-Oriented Interactive System for Algebraic
+Simplification",
+ YEAR = 1968, PAGES = "79-90",
+ EDITOR = "M. Klerer and J. Reinfelds",
+ BOOKTITLE = "Interactive Systems for Experimental Applied Mathematics",
+ PUBLISHER = "Academic Press", ADDRESS = "New York"}
+
+@ARTICLE{Hearn:69,
+ AUTHOR = "A. C. Hearn and P. K. Kuo and D. R. Yennie",
+ TITLE = "Radiative Corrections to an Electron-Positron Scattering
+Experiment",
+ JOURNAL = "Phys. Rev.",
+ YEAR = 1969, VOLUME = 187, PAGES = "2088-2096"}
+
+@INPROCEEDINGS{Hearn:69a,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "The Problem of Substitution",
+ YEAR = 1969, PAGES = "3-19",
+ EDITOR = "R.G. Tobey",
+ BOOKTITLE = "Proc. of the 1968 Summer Institute on Symbolic Mathematical
+Computation",
+ PUBLISHER = "IBM Boston Prog. Center", ADDRESS = "Cambridge, Mass",
+ COMMENT = "IBM Programming Laboratory Report No. FSC-69-0312"}
+
+@ARTICLE{Hearn:71,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "Applications of Symbolic Manipulation in Theoretical Physics",
+ JOURNAL = "Comm. ACM",
+ YEAR = 1971, VOLUME = 14, PAGES = "511-516"}
+
+@INPROCEEDINGS{Hearn:71a,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "{REDUCE} 2: A System and Language for Algebraic Manipulation",
+ YEAR = 1971, PAGES = "128-133",
+ EDITOR = "S.R. Petrick",
+ BOOKTITLE = "Proc. of Second Symposium on Symbolic and
+Algebraic Manipulation",
+ PUBLISHER = "ACM, New York"}
+
+@INPROCEEDINGS{Hearn:71b,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "Calculation of Traces of Products of Gamma Matrices",
+ YEAR = 1971, PAGES = "I-30 - I-44",
+ BOOKTITLE = "Proc. of the Second Colloquium on Advanced Computing
+Methods in Theoretical Physics, {CNRS}, Marseilles",
+ ABSTRACT = {A survey of the algorithms available for the calculation of
+traces of products of Dirac gamma matrices is presented.}}
+
+@INPROCEEDINGS{Hearn:71c,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "The Computer Solution of Algebraic Problems by Pattern Matching",
+ YEAR = 1971, PAGES = "I-45 - I-57",
+ BOOKTITLE = "Proc. of the Second Colloquium on Advanced Computing
+Methods in Theoretical Physics, {CNRS}, Marseilles",
+ ABSTRACT = {This paper discusses computer techniques for the solution of
+algebraic  problems in theoretical physics and related areas by pattern
+matching.}}
+
+@INPROCEEDINGS{Hearn:72,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "Computer Solution of Symbolic Problems in Theoretical Physics",
+ YEAR = 1972, PAGES = "567-596",
+ BOOKTITLE = "Computing as a Language of Physics, {IAEA}, Vienna",
+ ABSTRACT = {A survey of the computing techniques currently available for
+the solution of nonnumerical problems in theoretical physics and related
+areas is presented.}}
+
+@ARTICLE{Hearn:72a,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "Improved Non-modular Polynomial {GCD} Algorithm",
+ JOURNAL = "SIGSAM Bulletin",
+ YEAR = 1972, PAGES = "10-15",
+ ABSTRACT = {An improved non-modular algorithm for the calculation of the
+greatest common divisor of two multivariate polynomials is presented.}}
+
+@ARTICLE{Hearn:72b,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "A {REDUCE} Solution of Problem \#2 - The {Y(2n)} Functions",
+ JOURNAL = "SIGSAM Bulletin",
+ YEAR = 1972, VOLUME = 14,
+ ABSTRACT = {A {REDUCE} solution to {SIGSAM} Problem \#2 is described.}}
+
+@INPROCEEDINGS{Hearn:73,
+ AUTHOR = "Anthony C. Hearn and R{\"u}diger G. K. Loos",
+ TITLE = "Extended Polynomial Algorithms",
+ YEAR = 1973, PAGES = "147-152",
+ BOOKTITLE = "Proc. {ACM} 73",
+ ABSTRACT = {It is shown that standard polynomial algorithms may be
+applied to a much wider class of functions by making a straightforward
+generalization of the concept of the exponent.  The implementation of a
+computer algebra system from a standard set of polynomial programs which
+allows for any coefficient or exponent structure is also discussed.}}
+
+@INPROCEEDINGS{Hearn:73a,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "The {REDUCE} Program for Computer Algebra",
+ YEAR = 1973,
+ BOOKTITLE = "Proc. of the Third Colloquium on Advanced Computing Methods
+in Theoretical Physics, {CNRS}, Marseilles",
+ ABSTRACT = {The status of the {REDUCE} program for computer algebra in 1973
+is illustrated by a discussion of some aspects of its design philosophy.}}
+
+@INPROCEEDINGS{Hearn:74,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = " Polynomial and Rational Function Representations",
+ YEAR = 1974, PAGE = "211",
+ BOOKTITLE = "Proc. Math Software II, Purdue University",
+ ABSTRACT = {A survey of some current methods for computer manipulation of
+polynomials and rational functions is presented.  Particular emphasis
+is placed on the desirability of writing programs which avoid explicit
+reference to the data structures used in the manipulation."}}
+
+@INPROCEEDINGS{Hearn:74a,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "A Mode Analyzing Algebraic Manipulation Program",
+ YEAR = 1974, PAGES = "722-724",
+ BOOKTITLE = "Proc. {ACM} 74",
+ COMMENT = {Describes a version of the {REDUCE} program for algebraic
+manipulation which performs a complete mode analysis as a separate extension
+of the parse.}}
+
+@ARTICLE{Hearn:76,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "Scientific Applications of Symbolic Computation",
+ JOURNAL = "Computer Science and Scientific Comp.",
+ YEAR = 1976, PAGES = "83-108",
+ ABSTRACT = {This paper reviews the use of symbolic computation systems for
+problem solving in scientific research.}}
+
+@INPROCEEDINGS{Hearn:76a,
+ AUTHOR = "A. C. Hearn",
+ TITLE = "A New {REDUCE} Model for Algebraic Simplification",
+ YEAR = 1976, PAGES = "46-52",
+ BOOKTITLE = "Proc. {SYMSAC} 76, {ACM}",
+ ABSTRACT = {This paper shows how the general concepts of mode analysis can
+play a useful role in the design and implementation of programs
+for algebraic simplification.}}
+
+@INPROCEEDINGS{Hearn:76b,
+ AUTHOR = "A. C. Hearn",
+ TITLE = "Symbolic Computation",
+ YEAR = 1976, PAGES = "201-211",
+ BOOKTITLE = "Proc. {CERN} 1976 Computing School, {CERN} Geneva",
+ COMMENT = {Lecture Notes.}}
+
+@INPROCEEDINGS{Hearn:77,
+ AUTHOR = "A. C. Hearn",
+ TITLE = "The Structure of Algebraic Computations",
+ YEAR = 1977, PAGES = "1-15",
+ BOOKTITLE = "Proc. of the Fourth Colloquium on Advanced Comp.
+Methods in Theor. Physics. St. Maximin, France",
+ ABSTRACT = {Most algebraic computations which arise from physical problems
+have considerable structure in their specification because of the many
+physical conservation laws and the nature of our approximation techniques.
+The exploitation of this structure is often the reason why hand
+calculations of non-trivial problems are possible.  However, most
+available algebra systems do not preserve such structure in a consistent
+manner, and consequently produce results which are far less comprehensible
+than equivalent hand calculations.  In this paper we shall describe
+techniques which can utilize the algebraic structure more effectively and
+apply them to several examples.}}
+
+@INPROCEEDINGS{Hearn:78,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "Algebraic Manipulation by Computer",
+ YEAR = 1978, PAGES = "96-116",
+ BOOKTITLE = "Proc. Intern. Meeting on Programm. and Math. Meth. for
+Solving Phys. Probs., Dubna, USSR",
+ ABSTRACT = {This paper reviews the use of algebraic manipulation by computer
+as a tool for scientific problem solving.}}
+
+@INPROCEEDINGS{Hearn:79,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "Non-Modular Computation of Polynomial {GCDs} Using Trial
+Division",
+ YEAR = 1979, VOLUME = 72, PAGES = "227-239",
+ BOOKTITLE = "Proc. {EUROSAM} 79",
+ ABSTRACT = {This paper describes a new algorithm for the determination of
+the {GCD} of two multivariate polynomials by non-modular means.}}
+
+@ARTICLE{Hearn:79a,
+ AUTHOR = "Anthony C. Hearn and Arthur C. Norman",
+ TITLE = "A One-Pass Prettyprinter",
+ JOURNAL = "Sigplan Notices, ACM 12",
+ YEAR = 1979, VOLUME = 14, PAGES = "50-58",
+ ABSTRACT = {We propose a new method for program formatting which is
+described in terms of two coroutines.}}
+
+@INPROCEEDINGS{Hearn:80,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "The Personal Algebra Machine",
+ YEAR = 1980, PAGES = "621-628",
+ BOOKTITLE = "Information Processing 80, Proc. {IFIP}
+Congress 80"}
+
+@ARTICLE{Hearn:81,
+ AUTHOR = "Anthony C. Hearn and S. Watanabe",
+ TITLE = "Analytic Integration by Computer",
+ JOURNAL = "Information Processing Society of Japan 22",
+ YEAR = 1981, PAGES = "639-650"}
+
+@INPROCEEDINGS{Hearn:81a,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "Symbolic Computation and its Application to
+High-Energy Physics",
+ YEAR = 1981, PAGES = "390-406",
+ BOOKTITLE = "Proc. 1980 {CERN} School of Computing, Geneva"}
+
+@INPROCEEDINGS{Hearn:82,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "{REDUCE} - A Case Study in Algebra System Development",
+ YEAR = 1982, VOLUME = 144, PAGES = "263-272",
+ BOOKTITLE = "Proc. of {EUROCAM} '82, Lecture Notes on Comp.
+Science"}
+
+@INPROCEEDINGS{Hearn:82a,
+ AUTHOR = "Anthony C. Hearn and M. L. Griss and E. Benson",
+ TITLE = "Current Status of a Portable {LISP} Compiler",
+ YEAR = 1982,
+ BOOKTITLE = "Proc. {SIGPLAN} '82 Symp. on Compiler
+Construction, ACM", PAGES = "276-283"}
+
+@INPROCEEDINGS{Hearn:85,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "Structure:  The Key to Improved Algebraic Computation",
+ YEAR = 1985,
+ BOOKTITLE = "Proc. of the Second {RIKEN} International
+Symposium on Symbolic and Algebraic Computation by Computers",
+ PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "215-230"}
+
+@INPROCEEDINGS{Hearn:86,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "Optimal Evaluation of Algebraic Expressions",
+ BOOKTITLE = "Proc. {AAECC}-3, Lecture Notes on Comp. Science",
+ PUBLISHER = "Springer Verlag",
+ YEAR = 1986, VOLUME = 229, PAGES = "392-403"}
+
+@TECHREPORT{Hearn:91,
+ AUTHOR = "Anthony C. Hearn",
+ TITLE = "{REDUCE} User's Manual, {Version} 3.6",
+ INSTITUTION = "RAND",
+ YEAR = 1995, TYPE = "Report",
+ NUMBER = "CP 78", MONTH = "July"}
+
+@INPROCEEDINGS{Hearn:93,
+ AUTHOR = "Anthony C. Hearn and Eberhard Schr{\"u}fer",
+ TITLE = "An Order-sorted Approach to Algebraic Computation",
+ BOOKTITLE = "Proc. {DISCO '93}, Lecture Notes on Comp. Science",
+ YEAR = 1993, VOLUME = 722, PAGES = "134-144",
+ PUBLISHER = "Springer-Verlag",
+ ABSTRACT = {This paper presents the prototype design of an algebraic
+computation system that manipulates algebraic quantities as generic objects
+using order-sorted algebra as the underlying model.  The resulting programs
+have a form that is closely related to the algorithmic description of a
+problem, but with the secruity of full type checking in a compact, natural
+style.}}
+
+@ARTICLE{Hearn:95,
+ AUTHOR = "Anthony C. Hearn and Eberhard Schr{\"u}fer",
+ TITLE = "A Computer Algebra System based on Order-sorted Algebra",
+ JOURNAL = "Journ. Symbolic Computation",
+ YEAR = 1995, VOLUME=19, PAGES = "65-77",
+ ABSTRACT = "This paper presents the prototype design of an algebraic
+computation system that manipulates algebraic quantities as generic
+objects using order-sorted algebra as the underlying model.  The resulting
+programs have a form that is closely related to the algorithmic
+description of a problem, but with the security of full type checking in a
+compact, natural style."}
+
+@ARTICLE{Hehl:92,
+ AUTHOR = "Friedrich W. Hehl and Hartmut Meyer",
+ TITLE = "Mit Buchstaben auf dem Computer rechnen",
+ JOURNAL = "Physikalische {Bl\"{a}tter}",
+ YEAR = 1992, VOLUME = "48", PAGES = "377-381",
+ COMMENT = {(in German) Describes the application of
+ symbolic computation using examples coded in {REDUCE}. The CA systems
+ of interest for physicists are classified. A series of problems
+ from physics which have successfully been solved with CA methods
+ is given}}
+
+@BOOK{Hehl:92a,
+ AUTHOR = "F.W. Hehl and V. Winkelmann and H. Meyer",
+ TITLE = "Computer-Algebra. Ein Kompaktkurs {\"{u}ber} die Anwendung von
+REDUCE",
+ PUBLISHER = "Springer-Verlag, Berlin, Heidelberg, New York,
+   ISBN 3-540-55724-5",
+ YEAR = 1992}
+
+@ARTICLE{Hermann:83,
+ AUTHOR = "R. Hermann",
+ TITLE = "Geometric Construction and Properties of Some Families of
+Solutions of Nonlinear Partial Differential Equations",
+ JOURNAL = "J. Math. Phys.",
+ YEAR = 1983,  VOLUME = 24, NUMBER = "3", PAGES = "510-521",
+ COMMENT = {First of series of papers on 19th century pde theory.  The
+presentation is aimed at including systems such as {MACSYMA} and {REDUCE}
+as tools.  This paper is on Lagrange-Charpit method. "I have in mind
+developing the differential algebraic aspects of the formalism, going
+beyond the 19th century with the aid of symbolic computer systems".}}
+
+@ARTICLE{Hess:84,
+ AUTHOR = "P. O. Hess and W. Greiner",
+ TITLE = "The Collective Modes of Nuclear Molecules",
+ JOURNAL = "Il Nuovo Cimento",
+ YEAR = 1984, VOLUME = "83A", PAGES = "76-177",
+ COMMENT = {A long paper, admits use of {REDUCE} (on page 101) to invert
+11 x 11 matrix.}}
+
+@TECHREPORT{Hettich:77,
+ AUTHOR = "R. P. Hettich and J. A. van Hulzen",
+ TITLE = "Approximation with a Class of Rational Functions",
+ INSTITUTION = "Department of Applied Mathematics, Twente
+University of Technology, The Netherlands",
+ YEAR = 1977, TYPE = "Memorandum",
+ NUMBER = 165, MONTH = "May"}
+
+@ARTICLE{Hietarinta:83,
+ AUTHOR = "J. Hietarinta",
+ TITLE = "A search for integrable two-dimensional {Hamiltonian} systems
+with polynomial potential",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1983, VOLUME = "96A", PAGES = "273-278",
+ COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
+
+@ARTICLE{Hietarinta:83a,
+ AUTHOR = "J. Hietarinta",
+ TITLE = "Integrable Families of {Henon-Heiles} Type {Hamiltonians} and a
+New Duality",
+ JOURNAL = "Phys. Rev. A",
+ YEAR = 1983, VOLUME = 28, PAGES = "3670-3672",
+ COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
+
+@ARTICLE{Hietarinta:84,
+ AUTHOR = "J. Hietarinta",
+ TITLE = "Classical versus quantum integrability",
+ JOURNAL = "J. Math. Phys.",
+ YEAR = 1984, VOLUME = 25, PAGES = "1833-1840",
+ COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
+
+@ARTICLE{Hietarinta:84a,
+ AUTHOR = "J. Hietarinta",
+ TITLE = "New integrable {Hamiltonians} with transcendental invariants",
+ JOURNAL = "Phys. Rev. Lett.",
+ YEAR = 1984, VOLUME = 52, PAGES = "1057-1060",
+ COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
+
+@ARTICLE{Hietarinta:84b,
+ AUTHOR = "J. Hietarinta and B. Grammaticos and B. Dorizzi and A. Ramani",
+ TITLE = "Coupling-Constant Metamorphosis and Duality between
+Integrable {Hamiltonian} Systems",
+ JOURNAL = "Phys. Rev. Lett.",
+ YEAR = 1984, VOLUME = 53, PAGES = "1707-1710",
+ COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
+
+@ARTICLE{Hietarinta:85,
+ AUTHOR = "J. Hietarinta",
+ TITLE = "How to construct integrable {Fokker-Planck} and
+electromagnetic {Hamiltonians} from ordinary integrable {Hamiltonians}",
+ JOURNAL = "J. Math. Phys.",
+ YEAR = 1985, VOLUME = 26, PAGES = "1970-1975",
+ COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
+
+@ARTICLE{Hietarinta:87,
+ AUTHOR = "J. Hietarinta",
+ TITLE = "Direct methods for the search of the second invariant",
+ JOURNAL = "Physics Reports",
+ YEAR = 1987, VOLUME = 147, PAGES = "87-154",
+ COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
+
+@ARTICLE{Hietarinta:87a,
+ AUTHOR = "J. Hietarinta",
+ TITLE = "A search of bilinear equations passing {Hirota's} three-soliton
+condition: {I.} {KdV}-type bilinear equations",
+ JOURNAL = "J. Math. Phys.",
+ YEAR = 1987, VOLUME = 28, PAGES = "1732-1742",
+ COMMENT = {{REDUCE} is used to check when polynomials in 6 to 12 variables
+vanish on a affine manifold defined by {LET-rules}.  Large scale
+computation.}}
+
+@ARTICLE{Hietarinta:87b,
+ AUTHOR = "J. Hietarinta",
+ TITLE = "A search of bilinear equations passing {Hirota's} three-soliton
+condition: {II.} {mKdV}-type bilinear equations",
+ JOURNAL = "J. Math. Phys.",
+ YEAR = 1987, VOLUME = 28, PAGES = "2094-2101",
+ COMMENT = {{REDUCE} is used to check when polynomials in 6 to 12 variables
+vanish on a affine manifold defined by {LET-rules}.  Large scale
+computation.}}
+
+@ARTICLE{Hietarinta:87c,
+ AUTHOR = "J. Hietarinta",
+ TITLE = "A search of bilinear equations passing {Hirota's} three-soliton
+condition: {III.} {Sine-Gordon}-type bilinear equations",
+ JOURNAL = "J. Math. Phys.",
+ YEAR = 1987, VOLUME = 28, PAGES = "2586-2592",
+ COMMENT = {{REDUCE} is used to check when polynomials in 6 to 12 variables
+vanish on a affine manifold defined by {LET-rules}.  Large scale
+computation.}}
+
+@ARTICLE{Hietarinta:88,
+ AUTHOR = "J. Hietarinta",
+ TITLE = "A search of bilinear equations passing {Hirota's} three-soliton
+condition: {IV.} Complex bilinear equations",
+ JOURNAL = "J. Math. Phys.",
+ YEAR = 1988, VOLUME = 29, PAGES = "628-635",
+ COMMENT = {{REDUCE} is used to check when polynomials in 6 to 12 variables
+vanish on a affine manifold defined by {LET-rules}.  Large scale computation.
+computation.}}
+
+@ARTICLE{Hietarinta:89,
+ AUTHOR = "J. Hietarinta and B. Grammaticos",
+ TITLE = "On the $\hbar^{2}$-correction terms in quantum integrability",
+ JOURNAL = "J. Phys. A: Mat. Gen.",
+ YEAR = 1989, VOLUME = "TBD", PAGES = "TBD",
+ COMMENT = {{REDUCE} is used to construct and verify constants of motion.}}
+
+@INPROCEEDINGS{Hietarinta:91,
+ AUTHOR = "J. Hietarinta",
+ TITLE = "From an analytical formula to a movie by way of {REDUCE} and {C}",
+ BOOKTITLE = "Proc. of the Workshop on Symbolic and Numeric Computation",
+ PUBLISHER = "Research Reports, Computing Centre of Helsinki University",
+ YEAR = 1991, PAGES = "117-126"}
+
+@TECHREPORT{Hietarinta:92,
+ AUTHOR = "Jarmo Hietarinta",
+ TITLE = "Solving the {Yang-Baxter} equation in 2 dimensions with massive
+use of factorizing Gr{"\o}bner basis computations",
+ INSTITUTION = "University of Turku, Finland", YEAR = 1992,
+ MONTH = "January", TYPE = "Preprint",
+ COMMENT = {Submitted to ISSAC '92},
+ ABSTRACT = {The complete solution to the constant (quantum) Yang-Baxter
+equation was recently obtained in the two dimensional case
+(= all indices range over 1,2).  This amounts to solving a set of 64
+equations in 16 variables.  We describe here how the problem was solved,
+first by breaking it into smaller subproblems by using the symmetries of
+the equation, and then by solving each subproblem by computing the
+factorized Gr{"\o}bner basis using the {'grobner'-}package written by Melenk,
+M{"\o}ller and Neun for REDUCE 3.4.}}.
+
+@TECHREPORT{Hietarinta:92a,
+ AUTHOR = "Jarmo Hietarinta",
+ TITLE = "Solving the two-dimensional constant quantum {Yang-Baxter}
+  equation",
+ INSTITUTION = "University of Turku, Finland", YEAR = 1992,
+ MONTH = "May", TYPE = "Report", NUMBER = "TURKU-FL-R7"}
+
+@BOOK{Hirota:89,
+ AUTHOR = "Ryogo Hirota and Masaaki Ito",
+ TITLE = "Introduction to {REDUCE --- Doing} Symbolic Computation on {PC}",
+ PUBLISHER = "Science sha, Tokyo", MONTH = "June", YEAR = 1989,
+ COMMENT = {(In Japanese).}}
+
+@TECHREPORT{Horowitz:75,
+ AUTHOR = "E. Horowitz and D. R. Musser",
+ TITLE = "The Synthesis and Use of Algebraic Specifications of Data
+Structures",
+ INSTITUTION = "University of Southern California",
+ YEAR = 1975, TYPE = "Preprint"}
+
+@ARTICLE{Horwitz:83,
+ AUTHOR = "B. Horwitz",
+ TITLE = "Unequal Diameters and Their Effects on Time Varying Voltages
+in Branched Neurons",
+ JOURNAL = "BioPhys. J.",
+ YEAR = 1983, VOLUME = 41, PAGES = "51-66",
+ COMMENT = {Theoretical biophysics.  Much algebra, and used {REDUCE} to
+decrease mental labor.  "Crucial point is that the existence of such computer
+techniques allows higher-order correction terms to be used."}}
+
+@ARTICLE{Hughes:90,
+ AUTHOR = "D. I. Hughes",
+ TITLE = "Symbolic Computation with Fermions",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1990, VOLUME = 10, NUMBER = 6, PAGES = "657-664", MONTH = "December",
+ ABSTRACT = {A set of {REDUCE} routines for manipulating operators which
+anticommute amongst themselves is described.  These routines have
+applications in theories such as supergravity where anticommuting operators
+are used to represent fermions.  The Dirac bracket of the supersymmetry
+constraints arising in a quantum cosmological model based on N = 1
+supergravtiy coupled to a massless scalar multiplet is calculated as an
+example.}}
+
+@INPROCEEDINGS{Hulshof:84,
+ AUTHOR = "B. J. A. Hulshof and J. A. van Hulzen",
+ TITLE = "Automatic Error Cumulation Control",
+ BOOKTITLE = "Proc. {EUROSAM} 1984, Lecture Notes
+in Computer Science", YEAR = 1984, VOLUME = 174, PAGES = "260-271",
+ PUBLISHER = "Springer-Verlag"}
+
+@INPROCEEDINGS{Hulshof:85,
+ AUTHOR = "B. J. A. Hulshof and J. A. van Hulzen",
+ TITLE = "An Expression Compression Package for {REDUCE} based on
+Factorization and Controlled Expansion",
+ BOOKTITLE = "Proc. {EUROCAL} 1985, Lecture Notes
+in Computer Science", YEAR = 1985, VOLUME = 204, PAGES = "315-316",
+ PUBLISHER = "Springer-Verlag"}
+
+@TECHREPORT{Hulshof:81,
+ AUTHOR = "B. J. A. Hulshof and J. A. van Hulzen and J. Smit",
+ TITLE = "Code Optimization Facilities Applied in the {Netform} Context",
+ INSTITUTION = "Department of Applied Mathematics, Twente
+University of Technology, The Netherlands",
+ YEAR = 1981, TYPE = "Memorandum", NUMBER = 368,
+ MONTH = "December"}
+
+@ARTICLE{Hulshof:83,
+ AUTHOR = "B. J. A. Hulshof and J. A. van Hulzen",
+ TITLE = "Some {REDUCE} Facilities for Pretty Printing Subscripts and Formal
+Derivatives",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "16-20", MONTH = "February"}
+
+@ARTICLE{Hunt:91,
+ AUTHOR = "R. E. Hunt and D. G. Crighton",
+ TITLE = "Instability of flows in spatially developing media",
+ JOURNAL = "Proc. Roy. Soc. Lond. A",
+YEAR = 1991, VOLUME = 435, PAGES = "109-128",
+ COMMENT = {Uses {REDUCE} to find series solutions for two fluid-dynamical
+  problems, and then condenses the series into exact solutions}}
+
+@TECHREPORT{Husberg:81,
+ AUTHOR = "N. Husberg",
+ TITLE = "Preliminary {II} {REDUCE}-2 and {Analitik-74}, a Comparison",
+ INSTITUTION = "Helsinki University of Technology Computing
+Center", YEAR = 1981, MONTH = "November"}
+
+%                          REDUCE BIBLIOGRAPHY
+
+%                              Part 3:  I-O
+
+% Copyright (c) 1993 RAND.  All Rights Reserved.
+
+% Additions and corrections are solicited.  Please send them, in the
+% same format as these entries if possible, to reduce at rand.org.
+
+
+@TECHREPORT{Idesawa:77,
+ AUTHOR = "M. Idesawa and T. Yatagai",
+ TITLE = "General Theory of Projection-Type {Moir\'e} Topography",
+ INSTITUTION = "Institute of Physical and Chemical Research,
+Wako-Shi, Saitama", YEAR = 1977, TYPE = "Scientific Papers",
+ NUMBER = 71,
+ ABSTRACT = {The configuration of equi-order surfaces in the projection-type
+{Moire} topography is described in terms of system parameters
+without any restrictions on the measurement condition.}}
+
+@INPROCEEDINGS{Ilyin:87,
+ AUTHOR = "V. A. Ilyin and A. P. Kryukov",
+ TITLE = "{DIMREG} - The Package for Calculations in the Dimensional
+Regularization with {4-dimensional} $\gamma^{5}$ -matrix in Quantum Field
+Theory",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "225-232",
+ PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{Ilyin:89,
+ AUTHOR = "V. A. Ilyin and A. P. Kryukov and A. Ya. Rodioniov and
+A. Yu. Taranov",
+ TITLE = "Fast Algorithm for Calculation of {Dirac}'s Gamma-Matrices Traces",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1989, VOLUME = 23, NUMBER = 4, PAGES = "15-24", MONTH = "October"}
+
+@INPROCEEDINGS{Ilyin:91,
+ AUTHOR = "V. A. Ilyin and A. P. Kryukov",
+ TITLE = "Symbolic Simplification of Tensor Expressions Using Symmetries,
+Dummy Indices and Identities",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ EDITOR = "Stephen M. Watt",
+ PUBLISHER = "ACM Press", ADDRESS = "Maryland", PAGES = "224-228",
+ YEAR = 1991,
+ ABSTRACT = {The algorithm based on simple geometrical ideas is suggested
+for simplification of tensor expressions which takes into account
+symmetries, dummy indices, and linear identities with many terms.  The
+results of the realization in REDUCE system are adduced.}}
+
+@INPROCEEDINGS{Ilyin:91a,
+ AUTHOR = "V. A. Ilyin and A. P. Kryukov and A. Ya. Rodionov and A Yu.
+Taranov",
+ TITLE = "{PC} Implementation of Fast {Dirac} Matrix Trace Calculations",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ EDITOR = "Stephen M. Watt",
+ PUBLISHER = "ACM Press", ADDRESS = "Maryland", PAGES = "456-457",
+ YEAR = 1991,
+ COMMENT = {We present an implementation of fast algorithm for Dirac
+matrix trace calculations.  This implementation is made for {IBM}       i
+compatible {PC} and works under {REDUCE 3.3.1}.  Name of package is
+{CVIT}.  The algorithm itself was described in [1].  It is based on intense
+use of Fierz identities in N-dimensional space (N is arbitrary natural
+number or symbol) and may be considered as an extension of well known
+Kahane algorithm [2] on higher space dimensions.}}
+
+@TECHREPORT{Inada:80,
+ AUTHOR = "Nobuyuki Inada",
+ TITLE = "Fortran-Based {LISP} System for {REDUCE}",
+ INSTITUTION = "Information Science Laboratory, The Institute
+of Physical and Chemical Research",
+ YEAR = 1980}
+
+@TECHREPORT{Ioakimidis:90,
+ AUTHOR = "N. I. Ioakimidis",
+ TITLE = "Construction of the Equation of Caustics in Dynamic Plane
+Elasticity Problems with the Help of {REDUCE}",
+ INSTITUTION = "Division of Applied Mathematics and Mechanics, School of
+Engineering, University of Patras, Greece",
+ YEAR = 1990}
+ ABSTRACT = {The method of caustics has become a very efficient tool in
+crack, hole and many additional plane elasticity problems.  Unfortunately,
+the fundamental equation of the caustics frequently requires complicated
+algebraic computations including that of a Jacobian determinant.  Here we
+show that computer algebra software can prove very efficient in these
+computations, using as a vehicle for this illustration the already known
+fundamental equation of caustics in dynamic plane elasticity (both for crack
+problems in fracture mechanics as well as for hole and additional problems).
+We have used the programming capabilities of {REDUCE}, a very popular
+computer algebra system, for our algebraic computations.  Moreover, we
+illustrate the "learning" abilities of {REDUCE} especially for the
+derivation of the complex form of this equation.  The case of static plane
+elasticity results simply as a special case of dynamic plane elasticity.
+Additional possibilities are suggested in brief.}}
+
+@TECHREPORT{Ioakimidis:90a,
+ AUTHOR = "N. I. Ioakimidis",
+ TITLE = "Construction of Singular Integral Equations for Interacting
+Straight Cracks by Using {REDUCE}",
+ INSTITUTION = "Division of Applied Mathematics and Mechanics, School of
+Engineering, University of Patras, Greece",
+ YEAR = 1990}
+ ABSTRACT = {The method of singular integral equations has been applied to
+the solution of crack problems in plane and antiplane elasticity
+hundreds of times during the last twenty years.  Here we revisit the case of
+an arbitrary number of interacting straight cracks in plane elasticity and
+we illustrate the possibility of constructing (algebraically) the
+corresponding system of singular integral equations by using computer
+algebra software.  We present a procedure (computer program) by using
+{REDUCE} as well as several examples of application of the present approach,
+extensions and generalizations of which follow rather trivially.}}
+
+@ARTICLE{Ito:85,
+ AUTHOR = "M. Ito",
+ TITLE = "A {REDUCE} Program for Evaluating a {Lax} Pair Form",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1985, VOLUME = 34, PAGES = "325-331",
+ COMMENT = {{REDUCE} in nonlinear equations.}}
+
+@ARTICLE{Ito:85a,
+ AUTHOR = "M. Ito and F. Kako",
+ TITLE = "A {REDUCE} Program for Finding Conserved Densities of Partial
+Differential Equations with Uniform Rank",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1985, VOLUME = 38, PAGES = "415-419"}
+
+@ARTICLE{Ito:88,
+ AUTHOR = "Masaaki Ito",
+ TITLE = "A {REDUCE} Program for {Hirota's} Bilinear Operator and
+{Wronskian} Operations",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1988, VOLUME = 50, NUMBER = 3, PAGES = "321-330", MONTH = "August"}
+
+@ARTICLE{Ito:90,
+ AUTHOR = "Nobuyasu Ito and Tetsuhiko Chikyu",
+ TITLE = "Multi-Spin-Flip Dynamics of the {Ising} Chain",
+ JOURNAL = "Physica A",
+ YEAR = 1990, VOLUME = 166, PAGES = "193-205",
+ ABSTRACT = {Two kinds of multi-spin-flip discrete-time dynamics of the
+Ising chain are solved analytically.  One dynamics is the two sublattice
+type flip and each sublattice contains {\em n} sequential spins
+alternately.  The other has the overlapped multi-spin-flip sequence.  The
+state of {\em n} spins at the next time step is selected from ${2}^{n}$
+states using the heat-bath type transition probability.  These dynamics of
+the Ising chain are equivalent to the statics of the square-lattice Ising
+model with a 1 x 2 unit cell or of the triangular-lattice Ising model.
+The analytic solutions of the single spin relaxation time of these
+dynamics are obtained using these equivalences.}}
+
+@ARTICLE{Ito:90a,
+ AUTHOR = "Nobuyasu Ito",
+ TITLE = "Discrete-Time and Single-Spin-Flip Dynamics of the {Ising} Chain",
+ JOURNAL = "Progress of Theoretical Physics",
+ YEAR = 1990, VOLUME = 83, NUMBER = 4, PAGES = "682-692", MONTH = "April",
+ ABSTRACT = {Some stochastic dynamics of the Ising chain are discussed
+analytically and their flip-sequence dependences are studied in the
+present paper.  The dynamics are the discrete-time and single-spin-flip
+dynamics.  The flip sequence is of sequential or sublattice-type.  Their
+relaxation times of single spin expectation functions are calculated.  The
+sequential-flip dynamics of {\em n}-site chain has the same correlation
+time as the {\em n}-sublattice dynamics.  The relaxation becomes slow when
+this {\em n} is made large.  The static models equivalent to these dynamic
+models are the Ising models on a triangular lattice with a skew boundary
+condition which has the same couplings in two directions.  Spin-spin
+correlation lengths in the direction perpendicular to the anisotropic
+direction are obtained for these equivalent models.  They depend only on
+the ratio of the lattice width to boundary skew.}}
+
+@ARTICLE{Ito:94,
+ AUTHOR = "Masaaki Ito",
+ TITLE = "{SYMCD} - a {REDUCE} package for finding symmetries and conserved
+densitites of systems of nonlinear evolution equations",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1994, VOLUME = 79, NUMBER = 3, PAGES = "547-554", MONTH = "May"}
+
+@ARTICLE{Jansen:86,
+ AUTHOR = "Paul Jansen and Peter Weidner",
+ TITLE = "High-Accuracy Arithmetic Software--Some Tests of the
+{ACRITH} Problem-Solving Routines",
+ JOURNAL = "{ACM} {TOMS}",
+ YEAR = 1986, VOLUME = 12, NUMBER = 1, PAGES = "62-70", MONTH = "March",
+ COMMENT = {A criticism of {ACRITH}, shows {REDUCE} bigfloats are more
+accurate and comparable in speed.}}
+
+@ARTICLE{Janssen:87,
+ AUTHOR = "M. H. M. Janssen and D. H. Parker and S. Stolte",
+ TITLE = "Saturation in Laser-Induced Fluorescence:  Effects on
+Alignment Parameters",
+ JOURNAL = "Chemical Phys.",
+ YEAR = 1987, VOLUME = 113, PAGES = "357-382",
+ COMMENT = {"Computer algebra programs are used to generate simple analytical
+expressions which account for the influence of saturation on
+determining alignment parameters."  The system is {REDUCE}.}}
+
+@ARTICLE{Jeffrey:84,
+ AUTHOR = "D. J. Jeffrey and Y. Onishi",
+ TITLE = "The Forces and Couples Acting on Two Nearly Touching Spheres
+in Low-{Reynolds}-Number Flow",
+ JOURNAL = "Z. Ang. Math. Phys.",
+ YEAR = 1984, VOLUME = 35, PAGES = "634-641",
+ COMMENT = {Extends previous result from linear term to
+O$\epsilon$ in $\epsilon$.  "Otherwise the only new principle in the
+calculation is the handling of long algebraic expressions, which was
+accomplished by using the computer algebra systems {CAMAL} and {REDUCE}."}}
+
+@ARTICLE{Kadlecsik:88,
+ AUTHOR = "J. Kadlecsik",
+ TITLE = "New Approaches to the Axisymmetric Vacuum",
+ JOURNAL = "Zeitschrift {f\"{u}r} Physik C. Particles and Fields",
+ YEAR = 1988, VOLUME = 41, PAGES = "265-269"}
+
+@TECHREPORT{Kadlecsik:92,
+ AUTHOR = "Jo{\'o}zsef Kadlecsik",
+ TITLE = "Tensor Manipulation Package for General Relativity Calculations",
+ INSTITUTION = "Central Research Institute for Physics, Budapest",
+ YEAR = 1992, TYPE = "Preprint", NUMBER = "KFKI-1992-05/B+M",
+ ABSTRACT = {An experimental computer program is presented, which manipulates
+tensor expressions symbolically in general relativity calculations.}}
+
+@ARTICLE{Kagan:85,
+ AUTHOR = "Y. Y. Kagan and L. Knopoff",
+ TITLE = "The First-Order Statistical Moment of the Seismic Moment Tensor",
+ JOURNAL = "Geophys. J. R. Astron. Soc.",
+ YEAR = 1985, VOLUME = 81, PAGES = "429-444"}
+
+@ARTICLE{Kagan:88,
+ AUTHOR = "Y. Y. Kagan",
+ TITLE = "Static Sources of Elastic Deformation in a Homogeneous
+Half-Space",
+ JOURNAL = "J. Geophys. Res.",
+ YEAR = 1988, VOLUME = 93, NUMBER = "B9", PAGES = "10,560-10,574",
+ MONTH = "September"}
+
+@TECHREPORT{Kahn:69,
+ AUTHOR = "M. E. Kahn",
+ TITLE = "The Near-Minimum-Time Control of Open Loop Articulated
+Kinematic Chains",
+ INSTITUTION = "Stanford University, Computer Science Dept.",
+ YEAR = 1969, TYPE = "Report", NUMBER = "AIM-106"}
+
+@TECHREPORT{Kamal:81,
+ AUTHOR = "A. N. Kamal and J. Kodaira and T. Muta",
+ TITLE = "Gluon Jets From Heavy Paraquarkonium",
+ INSTITUTION = "University of Alberta, Canada and Stanford
+University, California and  Fermi National Accelerator
+Laboratory, Illinois",
+ YEAR = 1981, NUMBER = "SLAC-PUB-2725", MONTH = "April"}
+
+@TECHREPORT{Kamel:69,
+ AUTHOR = "A. A. Kamel",
+ TITLE = "Perturbation Method in the Theory of Non-Linear Oscillations",
+ INSTITUTION = "Stanford University, Dept. of Aeronautics
+and Astronautics", YEAR = 1969, TYPE = "Report"}
+
+@TECHREPORT{Kamel:69a,
+ AUTHOR = "A. A. Kamel",
+ TITLE = "Perturbation Theory Based on {Lie} Transforms and Its
+Application to the Stability of Motion Near {Sun}-Perturbed
+{Earth-Moon} Triangular Libration Points",
+ INSTITUTION = "Stanford University, Dept. of Aeronautics and
+Astronautics", YEAR = 1969, TYPE = "Report", NUMBER = "391"}
+
+@INPROCEEDINGS{Kamel:78,
+ AUTHOR = "A. A. Kamel",
+ TITLE = "Synchronous Satellite Ephemeris Due to Earth's
+Triaxiality and Luni-Solar Effects",
+ YEAR = 1978, MONTH = "August",
+ BOOKTITLE = "{AIAA/AAS} Astrodynamics Conference,
+Palo Alto, CA",
+ COMMENT = {Synchronous satellite ephemeris is developed in terms of
+non-singular orbital elements.}}
+
+@ARTICLE{Kanada:81,
+ AUTHOR = "Yasumasa Kanada and Tateaki Sasaki",
+ TITLE = "{LISP-based} {big-float} system is not slow",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1981, VOLUME = 15, NUMBER = 2, PAGES = "13-19", MONTH = "May"}
+
+@TECHREPORT{Kanada:75,
+ AUTHOR = "Y. Kanada",
+ TITLE = "Implementation of {HLISP} and Algebraic Manipulation
+Language {REDUCE} 2",
+ INSTITUTION = "University of Tokyo Information Science Lab",
+ YEAR = 1975, TYPE = "Report", NUMBER = "75-01"}
+
+@ARTICLE{Kaneko:89,
+ AUTHOR = "Toshiaki Kaneko and Setsuya Kawabata",
+ TITLE = "A Preprocessor for {Fortran} Source Code Produced by {REDUCE}",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1989, VOLUME = 55, NUMBER = 2, PAGES = "141-147",
+ MONTH = "September", PUBLISHER = "North Holland Publishing Company"}
+
+@ARTICLE{Kaps:85,
+ AUTHOR = "P. Kaps and S. W. H. Poon and T. D. Bui",
+ TITLE = "Rosenbrock Methods for Stiff {ODEs}:  A Comparison of {Richardson}
+Extrapolation and Embedding Techniques",
+ JOURNAL = "Computing",
+ YEAR = 1985, VOLUME = 34, PAGES = "17-40",
+ COMMENT = {Reference to {REDUCE} but not in text.}}
+
+@INPROCEEDINGS{Karr:85,
+ AUTHOR = "Michael Karr",
+ TITLE = "Canonical Form for Rational Exponential Expressions",
+ BOOKTITLE = "Proc. {EUROCAL} 1985, Lecture Notes
+in Computer Science", YEAR = 1985, VOLUME = 204, PAGES = "585-594",
+ PUBLISHER = "Springer-Verlag"}
+
+@INPROCEEDINGS{Katsura:85,
+ AUTHOR = "Shigetoshi Katsura",
+ TITLE = "Application of the Formula Manipulating System to Statistical
+ Mechanics", YEAR = 1985,
+ BOOKTITLE = "Proc. of the Second {RIKEN} International
+Symposium on Symbolic and Algebraic Computation by Computers",
+ PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "155-180"}
+
+@PHDTHESIS{Kauffman:73,
+ AUTHOR = "S. K. Kauffman",
+ TITLE = "Ortho-Positronium Annihilation:  Steps Toward Computing
+the First Order Radiative Corrections",
+ SCHOOL = "California Institute of Technology",
+ YEAR = 1973}
+
+@INPROCEEDINGS{Kazasov:87,
+ AUTHOR = "C. Kazasov",
+ TITLE = "Laplace Transformations in {REDUCE} 3",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "132-133",
+ PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{Keady:85,
+ AUTHOR = "Grant Keady",
+ TITLE = "The Power Concavity of Solutions of Some Semilinear Elliptic
+{Boundary-Value} Problems",
+ JOURNAL = "Bull. Austral. Math. Soc.",
+ YEAR = 1985, VOLUME = 31, PAGES = "181-184"}
+
+@ARTICLE{Keener:83,
+ AUTHOR = "James P. Keener",
+ TITLE = "Oscillatory coexistence in the {chemostat:} a codimension two
+unfolding",
+ JOURNAL = "{SIAM} J. Appl. Math.",
+ YEAR = 1983, VOLUME = 43, NUMBER = 5, PAGES = "1005-1018"}
+
+@ARTICLE{Keener:85,
+ AUTHOR = "James P. Keener",
+ TITLE = "Oscillatory coexistence in a food chain model with competing
+predators",
+ JOURNAL = "J. Math. Biology",
+ YEAR = 1985, VOLUME = 22, PAGES = "123-135"}
+
+@ARTICLE{Keener:89,
+ AUTHOR = "James P. Keener",
+ TITLE = "Knotted scroll wave filaments in excitable media",
+ JOURNAL = "Physica D 34",
+ YEAR = 1989, PAGES = "378-390"}
+
+@ARTICLE{Keener:90,
+ AUTHOR = "James P. Keener",
+ TITLE = "Knotted vortex filaments in an ideal fluid",
+ JOURNAL = "J. Fluid Mech.",
+ YEAR = 1990, VOLUME = 211, PAGES = "629-651"}
+
+@ARTICLE{Kendall:88,
+ AUTHOR = "W. S. Kendall",
+ TITLE = "Symbolic Computation and the Diffusion of Shapes of Triads",
+ JOURNAL = "Adv. Appl. Prob.",
+ YEAR = 1988, VOLUME = 20, PAGES = "775-797"}
+
+@TECHREPORT{Kendall:89,
+ AUTHOR = "W. S. Kendall",
+ TITLE = "The Diffusion of {Euclidean} Shape",
+ INSTITUTION = "University of Warwick, Dept. of Statistics", YEAR = 1989,
+ TYPE = "Research Report", NUMBER = 161}
+
+@TECHREPORT{Kendall:89a,
+ AUTHOR = "W. S. Kendall",
+ TITLE = "Probability, Convexity, and Harmonic Maps with Small Image I:
+Uniqueness and Fine Existence",
+ INSTITUTION = "University of Warwick, Dept. of Statistics", YEAR = 1989,
+ TYPE = "Research Report", NUMBER = 162}
+
+@ARTICLE{Kendall:90,
+ AUTHOR = "W. S. Kendall",
+ TITLE = "Computer Algebra and Stochastic Calculus",
+ JOURNAL = "Notices A.M.S.",
+ YEAR = 1990, VOLUME = 37, PAGES = "1254-1256"}
+
+@TECHREPORT{Kendall:91,
+ AUTHOR = "Wilfred S. Kendall",
+ TITLE = "Computer Algebra and Stochastic Calculus",
+ INSTITUTION = "University of Warwick, Dept. of Statistics", YEAR = 1991,
+ TYPE = "Research Report", NUMBER = 203}
+
+@TECHREPORT{Kendall:91a,
+ AUTHOR = "Wilfred S. Kendall",
+ TITLE = "Symbolic {It\^{o}} Calculus:  An Introduction",
+ INSTITUTION = "University of Warwick, Dept. of Statistics", YEAR = 1991,
+ TYPE = "Research Report", NUMBER = 217}
+ ABSTRACT = {The ito procedures are an implementation of stochastic calculus
+for the computer algebra package {REDUCE}.  In this paper it is explained
+how the implementation of ito grows naturally out of the formulation of
+stochastic calculus using modules of stochastic differentials.  Two examples
+are given of ito in action:  a simple example concerning various exponential
+martingales and a more involved example concerning the escape rate of the
+Bessel process of dimension exceeding 2.  A basic subset of the ito
+procedures is listed in six appendices; details are given of how to obtain
+the full set from the author.}}
+
+@TECHREPORT{Kendall:93a,
+ AUTHOR = "Wilfred S. Kendall",
+ TITLE = "Probability, Convexity, and Harmonic Maps II:  Smoothness via
+Probabilistic Gradient Inequalities",
+ INSTITUTION = "University of Warwick, Dept. of Statistics", YEAR = 1993,
+ MONTH = "October", TYPE = "Research Report", NUMBER = 260,
+ ABSTRACT = {A conformal change of metric is used to construct a coupling
+of two time-changed Riemannian Brownian motions, such that there is an
+upper bound on the prabability of no coupling before either process leaves
+a small geodesic ball, with the bound being linear in the distance between
+the two starting points.  This coupling is a more geometric (and
+probabilistically less technical) alternative to that introduced by
+Cranston (1991).  Together with some modifications it is used to provide a
+probabilistic approach to the regularity of harmonic maps, thus completing
+the probabilistic construction of solutions to small-image harmonic map
+Dirichlet problems described in Kendall (1990).  The approach includes a
+mild generalization to the case of harmonic maps defined using
+non-Riemannian connections in the target manifold and smooth strictly
+elliptic second-order differential operators in the domain.}}
+
+@INPROCEEDINGS{Kerner:75,
+ AUTHOR = "W. Kerner and R. C. Grimm",
+ TITLE = "{MHD} Spectra for {Tokamaks} with Non-circular Cross Sections",
+ YEAR = 1975,
+ BOOKTITLE = "Proc. Seventh Conference on
+Numerical Simulation of Plasmas, Courant Institute, {NYU}"}
+
+@ARTICLE{Kersten:83,
+ AUTHOR = "P. H. M. Kersten",
+ TITLE = "Infinitesimal Symmetries and Conserved Currents for Nonlinear
+{Dirac} Equation",
+ JOURNAL = "J. Math. Phys.",
+ YEAR = 1983, VOLUME = 24, PAGES = "2374-2376",
+ COMMENT = {Harrison-Estabrook and computer algebra, in {REDUCE}.  Very like
+{EXCALC} but predates it.}}
+
+@ARTICLE{Kersten:84,
+ AUTHOR = "P. Kersten and R. Martini",
+ TITLE = "The Harmonic Map and Killing Fields for Self-Dual {SU(3)}
+{Yang-Mills} Equations",
+ JOURNAL = "J. Phys. A",
+ YEAR = 1984, VOLUME = 17, PAGES = "L227-L230",
+ COMMENT = {%"{\ldots}and the determination of the general solution of the
+killing fields have been achieved by symbolic computations in a semi-automatic
+way using software developed in the symbolic language {REDUCE}{\ldots}"}}
+
+@ARTICLE{Kersten:86,
+ AUTHOR = "P. H. M. Kersten",
+ TITLE = "Creating and Annihilating {Lie-B\"acklund} Transformations
+of the {Federbush} Model",
+ JOURNAL = "J. Math. Phys.",
+ YEAR = 1986, VOLUME = 27, PAGES = "1139-1144",
+ COMMENT = {"We want to stress that all computations have been worked out on
+a {DEC-20} computer using {REDUCE} and a software package to do these
+calculations."  Lie algebra and Gragert's package.}}
+
+@ARTICLE{Kersten:86a,
+ AUTHOR = "P. H. M. Kersten and H. M. M. Ten Eikelder",
+ TITLE = "Infinite Hierarchies of t-independent and t-dependent
+Conserved Functionals of the {Federbush} Model",
+ JOURNAL = "J. Math. Phys.",
+ YEAR = 1986, VOLUME = 27, PAGES = "2140-2145",
+ COMMENT = {"We want to stress that all computations have been worked out on
+a {DEC-20} computer using {REDUCE} and a software package to do these
+calculations."}}
+
+@ARTICLE{Kersten:86b,
+ AUTHOR = "P. H. M. Kersten and H. M. M. Ten Eikelder",
+ TITLE = "An Infinite Number of Infinite Hierarchies of Conserved
+Quantities of the {Federbush} Model",
+ JOURNAL = "J. Math. Phys.",
+ YEAR = 1986, VOLUME = 27, PAGES = "2791-2796"}
+
+@ARTICLE{Killalea:80,
+ AUTHOR = "M. K. Killalea and B. J. McCoy",
+ TITLE = "Concentration Distribution and Spatial Moments of
+Moving Macromolecules Undergoing Isomerization",
+ JOURNAL = "Biopolymers",
+ YEAR = 1980, VOLUME = 19, PAGES = "1875-1886"}
+
+@TECHREPORT{Kinoshita:72,
+ AUTHOR = "T. Kinoshita and P. Cvitanovic",
+ TITLE = "Sixth Order Radiative Corrections to the Electron Magnetic Moment",
+ INSTITUTION = "Cornell Lab. for Nuclear Studies", YEAR = 1972,
+ TYPE = "Report", NUMBER = "CLNS-197", MONTH = "October"}
+
+@TECHREPORT{Kinoshita:73,
+ AUTHOR = "T. Kinoshita and P. Cvitanovic",
+ TITLE = "Feynman-{Dyson} Rules in Parametric Space",
+ INSTITUTION = "Cornell Lab. for Nuclear Studies", YEAR = 1973,
+ TYPE = "Report", NUMBER = "CLNS-209", MONTH = "January"}
+
+@ARTICLE{Kitatani:86,
+ AUTHOR = "H. Kitatani and S. Miyashita and M. Suzuki",
+ TITLE = "Reentrant Phenomena in Some {Ising} Spin Systems - Rigorous
+Results and Effects of an External Field",
+ JOURNAL = "J. Phys. S. Japan",
+ YEAR = 1986, VOLUME = 55, NUMBER = 3, PAGES = "865-876",
+ COMMENT = {{REDUCE} used to calculate formula before numerical
+calculation.}}
+
+@ARTICLE{Klimov:93,
+ AUTHOR = "D. M. Klimov and V. V. Leonov and V. M. Rudenko",
+ TITLE = "The Study of Motion for a Gyroscope with Gimbal Suspension:
+Obtaining the Highest Approximations for a Drift of Magnus",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1993, VOLUME = 15, NUMBER = 1, PAGES = "73-78", MONTH = "January",
+ COMMENT = {Here we give a solution to the classic problem of the applied
+mechanics of the gyroscope.  The problem is reduced to using the computer
+algebra system {REDUCE}.  We show that symbolic computation is very
+convenient for applied mechanics.}}
+
+@TECHREPORT{Kobayashi:84,
+ AUTHOR = "Hidestune Kobayashi",
+ TITLE = "Weierstrass Points on a Curve, $X^{7}_{0}+X^{7}_{1}
++X^{7}_{2}=0$",
+ INSTITUTION = "Research Institute of Science and Technology, Nihon
+University", YEAR = 1984, TYPE = "Preprint", NUMBER = 28, MONTH = "March"}
+
+@INPROCEEDINGS{Kobayashi:88,
+ AUTHOR = "H. Kobayashi and S. Moritsugu and R. W. Hogan",
+ TITLE = "Solving Systems of Algebraic Equations",
+ BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
+ YEAR = 1988, VOLUME = 358, PAGES = "139-149"}
+
+@INPROCEEDINGS{Kodaira:85,
+ AUTHOR = "Hiroshi Kodaira and Hiroshi Toshima",
+ TITLE = "Gini Coefficient of Wealth in Life Cycle Model",
+ YEAR = 1985,
+ BOOKTITLE = "Proc. of the Second {RIKEN} International
+Symposium on Symbolic and Algebraic Computation by Computers",
+ PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "119-151"}
+
+@ARTICLE{Koh:82,
+ AUTHOR = "I. G. Koh and Y. D. Kim and Y. J. Park and C. H. Kim and
+Y. S. Kim",
+ TITLE = "Complete Set of {SU(5)} Monopole Solution",
+ JOURNAL = "J. Math. Phys.",
+ YEAR = 1982, VOLUME = 23, PAGES = "1210-1212",
+ COMMENT = {Calculation checked by {REDUCE} after hand calculation.}}
+
+@ARTICLE{Koelbig:81,
+ AUTHOR = "K. S. K{\"o}lbig and F. Schwarz",
+ TITLE = "On Positive Function Series",
+ JOURNAL = "Computing",
+ YEAR = 1981, VOLUME = 27, PAGES = "319-337",
+ COMMENT = {{REDUCE} for algebra on constraints on a functional form and
+Jacobi polynomials.}}
+
+@ARTICLE{Koelbig:81b,
+ AUTHOR = "K. S. K{\"o}lbig",
+ TITLE = "A Program for Computing the Conical functions of the
+First Kind ${P}^{m}_{-1/2+i\tau}(x)$ for $m = 0$ and $m = 1$",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1981, VOLUME = 23, PAGES = "51-61",
+ PUBLISHER = "North Holland Publishing Company"}
+
+@ARTICLE{Koelbig:82,
+ AUTHOR = "K. S. K{\"o}lbig",
+ TITLE = "Closed Expressions for $\int_{0}^{1} t^{-1} $log$^{n-1}t\,
+ $log$^{p}(1 - t) dt$",
+ JOURNAL = "Math. Comp.",
+ YEAR = 1982, VOLUME = 39, NUMBER = 160, PAGES = "647-654",
+ MONTH = "October",
+ COMMENT = {Closed form of integral for easy calculation.  Used {REDUCE} for
+manipulations.  This class includes dilog, Spence functions etc.
+Remarks that {REDUCE} is easier than {FORTRAN}.}}
+
+@ARTICLE{Koelbig:82a,
+ AUTHOR = "K. S. K{\"o}lbig and W. R{\"u}hl",
+ TITLE = "Complex Zeros of the Partition Function for
+Two-Dimensional {U(N)} Lattice Gauge Theories",
+ JOURNAL = "Z. Phys. C - Particles and Fields",
+ YEAR = 1982, VOLUME = 12, PAGES = "135-143",
+ COMMENT = {The Complex Zeros of the Partition Function for Two-Dimensional
+U(N) Lattice Gauge Theories.}}
+
+@ARTICLE{Koelbig:83,
+ AUTHOR = "K. S. K{\"o}lbig",
+ TITLE = "On the Integral $\int_{0}^{\pi/2} $log$^{n}$cos$\,x\,$
+log$^{p}$sin$\,x\,dx$",
+ JOURNAL = "Math. Comp.",
+ MONTH = "April",
+ YEAR = 1983, VOLUME = 40, PAGES = "565-570",
+ COMMENT = {A formula is derived for the integral in the title which allows
+easy evaluation by formula manipulation on a computer.}}
+
+@ARTICLE{Koelbig:83a,
+ AUTHOR = "K. S. K{\"o}lbig",
+ TITLE = "On the Integral $\int_{0}^{\infty} e^{-\mu t} t^{\nu -1}
+   $log$^{m} t dt$",
+ JOURNAL = "Math. Comp.",
+ YEAR = 1983, VOLUME = 41, PAGES = "171-182",
+ COMMENT = {A recurrence relation is given for the integral in the title.}}
+
+@ARTICLE{Koelbig:84,
+ AUTHOR = "K. S. K{\"o}lbig and B. Schorr",
+ TITLE = "Asymptotic Expansions for the {Landau} Density and
+Distribution Function",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1984, VOLUME = 32, PAGES = "121-131"}
+
+@ARTICLE{Koelbig:84a,
+ AUTHOR = "K. S. K{\"o}lbig and B. Schorr",
+ TITLE = "A Program Package for the {Landau} Distribution",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1984, VOLUME = 31, PAGES = "97-111"}
+
+@TECHREPORT{Koelbig:84b,
+ AUTHOR = "K. S. K{\"o}lbig",
+ TITLE = "Some Problems Involving Special Functions
+Arising From Physics at {CERN}",
+ INSTITUTION = "CERN, Data Handling Division",
+ YEAR = 1984, NUMBER = "DD 84-14", MONTH = "September"}
+
+@TECHREPORT{Koelbig:85,
+ AUTHOR = "K. S. K{\"o}lbig",
+ TITLE = "On the Integral $\int_{0}^{1} x^{\nu -1} (1 - x)^{-\lambda}
+ $ln$^{m} x dx$",
+ INSTITUTION = "CERN, Data Handling Division",
+ YEAR = 1985, NUMBER = "DD/85/18", MONTH = "September"}
+
+@ARTICLE{Koelbig:85a,
+ AUTHOR = "K. S. K{\"o}lbig",
+ TITLE = "Explicit Evaluation of Certain Definite Integrals Involving
+Powers of Logarithms",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1985, VOLUME = 1, NUMBER = 1, PAGES = "109-114", MONTH = "March"}
+
+@ARTICLE{Koelbig:86,
+ AUTHOR = "K. S. K{\"o}lbig",
+ TITLE = "On the Integral $\int_{0}^{\infty} x^{\nu -1}
+ (1 + \beta x)^{-\lambda} $ln$^{m} x dx$",
+ JOURNAL = "Journal of Comp. and Appl. Math.",
+ YEAR = 1986, VOLUME = 14, PAGES = "319-344"}
+
+@TECHREPORT{Koepf:94,
+ AUTHOR = "Wolfram Koepf and Dieter Schmersau",
+ TITLE = "Spaces of Functions Satisfying Simple Differential Equations",
+ INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
+ YEAR = 1994, MONTH = "March", TYPE = "Preprint", NUMBER = "TR 94-2"}
+
+@TECHREPORT{Koepf:94a,
+ AUTHOR = "Wolfram Koepf",
+ TITLE = "Algebraische Darstellung transzendenter Funktionen (in {German})",
+ INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
+ YEAR = 1994, MONTH = "October", TYPE = "Preprint", NUMBER = "SC 94-24"}
+
+@TECHREPORT{Koepf:94b,
+ AUTHOR = "Wolfram Koepf",
+ TITLE = "Algorithms for the Indefinite and Definite Summation",
+ INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
+ YEAR = 1994, MONTH = "December", TYPE = "Preprint", NUMBER = "SC 94-33"}
+
+@ARTICLE{Koepf:95,
+ AUTHOR = "Wolfram Koepf",
+ TITLE = "{REDUCE} package for the Indefinite and Definite Summation",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1995, VOLUME = 29, NUMBER = 1, PAGES = "14-30", MONTH = "January",
+Abstract ={The {REDUCE} package {ZEILBERG} is a careful implementation of
+the Gosper and Zeilberger algorithms for indefinite, and definite
+summation of hypergeometric terms respectively.  An expression $a_k$ is
+called a hypergeometric term (or closed form) if $a_k/a_{k-1}$ is a
+rational function with respect to $k$.  Typical hypergeometric terms are
+ratios of products of powers, factorial, Gamma function terms, binomial
+coefficients, and shifted factorials (Pochhammer symbols) that are
+integer-linear in their arguments.  The package covers further extensions
+of both Gosper's and Zeilberger's algorithms.}}
+
+@TECHREPORT{Koepf:95a,
+ AUTHOR = "Wolfram Koepf",
+ TITLE = "Identities for families of orthogonal polynomials and special
+functions",
+ INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
+ YEAR = 1995, MONTH = "January", TYPE = "Preprint", NUMBER = "SC 95-1",
+ ABSTRACT = {In this article we present new results for families of
+orthogonal polynomials and special functions, that are determined by
+algorithmical approaches.
+
+In the first section, we present new results, especially for discrete
+families of orthogonal polynomials, obtained by an application of the
+celebrated Zeilberger algorithm.
+
+Next, we present algorithms for holonomic families $f(n,x)$ of special
+functions which possess a derivative rule.  We call those families
+admissible.  A family $f(n,x)$ is holonomic if it satisfies a holonomic
+recurrence equation with respect to n, and a holonomic differential
+equation with respect to x, i.e. linear homogeneous equations with
+polynomial coefficients.
+
+The rather rigid property of admissibility has many interesting
+consequences, that can be used to generate and verify identities for these
+functions by linear algebra techniques.  On the other hand, many families
+of special functions, in particular families of orthogonal polynomials, are
+admissible.  We moreover present a method that generates the derivative
+rule from the holonomic representation of a holonomic family.
+
+As examples, we find new identities for the Jacobi polynomials and for the
+Whittaker functions, and for families of discrete orthogonal polynomials by
+the given approach.
+
+Finally, we present representations for the parameter derivatives of the
+Gegenbauer and the generalized Laguerre polynomials.}}
+
+@ARTICLE{Koike:92,
+ AUTHOR = "F. Koike",
+ TITLE = "Explicit formulae of angular momentum coupling coefficients",
+ JOURNAL = "Comp. Phys. Commun.",
+ YEAR = 1992, VOLUME = 72, NUMBERS = "2 and 3", PAGES = "154-164",
+ MONTH = "November",
+ COMMENT = {A program has been developed to generate algebraic formulae of
+the coupling coefficients of angular momenta.  The algebraic programming
+system {REDUCE} version 3.3 is used for programming.  The program
+consists of several {REDUCE} prefix operators.  They carry out symbolic
+reductions of Clebsch-Gordan coefficients.  Racah coefficients,
+X-coefficients, and related coefficients.  Both variables and values of
+angular momentum can be their arguments.  The program allows one to use
+these operators in the same way as the {REDUCE} built-in operators.}}
+
+@ARTICLE{Kolar:90,
+ AUTHOR = "M. Kol{\'a}\u{r} and M. K. Ali",
+ TITLE = "Trace maps associated with general {two-letter} substitution
+rules",
+ JOURNAL = "Physical Review {A}",
+ YEAR = 1990, VOLUME = 42, NUMBER = 12, PAGES = "7112-7124",
+ MONTH = "December",
+ ABSTRACT = {Spectral properties, as determined by trace maps, of the
+one-dimensional chains (layered structures) constructed according to
+general two-letter substitution rules are investigated.  In all trace maps
+thus obtained an important role is played by the quantity
+$I=x^{2}+y^{2}+z^{2}-xyz-4$ However, only a very small fraction of all
+such trace maps are similar to the Fibonacci golden-mean trace map in that
+I is their invariant.  In addition to the known case of the precious-mean
+lattices (precious means are ratios of the form
+$^{1}_{2}[m+(m^{2}+4)^{1/2}]$, m being any positive integer; m=1 gives the
+golden mean), we have identified two new large clases of substitution
+rules that give trace maps with invariant I.  One of them is a superset of
+the precious-mean lattices.  All other cases represent a vast assortment
+of different trace maps (and thus the potential for various hitherto
+unexplored spectral properties) with a unifying feature that the set I=0
+plays the role of an attractor in the trace space.  In most (but not all)
+cases, two chains with identical trace maps (and thus identical spectra)
+are locally isomorphic.  Generally, local isomorphism equivalence classes
+seem to be subsets of identical spectrum equivalence classes.}}
+
+@TECHREPORT{Kornyak:87,
+ AUTHOR = "V. V. Kornyak and R. N. Fedorova",
+ TITLE = "A {REDUCE} Program to Calculate Determining Equations of
+{Lie-Baecklund} Symmetries of Differential Equations",
+ INSTITUTION = "J.I.N.R., Dubna",
+ YEAR = 1987, NUMBER = "P11-87-19"}
+
+@ARTICLE{Kotorynski:86,
+ AUTHOR = "W. P. Kotorynski",
+ TITLE = "Steady Laminar Flow Through a Twisted Pipe of Elliptical
+Cross-Section",
+ JOURNAL = "Computers and Fluids",
+ YEAR = 1986, VOLUME = 14, PAGES = "433-444",
+ COMMENT = {Used {REDUCE} to perform the calculations for steady flow through
+twisted pipes, but who also remarked that the techniques he developed
+for this problem are applicable to a variety of other pipe flow tasks.}}
+
+@ARTICLE{Krack:82,
+ AUTHOR = "K. Krack",
+ TITLE = "Rechnerunterst{\"u}tzte {Entwicklung} der {Mittelbreitenformeln}
+und Absch{\"a}tzung ihrer ellipsoidischen {Anteile} zur L{\"o}sung der
+zweiten geod{\"a}tischen {Hauptaufgabe} auf dem {Rotationsellipsoid}",
+ JOURNAL = "Z. Vermessungswes.",
+ YEAR = 1982, VOLUME = 107, PAGES = "502-513",
+ COMMENT = {(In German) Used {REDUCE} to develop the Gauss mid-latitude
+formulae for inverse positioning to the 7th order (Geodesy).}}
+
+@PHDTHESIS{Kraus:73,
+ AUTHOR = "J. Kraus",
+ TITLE = "Delbr{\"u}ckstreuung und Pr{\"u}fung der
+Quantenelektrodynamik",
+ SCHOOL = "Ludwig-Maximilians-Universit{\"a}t zu M{\"u}nchen",
+ YEAR = 1973}
+
+@ARTICLE{Kredel:88,
+ AUTHOR = "Heinz Kredel",
+ TITLE = "Admissible termorderings used in Computer Algebra Systems",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1988, VOLUME = 22, NUMBER = 1, PAGES = "28-31", MONTH = "January"}
+
+@ARTICLE{Kruse:83,
+ AUTHOR = "Hans-Guenther Kruse and Karin Ohlsen",
+ TITLE = "About the Realization of an Extended, but Really Interactive
+{REDUCE} by Integration of a Small Editing and Executing System",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "21-25", MONTH = "February"}
+
+@TECHREPORT{Kryukov,
+ AUTHOR = "A. P. Kryukov and A. Ya. Rodionov",
+ TITLE = "Usage of {REDUCE} for Computations of Group-Theoretical Weight of
+{Feynman} Diagrams in Non-Abelian Gauge Theories",
+ INSTITUTION = "Institute of Nuclear Physics, Moscow, USSR", YEAR = "TBD"}
+
+@ARTICLE{Kryukov:84,
+ AUTHOR = "A. P. Kryukov",
+ TITLE = "An Antitranslator of the {RLISP} Language",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1984, VOLUME = 18, NUMBER = 3, PAGES = "12-15", MONTH = "August"}
+
+@ARTICLE{Kryukov:85,
+ AUTHOR = "A. P. Kryukov and A. Ya. Rodionov",
+ TITLE = "Dynamic-Debugging System for the {REDUCE} Programs",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1985, VOLUME = 19, NUMBER = 2, PAGES = "34-37", MONTH = "May"}
+
+@ARTICLE{Kryukov:85a,
+ AUTHOR = "A. P. Kryukov and A. Ya. Rodionov",
+ TITLE = "Interactive {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1985, VOLUME = 19, NUMBER = 3, PAGES = "43-45", MONTH = "August"}
+
+@TECHREPORT{Kryukov:87,
+ AUTHOR = "A. P. Kryukov and A. Ya. Rodionov and V. A. Rostovtsev",
+ TITLE = "Pattern Compilation in {REDUCE}",
+ INSTITUTION = "J.I.N.R., Dubna",
+ YEAR = 1987, NUMBER = "P11-87-302"}
+
+@INPROCEEDINGS{Kryukov:87a,
+ AUTHOR = "A. P. Kryukov and A. Ya. Rodionov",
+ TITLE = "{CTS} - Algebraic Debugging System for {REDUCE} Programs",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "233-243",
+ PUBLISHER = "Springer-Verlag"}
+
+@TECHREPORT{Kryukov:88,
+ AUTHOR = "A. P. Kryukov and A. Ya. Rodionov and V. A. Rostovtsev",
+ TITLE = "New Programming Tools for Computing Substitution
+Rules in {REDUCE} System",
+ INSTITUTION = "J.I.N.R., Dubna",
+ YEAR = 1988, NUMBER = "P11-88-402",
+ COMMENT = {New programming tools allowing to compile patterns in
+{REDUCE} system are described.  A guide for using
+these tools and examples of their working are presented.}}
+
+@ARTICLE{Kryukov:88a,
+ AUTHOR = "A. P. Kryukov and A. Ya. Rodionov",
+ TITLE = "Program {``COLOR''} for Computing the Group-Theoretic Weight
+of {Feynman} Diagrams in {Non-Abelian} Gauge Theories",
+ JOURNAL = "Comp. Phys. Commun.",
+ YEAR = 1988, VOLUME = 48, NUMBER = 2, PAGES = "327-334", MONTH = "February"}
+
+@TECHREPORT{Kryukov:88b,
+ AUTHOR = "A. P. Kryukov and D. A. Slavnov",
+ TITLE = "The Role of the $gg \rightarrow c\overline{c}g$ Process in the
+Cross Section of Production of Charmed Particles (in {Russian})",
+ INSTITUTION = "Moscow State University",
+ YEAR = 1988, NUMBER = "88-49/70", TYPE = "Preprint"}
+
+@BOOK{Kryukov:91,
+ AUTHOR = "A. P. Kryukov and A. Ya. Rodionov and A. Yu. Taranov and
+E. Shablygin",
+ TITLE = "Programming in R-Lisp",
+ PUBLISHER = "Radio and Connective Publishers, Moscow", YEAR = 1991,
+ ABSTRACT = {Various Lisp dialects become more and more popular as
+high-level programming languages.  In this book basic Lisp concepts, its
+data structures and build in functions are introduced using R-Lisp.
+R-Lisp is the implementation language of a famous REDUCE computer algebra
+system.  All concepts are illustrated by simple but by no means trivial
+programming examples.  The description of compiler and full function
+reference are included.  The book will be interesting for beginners as
+well as Lisp programmers. In Russian}}
+
+@TECHREPORT{Kuppers:71,
+ AUTHOR = "G. Kuppers and D. Pfirsch and H. Tasso",
+ TITLE = "{M.H.D.} - Stability of Axisymmetric Plasmas",
+ INSTITUTION = "Max-Planck-Institut fuer Plasmaphysik",
+ YEAR = 1971, TYPE = "Report", NUMBER = "CN -28/F-14"}
+
+@ARTICLE{Lambin:84,
+ AUTHOR = "P. Lambin and J. P. Vigneron",
+ TITLE = "Computation of Crystal {Green's} Functions in the Complex-Energy
+Plane with the Use of the Analytical Tetrahedron Method",
+ JOURNAL = "Phys. Rev. B",
+ YEAR = 1984, VOLUME = 29, NUMBER = 6, PAGES = "3430-3437",
+ COMMENT = {Crystallography, {REDUCE}, quantum theory.}}
+
+@TECHREPORT{Lang:79,
+ AUTHOR = "C. B. Lang and W. Porod",
+ TITLE = "Symmetry Breaking and $\pi$ {K} Amplitudes in the Unphysical
+Region",
+ INSTITUTION = "Institut f{\"u}r Theor. Physik, Univ. Graz",
+ YEAR = 1979, TYPE = "Report", NUMBER = "UNIGRAZ-UTP 08/79",
+ ABSTRACT = {We apply two different methods of analytic continuation
+(fixed-t and hyperbolic dispersion relations with discrepancy) to
+determine the expansion parameters of the pi K amplitudes in the
+unphysical region near the symmetry point.},
+ COMMENT = {To be published in Phys. Rev. D, September, 1979.}}
+
+@TECHREPORT{Laursen:79,
+ AUTHOR = "M. L. Laursen and M. A. Samuel",
+ TITLE = "The n-Bubble Diagram Contribution to the g-2 of the Electron -
+{Mathematical} Structure of the Analytical Expression",
+ INSTITUTION = "Oklahoma State Univ. Quantum Theoretical Research Group",
+ YEAR = 1979, TYPE = "Research Note", NUMBER = "96",
+ ABSTRACT = {We obtain an exact integrated expression for the contribution
+of the mass-independent n-bubble diagram to the leptonic g-2.}}
+
+@TECHREPORT{Laursen:80,
+ AUTHOR = "Morten L. Laursen and Mark A. Samuel",
+ TITLE = "Borel Transform Technique and the {n-Bubble} Diagram
+Contribution to the Lepton Anomaly",
+ INSTITUTION = "Oklahoma State Univ. Quantum Theoretical Research Group",
+ YEAR = 1980, TYPE = "Research Note", NUMBER = 10, MONTH = "August",
+ ABSTRACT = {By using the {Borel} transform technique we calculate
+analytically the muon anomaly from the mass-dependent n-bubble diagram in the
+limit where the mass ratio is large.}}
+
+@ARTICLE{Laursen:81,
+ AUTHOR = "M. L. Laursen and M. A. Samuel",
+ TITLE = "The n-bubble Diagram Contribution to g-2",
+ JOURNAL = "J. Maths. Phys.",
+ YEAR = 1981, VOLUME = 22, PAGES = "1114-1126",
+ COMMENT = {Exact integration for contribution to mass indep. {n-bubble}
+diagram to {leptonic g-2}.  {REDUCE} used to calculate explicitly to {n=13},
+involves summing series and rational coefficients.}}
+
+@ARTICLE{Lecourtier:85,
+ AUTHOR = "Y. Lecourtier and A. Raksanyi",
+ TITLE = "Algebraic Manipulation Routines for Testing Structural Properties",
+ JOURNAL = "IFAC Identification and System Parameter Estimation",
+ YEAR = 1985, PAGES = "543-549"}
+
+@ARTICLE{Lee:85,
+ AUTHOR = "H-C Lee and M. S. Milgram",
+ TITLE = "On the Axial Gauge:  Ward Identities and the Separation of
+Infrared and Ultraviolet Singularities by Analytical Regularization",
+ JOURNAL = "J. Math. Phys.",
+ YEAR = 1985, VOLUME = 26, PAGES = "1793-1804",
+ COMMENT = {Yang-Mills theories on the axial gauge.  Uses {SCHOONSCHIP} and
+{REDUCE}.}}
+
+@ARTICLE{Leler:85,
+ AUTHOR = "Wm Leler and Neil Soiffer",
+ TITLE = "An Interactive Graphical Interface for {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1985, VOLUME = 19, NUMBER = 3, PAGES = "17-23", MONTH = "August"}
+
+@ARTICLE{Lepage:83,
+ AUTHOR = "G. P. Lepage and P. B. Mackenzie and K. H. Streng and
+P. M. Zernas",
+ TITLE = "Multiphoton Decays of Positronium",
+ JOURNAL = "Phys. Rev. A",
+ YEAR = 1983, VOLUME = 28, PAGES = "3090-3091",
+ COMMENT = {Same as Adkins and Brown (1983) but independent of it.}}
+
+@INPROCEEDINGS{Levi:70,
+ AUTHOR = "I. Levi and N. Hoff",
+ TITLE = "Non-Symmetric Creep Buckling of Circular
+Cylindrical Shells in Axial Compression",
+ YEAR = 1970, MONTH = "August",
+ BOOKTITLE = "Proc. Intern. Symp. in Creep Effect in Structures,
+Gotenburg, Sweden"}
+
+@INPROCEEDINGS{Levi:71,
+ AUTHOR = "I. M. Levi",
+ TITLE = "Symbolic Algebra by Computer - Applications to
+Structural Mechanics",
+ YEAR = 1971, MONTH = "April",
+ BOOKTITLE = "{AIAA/ASME} 12th Structures, Structural Dynamics
+and Materials Conference, Anaheim, California"}
+
+@ARTICLE{Liebermann:75,
+ AUTHOR = "R. Liebermann",
+ TITLE = "Traces of High Energy Processes in Strong Magnetic Fields",
+ JOURNAL = "J. Comp. Phys.",
+ YEAR = 1975}
+
+@ARTICLE{Liska:84,
+ AUTHOR = "R. Liska",
+ TITLE = "Program for Stability and Accuracy Analysis of
+Finite Difference Methods",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1984, VOLUME = 34, PAGES = "175-186"}
+
+@INPROCEEDINGS{Liska:87,
+ AUTHOR = "R. Liska and D. Drska",
+ TITLE = "Evaluation of Plasma Fluid Equations Collision Integrals Using
+{REDUCE}",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = 178,
+ PUBLISHER = "Springer-Verlag"}
+
+@InProceedings{Liska90,
+  author =      "R. Liska and L. Drska",
+  title =       "{FIDE}: A {REDUCE} package for automation of {FI}nite
+                 difference method for solving {pDE}",
+  booktitle =   "Proceedings of the 1990 International Symposium on
+                 Symbolic and Algebraic Computation",
+  year =        "1990",
+  editor =      "S. Watanabe and Morio Nagata",
+  pages =       "169-176",
+  organization =        "ACM",
+  publisher =   "Addison-Wesley"
+}
+
+@INPROCEEDINGS{Liska:91,
+ AUTHOR = "Richard Liska and Michail Yu. Shashkov",
+ TITLE = "Algorithms for Difference Schemes Construction on Non-orthogonal
+Logically Rectangular Meshes",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ EDITOR = "Stephen M. Watt",
+ PUBLISHER = "ACM Press", ADDRESS = "Maryland", PAGES = "419-426",
+ YEAR = 1991,
+ ABSTRACT = {The paper deals with the formalization of the basic operator
+method for construction of difference schemes for the numerical solving
+of partial differential equations.  The strength of the basic operator
+method lies on the fact that it produces fully conservative difference
+schemes.  The difference mesh can be non-orthogonal but has to be logically
+orthogonal.  Algorithms for working with grid functions and grid operators
+in symbolic form which are necessary in the basic operator method are
+described.  The algorithms have been implemented in the computer algebra
+system REDUCE.}}
+
+@ARTICLE{Lloyd:90,
+ AUTHOR = "N. G. Lloyd and J. M. Pearson",
+ TITLE = "{REDUCE} and the Bifurcation of Limit Cycles",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1990, VOLUME = 9, NUMBER = 2, PAGES = "215-224", MONTH = "February"}
+
+@INPROCEEDINGS{Loe:85,
+ AUTHOR = "Kia Fock Loe and Noritaka Ohsawa and Eiichi Goto",
+ TITLE = "Circuit Simulation Code Generation by Computer Algebra",
+ YEAR = 1985,
+ BOOKTITLE = "Proc. of the Second {RIKEN} International
+Symposium on Symbolic and Algebraic Computation by Computers",
+ PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "87-103"}
+
+@INPROCEEDINGS{London:74,
+ AUTHOR = "R. London and D. R. Musser",
+ TITLE = "The Application of a Symbolic Mathematical System
+to Program Verification",
+ YEAR = 1974, PAGES = "265-273",
+ BOOKTITLE = "Proc. {ACM} 74"}
+
+@ARTICLE{Loos:72,
+ AUTHOR = "R{\"u}diger Loos",
+ TITLE = "Analytic Treatment of Three Similar {Fredholm} Integral
+Equations",
+ JOURNAL = "SIGSAM Bulletin",
+ YEAR = 1972, VOLUME = 11, PAGES = "32-40",
+ ABSTRACT = {A {REDUCE} solution to {SIGSAM} Problem \#1 is presented.}}
+
+@INPROCEEDINGS{Lottati,
+ AUTHOR = "Itzhak Lottati and Isaac Elishakoff",
+ TITLE = "Refined Dynamical Theories of Beams, Plates
+and Shells and Their Applications",
+ BOOKTITLE = "Proc. Euromech-Colloquium 219"}
+
+@ARTICLE{Louw:86,
+ AUTHOR = "J. A. Louw and F. Schwarz and W. H. Steeb",
+ TITLE = "First Integrals and {Yoshida} Analysis of {Nahm}'s Equation",
+ JOURNAL = "J. Phys. A",
+ YEAR = 1986, VOLUME = 19, PAGES = "L569-L573",
+ COMMENT = {Monopole solutions in Yang-Mills theories explicitely given in
+special cases.  {REDUCE} used for polynomial first integrals and
+Kowalewski exponents.  An application of spde.}}
+
+@ARTICLE{Luegger:73,
+ AUTHOR = "J. Luegger and H. Melenk",
+ TITLE = "Darstellung und {Bearbeitung} Umfangreicher {LISP-Programme}",
+ JOURNAL = "Angewandte Informatik",
+ YEAR = 1973, MONTH = "June", PAGES = "257-263"}
+
+@TECHREPORT{Luegger:91,
+ AUTHOR = "Joachim L{\"u}gger and Wolfgang Dalitz",
+ TITLE = "Verteilung mathematischer {Software} mittels elektronischer
+{Netze:} {Die} elektronische {Softwarebibliothek} {eLib}",
+ INSTITUTION = "Konrad-Zuse-Zentrum {f\"u}r Informationstechnik Berlin",
+ YEAR = 1991, MONTH = "February", TYPE = "Preprint", NUMBER = "TR 91-2"}
+
+@TECHREPORT{Lukacs,
+ AUTHOR = "B. Luk{\'a}cs and Z. Perj{\'e}s and
+A. Sebesty{\'e}n and A. Valentini",
+ TITLE = "Stationary Vacuum Fields with a Conformally Flat
+Three-Space, II. Proof of Axial Symmetry",
+ INSTITUTION = "Central Research Institute for Physics,
+Budapest, Hungary",
+ YEAR = 1982, NUMBER = "KFKI-1982-19"}
+
+@ARTICLE{Lukaszuk:87,
+ AUTHOR = "L. L{\'u}kaszuk and D. M. Siemienczuk and L. Szymanowski",
+ TITLE = "Evaluation of Helicity Amplitudes",
+ JOURNAL = "Phys. Rev. D",
+ YEAR = 1987, VOLUME = 35, PAGES = "326-329"}
+
+@PHDTHESIS{Lux:75,
+ AUTHOR = "Augustin Lux",
+ TITLE = "Etude d'un Modele Abstrait pour une Machine {LISP} et de
+son Implantation",
+ SCHOOL = "Universit{\'e} Scientifique et Medicale de Grenoble",
+ YEAR = 1975, MONTH = "March",
+ COMMENT = {Thesis presented to Universit{\'e} Scientifique et Medicale de
+Grenoble, Institut National Polytechnique de Grenoble.}}
+
+@BOOK{MacCallum:86,
+ AUTHOR = "M. A. H. MacCallum",
+ TITLE = "Dynamical Spacetimes and Numerical Relativity",
+ PUBLISHER = "Cambridge University Press", YEAR = 1986}
+
+@TECHREPORT{MacCallum:86a,
+ AUTHOR = "M. A. H. MacCallum",
+ TITLE = "Algebraic Computing in Relativity",
+ INSTITUTION = "Queen Mary College, University of London",
+ YEAR = 1986, NUMBER = "TAU 86-04"}
+
+@INPROCEEDINGS{MacCallum:87,
+ AUTHOR = "M. A. H. MacCallum",
+ TITLE = "Symbolic Computation in Relativity Theory",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "34-43",
+ PUBLISHER = "Springer-Verlag"}
+
+@INPROCEEDINGS{MacCallum:88,
+ AUTHOR = "M. A. H. MacCallum",
+ TITLE = "An Ordinary Differential Equation Solver for {REDUCE}",
+ BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
+ YEAR = 1988, VOLUME = 358, PAGES = "196-205"}
+
+@ARTICLE{MacCallum:89,
+ AUTHOR = "Malcolm A. H. MacCallum",
+ TITLE = "Comments on the performance of algebra systems in general
+relativity and a recent paper by {Nielsen} and {Pedersen}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1989, VOLUME = 23, NUMBER = 2, PAGES = "22-25", MONTH = "April"}
+
+@BOOK{MacCallum:91,
+ AUTHOR = "Malcolm MacCallum and Francis Wright",
+ TITLE = "Algebraic Computing with {REDUCE}",
+ PUBLISHER = "Oxford University Press", YEAR = 1991,
+ ISBN = "0-19-853444-2, 0-19-853443-4 (paperback)"}
+
+@ARTICLE{MacCallum:92,
+ AUTHOR = "M. A. H. MacCallum and S. T. C. Siklos",
+ TITLE = "Algebraically special hypersurface-homogeneous {Einstein} spaces
+in general relativity",
+ JOURNAL = "Journal of Geometry and Physics",
+ YEAR = 1992, VOLUME = 8, PAGES = "221-242"}
+
+@BOOK{MacDonald:94,
+  AUTHOR = "N. MacDonald",
+  TITLE = "{REDUCE} for Physics",
+  PUBLISHER = "Institute of Physics Publishing",
+  ADDRESS = "Bristol, England",
+  YEAR = 1994, MONTH = "March",
+  NOTE = "ISBN 0 7503 0277 1",
+  COMMENT = {This book provides an introduction to {REDUCE} with the needs
+of physicists primarily in mind.  Each chapter introduces some aspects of
+{REDUCE} and illustrates them with applications from various branches of
+physics including mechanics, dynamics, dimensional analysis, quantum
+mechanics, plasma physics.  Exercises to test understanding are included
+throughout.  The emphasis is on hands-on working with {REDUCE} as a tool to
+tackle real physical problems.  The book takes account of changes to
+{REDUCE} for Version 3.4.
+Students and researchers in the physical sciences and engineering using
+{REDUCE} for the first time should find this book useful.}}
+
+@PHDTHESIS{Mack:73,
+ AUTHOR = "D. Mack",
+ TITLE = "Nichtnumerische Verfahren und deren Anwendung
+in der Elementarteilchen-Physik",
+ SCHOOL = "University of Tuebingen",
+ YEAR = 1973}
+
+@ARTICLE{Mack:73a,
+ AUTHOR = "D. Mack and H. Mitter",
+ TITLE = "Calculation of Electron-Electron-Bremsstrahlung Cross-Sections",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1973, VOLUME = "44A", PAGES = "71-72"}
+
+@ARTICLE{Maclaren:89,
+ AUTHOR = "N. M. Maclaren",
+ TITLE = "The Generation of Sequences of Multiple Independent Sequences
+of Pseudorandom Numbers",
+ JOURNAL = "Applied Statistics {JRSS Series C}",
+ YEAR = 1989, VOLUME = 38, NUMBERS = 2, PAGES = "351-359"}
+
+@MASTERSTHESIS{Maguire:81,
+ AUTHOR = "Gerald Quentin {Maguire Jr.}",
+ TITLE = "Program Transformation in {REDUCE} Using Rule Sequencing",
+ SCHOOL = "Department of Computer Science, The University of Utah",
+ YEAR = 1981, MONTH = "March"}
+
+@INPROCEEDINGS{Malm:82,
+ AUTHOR = "Bengt Malm",
+ TITLE = "A Program in {REDUCE} for Finding Explicit Solutions",
+ BOOKTITLE = "Proc. {EUROCAM} 1982, Lecture Notes
+in Computer Science", YEAR = 1982, VOLUME = 144, PAGES = "289-293",
+ PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{Man:93,
+ AUTHOR = "Yiu-Kwong Man",
+ TITLE = "On Computing Closed Forms for Indefinite Summations",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1993, MONTH = "October", VOLUME = 16, NUMBER = 4, PAGES = "355 - 376",
+ COMMENT = {A decision procedure for finding closed forms for indefinite
+summation of polynomials, rational functions, quasipolynomials and
+quasirational functions is presented.  It is also extended to deal with
+some non-hypergeometric sums with rational inputs, which are not summable
+by means of Gosper's algorithm.  Discussion of its implementation, analysis
+of degree bounds and some illustrative examples are included.}}
+
+@ARTICLE{Man:93a,
+ AUTHOR = "Yiu-Kwong Man",
+ TITLE = "Computing Closed Form Solutions of First Order {ODE}s Using the
+{Prelle-Singer} Procedure",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1993, MONTH = "November", VOLUME = 16, NUMBER = 5, PAGES = "423 - 443",
+ COMMENT = {The {Prelle-Singer} procedure is an important method for formal
+solution of first order ODEs.  Two different REDUCE implementations (PSODE
+versions 1 & 2) of this procedure are presented in this paper.  The aim is
+to investigate which implementation is more efficient in solving different
+types of ODEs (such as exact, linear, separable, linear in coefficients,
+homogeneous or Bernoulli equations).  The test pool is based on Kamke's
+collection of first order and first degree ODEs.  Experimental results,
+timings and comparison of efficiency and solvability with the present
+REDUCE differential equation solver (ODESOLVE) and a MACSYMA implementation
+(ODEFI) of the {Prelle-Singer} procedure are provided.  Discussion of
+technical difficulties and some illustrative examples are also included.}}
+
+@InProceedings{Man:94,
+  author =       {Yiu-Kwong Man and Francis J. Wright},
+  title =        {Fast Polynomial Dispersion Computation and its
+		 Application to Indefinite Summation},
+  booktitle =    {Symbolic and Algebraic Computation},
+  editor =       {},
+  series =       {ISSAC},
+  year =         {1994},
+  organization = {SIGSAM},
+  publisher =    {ACM},
+  pages =        {175--180}
+}
+
+@ARTICLE{Marti:78,
+ AUTHOR = "Jed Marti",
+ TITLE = "The {META/REDUCE} Translator Writing System",
+ JOURNAL = "Sigplan Notices",
+ YEAR = 1978, VOLUME = 13, PAGES = "42-49",
+ COMMENT = {The {META/REDUCE} translator writing system operates in a
+{LISP} and {REDUCE} syntax.  The language supports: {BNF} like syntax,
+recursive descent parsing schemes, lexical primitives, symbol table
+primitives and automatic syntax error message generation.}}
+
+@ARTICLE{Marti:79,
+ AUTHOR = "J. B. Marti and A. C. Hearn and M. L. Griss and C. Griss",
+ TITLE = "Standard {Lisp} Report",
+ JOURNAL = "Sigplan Notices, ACM",
+ YEAR = 1979, VOLUME = 14, NUMBER = 10, PAGES = "48-68",
+ ABSTRACT = {A description of Standard {LISP} primitive data structures and
+functions is presented.}}
+
+@ARTICLE{Marti:80,
+ AUTHOR = "J. Marti and A. C. Hearn and M. L. Griss and C. Griss",
+ TITLE = "Standard {Lisp} Report",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1980, VOLUME = 14, NUMBER = 1, PAGES = "23-41", MONTH = "February"}
+
+@ARTICLE{Marti:83,
+ AUTHOR = "Jed Marti and John Fitch",
+ TITLE = "{REDUCE} 2 for {CP/M}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "26-27", MONTH = "February"}
+
+@ARTICLE{Marti:85,
+ AUTHOR = "Jed B. Marti and Anthony C. Hearn",
+ TITLE = "{REDUCE} as a {LISP} Benchmark",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1985, VOLUME = 19, NUMBER = 3, PAGES = "8-16", MONTH = "August"}
+
+@INPROCEEDINGS{Marti:85a,
+ AUTHOR = "Jed B. Marti",
+ TITLE = "The Role of Explanation in Symbolic Computation",
+ YEAR = 1985,
+ BOOKTITLE = "Proc. of the Second {RIKEN} International
+Symposium on Symbolic and Algebraic Computation by Computers",
+ PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "13-34"}
+
+@INPROCEEDINGS{Marti:88,
+ AUTHOR = "J. Marti",
+ TITLE = "A Graphics Interface to {REDUCE}",
+ BOOKTITLE = "Proc. {AAECC-6} 1988, Lecture Notes in Computer Science",
+ YEAR = 1988, VOLUME = 357, PAGES = "274-296",
+ PUBLISHER = "Springer-Verlag"}
+
+@BOOK{Marti:93a,
+  AUTHOR = "Jed Marti",
+  TITLE = "{RLISP} '88 An Evolutionary Approach to Program Design and Reuse",
+  PUBLISHER = "World Scientific",
+  ADDRESS = "Singapore",
+  YEAR = 1993,
+  NOTE = "SBN 981-02-14790"}
+
+@INPROCEEDINGS{Marzinkewitsch:91,
+ AUTHOR = "Reiner Marzinkewitsch",
+ TITLE = "Operating Computer Algebra Systems by Handprinted Input",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
+ PAGES = "411-413", YEAR = 1991,
+ ABSTRACT = {A prototype of a workstation is presented for calculation
+with mathematical formulas by hand and support by computer algebra systems.
+Keywords:  Character recognition, neural network, computer algebra system,
+context free grammar, parsing of two dimensional structures.}}
+
+@ARTICLE{Matveev:87,
+ AUTHOR = "V. A. Matveev and Ya. Z. Darbaidze and
+Z. V. Merebashvili and L. A. Slepchenko",
+ TITLE = "Gluon Fusion in {SUSY QCD}",
+ JOURNAL = "Phys. Lett. B",
+ YEAR = 1987, VOLUME = 191, NUMBER = "1 and 2", PAGES = "179-181",
+ MONTH = "June"}
+
+@ARTICLE{Maurer:86,
+ AUTHOR = "M. Maurer and A. Hayd and H. J. Kaeppeler",
+ TITLE = "Quasi-Analytical Method for Solving Nonlinear Differential
+Equations for Turbulent Self-Confined Magneto-Plasma",
+ JOURNAL = "J. Comp. Phys.",
+ YEAR = 1986, VOLUME = 66, PAGES = "151-172",
+ COMMENT = {Mixed {REDUCE} and {FORTRAN}.  Enthusiastic about this style of
+mixed working.}}
+
+@TECHREPORT{Mazepa:85,
+ AUTHOR = "N. E. Mazepa and S. I. Serdyukova",
+ TITLE = "The Stability Investigation of Some Difference Boundary Problem
+with the Application of Symbolic Computation System",
+ INSTITUTION = "J.I.N.R., Dubna",
+ YEAR = 1985, NUMBER = "E5-85-39"}
+
+@ARTICLE{Mazzarella:85,
+ AUTHOR = "Giuseppe Mazzarella",
+ TITLE = "Improved Simplification of Odd and Even Functions in {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1985, VOLUME = 19, NUMBER = 2, PAGES = "29-30", MONTH = "May"}
+
+@ARTICLE{McCrea:81,
+ AUTHOR = "J. D. McCrea",
+ TITLE = "The {Petrov} Type of a Static Vacuum Spacetime Near a
+Normal-Dominated Singularity",
+ JOURNAL = "J. Phys.",
+ YEAR = 1981, VOLUME = "A14", PAGES = "1351-1356"}
+
+@ARTICLE{McCrea:82,
+ AUTHOR = "J. D. McCrea",
+ TITLE = "A Stationary Cylindrically Symmetric Electrovac Spacetime",
+ JOURNAL = "J. Phys.",
+ YEAR = 1982, VOLUME = "A15", PAGES = "1587-1590"}
+
+@ARTICLE{McCrea:83,
+ AUTHOR = "J. D. McCrea",
+ TITLE = "Static, Vacuum, Cylindrical and Plane Symmetric Solutions
+of the Quadratic {Poincar{\'e}} Gauge Field Equations",
+ JOURNAL = "J. Phys.",
+ YEAR = 1983, VOLUME = "A16", PAGES = "997-1004"}
+
+@ARTICLE{McCrea:84,
+ AUTHOR = "J. D. McCrea",
+ TITLE = "A {NUT}-Like Solution of the Quadratic-{Poincar{\'e}} Gauge
+Field Equations",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1984, VOLUME = "100A", PAGES = "397-399"}
+
+@INPROCEEDINGS{McCrea:84a,
+ AUTHOR = "J. D. McCrea",
+ TITLE = "The Use of {REDUCE} in Finding Exact Solutions of the
+Quadratic {Poincar{\'e}} Gauge Field Equations",
+ BOOKTITLE = "Classical General Relativity",
+ PUBLISHER = "Cambridge University", YEAR = 1984, PAGES = "173-182"}
+
+@INPROCEEDINGS{McCrea:87,
+ AUTHOR = "J. D. McCrea",
+ TITLE = "{Poincar{\'e}} Gauge Theory of Gravitation:  Foundations,
+Exact Solutions and Computer Algebra",
+ YEAR = 1987, PAGES = "16",
+ BOOKTITLE = "Differential Geometric Methods in Mathematical
+Physics, Proc. {14th} International Conference,
+Salamanca, 1985 (Springer Lecture Notes in Mathematics, No. 1251)"}
+
+@ARTICLE{McCrea:87a,
+ AUTHOR = "J. D. McCrea and P. Baekler and M. Guerses",
+ TITLE = "A {Kerr}-Like Solution of the {Poincar{\'e}} Gauge Field
+Equations",
+ JOURNAL = "Il Nuovo Cim",
+ YEAR = 1987, VOLUME = "99B", PAGES = "171-177"}
+
+@ARTICLE{McCrea:88,
+ AUTHOR = "J. D. McCrea and E. W. Mielke and F. W. Hehl",
+ TITLE = "A Remark on the Axisymmetric {Chen} et al. Solution of the
+{Poincar{\'e}} Gauge Theory",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1988, VOLUME = "127A", PAGES = "65-69"}
+
+@ARTICLE{McIsaac:85,
+ AUTHOR = "Kevin McIsaac",
+ TITLE = "Pattern Matching Algebraic Identities",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1985, VOLUME = 19, NUMBER = 2, PAGES = "4-13", MONTH = "May"}
+
+@TECHREPORT{Melenk:88,
+ AUTHOR = "H. Melenk and H. M. M{\"o}ller and W. Neun",
+ TITLE = "On {Gr{\"o}bner} Bases Computation on a Supercomputer
+Using {REDUCE}",
+ INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik
+Berlin",
+ YEAR = 1988, TYPE = "Preprint", NUMBER = "SC 88-2", MONTH = "January"}
+
+@ARTICLE{Melenk:89,
+ AUTHOR = "H. Melenk and H. M. M{\"o}ller and W. Neun",
+ TITLE = "Symbolic Solution of Large Stationary Chemical
+Kinetics Problems",
+ JOURNAL = "Impact of Computing in Science and Engineering",
+ YEAR = 1989, VOLUME = 1, NUMBER = 2, PAGES = "138-167", MONTH = "June"}
+
+@TECHREPORT{Melenk:89a,
+ AUTHOR = "Herbert Melenk and Winfried Neun",
+ TITLE = "Implementation of {Portable Standard LISP} for the {SPARC}
+Processor",
+ INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin",
+ YEAR = 1989, TYPE = "Preprint", NUMBER = "SC 89-6", MONTH = "July"}
+
+@ARTICLE{Melenk:89b,
+ AUTHOR = "Herbert Melenk and Winfried Neun",
+ TITLE = "Parallel Polynomial Operations in the Large {Buchberger}
+Algorithm",
+ JOURNAL = "Computer Algebra and Parallelism", EDITOR = "J. Della Dora
+and J. Fitch",
+ YEAR = 1989, PAGES = "143-158", PUBLISHER = "Academic Press, London"}
+
+@ARTICLE{Melenk:90,
+ AUTHOR = "H. Melenk",
+ TITLE = "Solving Polynomial Equation Systems by {Groebner} Type Methods",
+ JOURNAL = "CWI Quarterly",
+ YEAR = 1990, VOLUME = 3, NUMBER = 2, PAGES = "121-136", MONTH = "June"}
+
+@INPROCEEDINGS{Melenk:91,
+ AUTHOR = "H. Melenk",
+ TITLE = "Practical Application of {Gr{\"o}bner} Bases for the Solution
+  of Polynomial Equation Systems",
+ BOOKTITLE = "IV. International Conference on Computer Algebra in
+ Physical Research, 1990",
+ EDITOR = "D. V. Shirkov, V. A. Tostovtsev, V. P. Gerdt",
+ YEAR = "1991", PAGES = "230-235", PUBLISHER="World Scientific",
+ ADDRESS="Singapore"}
+
+@TECHREPORT{Melenk:93,
+ AUTHOR = "Herbert Melenk",
+ TITLE = "Algebraic Solution of Nonlinear Equation Systems in {REDUCE}",
+ INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin",
+ YEAR = 1993, TYPE = "Preprint", NUMBER = "TR 93-2", MONTH = "January"}
+
+@InProceedings{Melenk:93a,
+  author =      "H. Melenk",
+  title =       "Automatic Symbolic Solution of Nonlinear Equation Systems in
+		 {REDUCE}",
+  booktitle =   "Proceedings of the 1993 International IMACS Symposium on
+                 Symbolic Computation",
+  year =        "1993",
+  editor =      "G. Jacob and N. E. Oussous and S. Steinberg",
+  pages =       "175-180",
+  organization ="IMACS",
+  publisher =   "Laboratoire d'Informatique Fondamentale de Lille, France",
+  comment =     {Mathematical background and algorithmic structure of the
+                 nonlinear system part of the {REDUCE} 3.4.1 SOLVE package.}
+}
+
+@TECHREPORT{Melenk:94,
+ AUTHOR = "Herbert Melenk",
+ TITLE = "The Complexity Barrier in {REDUCE} a Case Study",
+ INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin",
+ YEAR = 1994, TYPE = "Preprint", NUMBER = "TR 94-6", MONTH = "January"}
+
+@ARTICLE{melfo:92,
+ AUTHOR = "A. Melfo and L. A. N\'u\~nez",
+ TITLE =  "Checking Collineation Vectors with {REDUCE}",
+ JOURNAL = "Gen. Rel. Grav.",
+ YEAR = "1992",
+ VOLUME = "24",
+ NUMBER = "11",
+ PAGES = "1125--1129",
+ NOTE  = "A package of programs for writing and checking the solutions
+to the equations for various types of collineations (symmetries of the
+metric, christoffel, riemman and ricci tensors) is presented. Some
+examples of previously found  collineations that have been checked are
+given, and new results reported."}
+
+@ARTICLE{Mirie:84,
+ AUTHOR = "R. M. Mirie and C. H. Su",
+ TITLE = "Internal Solitary Waves and Their Head-On Collision Part I",
+ JOURNAL = "J. Fluid Mechanics",
+ YEAR = 1984, VOLUME = 147, PAGES = "213-231",
+ COMMENT = {Lengthy calculation "acknowledge the use of {REDUCE-2}."
+Perturbation and integration.}}
+
+@INPROCEEDINGS{Molenkamp:91,
+ AUTHOR = "J.H.J. Molenkamp and V.V. Goldman and J.A. van Hulzen",
+ TITLE = "An Improved Approach to Automatic Error Cumulation Control",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
+ PAGES = "414-418", YEAR = 1991,
+ ABSTRACT = {For evaluation of arithmetical expressions using multiple
+precision floating-point arithmetic, a method is given to automatically
+perform error cumulation control prior to the actual computations.
+Individual errors and their effects are identified, and it is shown how to
+compute these effects efficiently via automatic differentiation.  In the
+presented approach these effects are used to determine which precisions have
+to be chosen during the real computations, in order to limit error cumulation
+to admissible, user chosen error bounds.}}
+
+@TECHREPORT{Moller:89,
+ AUTHOR = "H. Michael M{\"o}ller",
+ TITLE = "Multivariate Rational Interpolation Reconstruction of Rational
+Functions",
+ INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik
+Berlin",
+ YEAR = 1989, TYPE = "Preprint", NUMBER = "SC 89-4", MONTH = "July"}
+
+@TECHREPORT{Moller:92,
+ AUTHOR = "H. Michael M{\"o}ller",
+ TITLE = "On Decomposing Systems of Polynomial Equations With Finitely
+Many Solutions",
+ INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik
+Berlin",
+ YEAR = 1992, TYPE = "Preprint", NUMBER = "SC 92-15", MONTH = "June"}
+
+@INPROCEEDINGS{Moritsugu:85,
+ AUTHOR = "S. Moritsugu and N. Inada and E. Goto",
+ TITLE = "Symbolic {Newton} Iteration and its Application",
+ YEAR = 1985,
+ BOOKTITLE = "Proc. of the Second {RIKEN} International
+Symposium on Symbolic and Algebraic Computation by Computers",
+ PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "105-117"}
+
+@TECHREPORT{Moritsugu:88,
+ AUTHOR = "S. Moritsugu and E. Goto",
+ TITLE = "A Proposal for Improvement of Facilities of {REDUCE}",
+ INSTITUTION = "Department of Information Science,
+University of Tokyo, Japan",
+ YEAR = 1988, MONTH = "December"}
+
+@ARTICLE{Moritsugu:89,
+ AUTHOR = "Shuichi Moritsugu and Eiichi Goto",
+ TITLE = "A Note on the Preconditioning for Factorization of Homogeneous
+Polynomials",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1989, VOLUME = 23, NUMBER = 1, PAGES = "9-12", MONTH = "January"}
+
+@ARTICLE{Moritsugu:89a,
+ AUTHOR = "Shuichi Moritsugu and Makoto Matsumoto",
+ TITLE = "A Note on the Numerical Evaluation of Arctangent Function",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1989, VOLUME = 23, NUMBER = 3, PAGES = "8-12", MONTH = "July"}
+
+@ARTICLE{Muroa:91,
+ AUTHOR = "Hirokazu Murao",
+ TITLE = "Vectorization of symbolic determinant calculation",
+ JOURNAL = "Supercomputer",
+ YEAR = 1991, VOLUME = "43,VIII-3", PAGES = "36-48"}
+
+@ARTICLE{Mueller:81,
+ AUTHOR = "R. M{\"u}ller and H. J. W. M{\"u}ller-Kirsten",
+ TITLE = "Iteration of Single- and Two-Channel {Schr{\"o}dinger} Equations",
+ JOURNAL = "J. Math. Phys.",
+ YEAR = 1981, VOLUME = 22, PAGES = "733-749",
+ ABSTRACT = {{\dots} we describe an iteration procedure which has already
+been applied to a large number of other problems.  With the help of
+{REDUCE} it is now possible to do these algebraic computations on the
+computer, so that the necessary expressions are obtained within a
+reasonable time.}}
+
+@InProceedings{Mueller-Hoissen:93,
+  author =      "F. Mueller-Hoissen",
+  title =       "Noncommutative Differential Calculus, Quantum Groups and
+                 Computer Algebra",
+  booktitle =   "Proceedings of the 1993 International IMACS Symposium on
+                 Symbolic Computation",
+  year =        "1993",
+  editor =      "G. Jacob and N. E. Oussous and S. Steinberg",
+  pages =       "97-102",
+  organization ="IMACS",
+  publisher =   "Laboratoire d'Informatique Fondamentale de Lille, France"
+}
+
+@ARTICLE{Murzin:85,
+ AUTHOR = "F. A. Murzin",
+ TITLE = "Syntactic Properties of the {REFAL} Language",
+ JOURNAL = "Int. J. Computer Maths.",
+ YEAR = 1985, VOLUME = 17, PAGES = "123-139",
+ COMMENT = {{SNOBOL-like} special purpose algebra system.  Designed for
+Cartan  work.  "{REFAL} is rather an unusual programming language.  It is
+natural to ask in which situations it is useful."  Concludes {MACSYMA}
+or {REDUCE} for standard manipulations, {REFAL} for nonstandard.}}
+
+@TECHREPORT{Nagata:82,
+ AUTHOR = "Morio Nagata and Makoto Shibayama",
+ TITLE = "{COSMOS:}  A Conversational Algebraic System",
+ INSTITUTION = "Department of Administration Engineering,
+Keio University",
+ YEAR = 1982, TYPE = "Technical Report", NUMBER = "No. 8201",
+ MONTH = "March"}
+
+@INPROCEEDINGS{Nagata:85,
+ AUTHOR = "Morio Nagata and Makoto Shibayama",
+ TITLE = "An Interactive Algebraic System for Personal Computing",
+ YEAR = 1985,
+ BOOKTITLE = "IEEE International Symposium on New Directions
+in Computing"}
+
+@BOOK{Nakamura:89,
+ AUTHOR = "Hideharu Nakamura and Shouichi Matsui",
+ TITLE = "Symbolic Computation in Structural Mechanics using {REDUCE}",
+ PUBLISHER = "Gihodo Shuppan Company Ltd.", ADDRESS = "1-11-41,
+Akasaka, Minato-Ku, 107 Tokyo, {Japan}", YEAR = 1989}
+
+@ARTICLE{Nakashima:84,
+ AUTHOR = "T. T. Nakashima and R. E. D. McClung and B. K. John",
+ TITLE = "A Simple Method for the Determination of the Deuterium
+Decoupler Pulse Angle",
+ JOURNAL = "J. Magnetic Resonance",
+ YEAR = 1984, VOLUME = 56, PAGES = "262-274",
+ COMMENT = {{REDUCE} used in theoretical part.  "All density matrix
+calculations presented here were performed on a digital computer using
+REDUCE-2." Essentially matrix products.}}
+
+@ARTICLE{Nakashima:84a,
+ AUTHOR = "T. T. Nakashima and R. E. D. McClung and B. K. John",
+ TITLE = "Experimental and Theoretical Investigation of
+$_{2}D-_{13}C$ DEPT Spectra on $CD_{N}$",
+JOURNAL = "J. Magnetic Resonance",
+ YEAR = 1984, VOLUME = 58, PAGES = "27-36",
+ COMMENT = {"All calculations were performed using {REDUCE-2}."}}
+
+@ARTICLE{Namba:86,
+ AUTHOR = "Kenji Namba",
+ TITLE = "Some Improvements on {Utah} {Standard} {Lisp}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1986, VOLUME = 20, NUMBER = "1 and 2", PAGES = "29-36",
+ MONTH = "February and May"}
+
+@ARTICLE{Nemeth:82,
+ AUTHOR = "G. N{\'e}meth and M. Zim{\'a}nyi",
+ TITLE = "Polynomial Type {Pad\'e} Approximants",
+ JOURNAL = "Math. Comp.",
+ YEAR = 1982, VOLUME = 38, PAGES = "553-565",
+ COMMENT = {Looking for approximants where $R_{n}(x)$ is
+$P_{n}(x)$/P_{n-1}(x)$.  Applied in special functions.  Used
+REDUCE and FORMAC mainly for bignum calculations.}}
+
+@INPROCEEDINGS{Nemeth:87,
+ AUTHOR = "G. N{\'e}meth and M. Zim{\'a}nyi",
+ TITLE = "Computation of Generalized {Pad\'e} Approximants",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "450-451",
+ PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{Neun:89,
+ AUTHOR = "W. Neun and H. Melenk",
+ TITLE = "Implementation of the {LISP-}Arbitrary Precision Arithmetic
+for a vector Processor",
+ JOURNAL = "Computer Algebra and Parallelism", EDITOR = "J. Della Dora
+and J. Fitch",
+ YEAR = 1989, PAGES = "75-89", PUBLISHER = "Academic Press, London"}
+
+@ARTICLE{Neutsch:85,
+ AUTHOR = "W. Neutsch and E. Schr{\"u}fer and A. Jessner",
+ TITLE = "Note on Efficient Integration on the Hypersphere",
+ JOURNAL = "J. Comp. Phys.",
+ YEAR = 1985, VOLUME = 59, PAGES = "167-175",
+ COMMENT = {{REDUCE} used for integration on 4-D hypersphere.  {REDUCE}
+use rather small.}}
+
+@ARTICLE{Neutsch:86,
+ AUTHOR = "W. Neutsch and E. Schr{\"u}fer",
+ TITLE = "Simple Integrals for Solving {Kepler}'s Equation",
+ JOURNAL = "Astrophysics and Space Science",
+ YEAR = 1986, VOLUME = 125, PAGES = "77-83",
+ COMMENT = {Uses {REDUCE} to verify calculations to give integral form which
+is numerically good, involving only rationals and exponentials.}}
+
+@ARTICLE{Ng:89,
+ AUTHOR = "Tze Beng Ng",
+ TITLE = "Computation of the Cohomology of ${B\hat{S}O_{n}<16>}$ for
+$23 \leq n \leq 26$ using {REDUCE}",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1989, VOLUME = 7, NUMBER = 1, PAGES = "93-99", MONTH = "January"}
+
+@ARTICLE{Niki:84,
+ AUTHOR = "Naoto Niki and Sadanori Konishi",
+ TITLE = "Higher Order Asymptotic Expansions for the
+Distribution of the Sample Correlation Coefficient",
+ JOURNAL = "Comm. Statist.-Simula. Comp.",
+ YEAR = 1984, VOLUME = 13, NUMBER = 2, PAGES = "169-182"}
+
+@TECHREPORT{Nikityuk:87,
+ AUTHOR = "N. M. Nikityuk",
+ TITLE = "Some Questions of Using Coding Theory and Analytical
+Calculation Methods on Computers",
+ INSTITUTION = "J.I.N.R., Dubna",
+ YEAR = 1987, NUMBER = "E11-87-10"}
+
+@ARTICLE{Noor:79,
+ AUTHOR = "A. K. Noor and C. M. Andersen",
+ TITLE = "Computerized Symbolic Manipulation in Structural Mechanics -
+Progress and Potential",
+ JOURNAL = "Computers and Structures",
+ YEAR = 1979, VOLUME = 10, PAGES = "95-118",
+ COMMENT = {Concentrates on {MACSYMA} but mentions {FORMAC} and {REDUCE}
+as also having been used in structures.  Mainly finite elements.  Includes
+program and output.}}
+
+@INPROCEEDINGS{Norman:77,
+ AUTHOR = "A. C. Norman and P. M. A. Moore",
+ TITLE = "Implementing the New {Risch} Integration Algorithm",
+ YEAR = 1977, MONTH = "March",
+ BOOKTITLE = "Proc. of the Fourth Colloquium on Advanced Comp.
+Methods in Theor. Phys., St. Maximin, France"}
+
+@ARTICLE{Norman:78,
+ AUTHOR = "Arthur Norman",
+ TITLE = "Towards a {REDUCE} solution to {SIGSAM} Problem 7",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1978, VOLUME = 12, NUMBER = 4, PAGES = "14-18", MONTH = "November"}
+
+@INPROCEEDINGS{Norman:79,
+ AUTHOR = "A. C. Norman and J. H. Davenport",
+ TITLE = "Symbolic Integration - The Dust Settles?",
+ BOOKTITLE = "Proc. {EUROSAM} 1979, Lecture Notes
+in Computer Science", YEAR = 1979, VOLUME = 72, PAGES = "398-407",
+ PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{Norman:83,
+ AUTHOR = "Arthur C. Norman and Paul S. Wang",
+ TITLE = "A Comparison of {Vaxima} and {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "28-30",
+ MONTH = "February"}
+
+@InProceedings{Norman90,
+  author =      "A. C. Norman",
+  title =       "A Critical-Pair/Completion based Integration Algorithm",
+  booktitle =   "Proceedings of the International Symposium on
+                 Symbolic and Algebraic Computation",
+  year =        "1990",
+  editor =      "S. Watanabe and Morio Nagata",
+  pages =       "201-205",
+  organization =        "ACM",
+  publisher =   "Addison-Wesley"
+}
+
+@INPROCEEDINGS{Norman:93,
+ AUTHOR = "A. C. Norman",
+ TITLE = "Compact Delivery Support for {REDUCE}",
+ BOOKTITLE = "Proc. {DISCO '93}, Lecture Notes on Comp. Science",
+ YEAR = 1993, VOLUME = 722, PAGES = "331-340",
+ PUBLISHER = "Springer-Verlag",
+ ABSTRACT = {The {CSL} Lisp system is one designed primarily for delivering
+Lisp applications to users.  It thus emphasises robustness, portability and
+small size rather than support for an integrated programming environment.
+Both portability and compactness are served by making CSL compile the bulk
+of applications code into a compact byte-code instruction set which is then
+emulated.  The speed penalities inherent in this are offset by providing
+instrumentation that makes it easy to identify code hot-spots, and a second
+compiler that translates critical parts of the original Lisp into C for
+incorporation in the CSL kernel.  For use with REDUCE it is found that
+compiling about 5% of the source code into C led to overall performance
+competetive with other Lisp implementations.}}
+
+@ARTICLE{Norman:95,
+ AUTHOR = "A.C. Norman",
+ TITLE = "Compact Delivery Support for {REDUCE}",
+ JOURNAL = "Journ. Symbolic Computation",
+ YEAR = 1995, VOLUME=19, PAGES = "133-143",
+ ABSTRACT = "{CSL} is a {Lisp} system specifically designed to support the
+{REDUCE} algebra system.  This paper views the {Lisp} system upon which a
+{Lisp-coded} algebra system is coded as in effect a micro-kernel -- it
+provides basic compilation, storage management and extended arithmetic
+capabilities that algebra needs, but is not much concerned with higher level
+algebraic algorithms or with user interfaces.  The description of {CSL}
+given here discusses the major design decisions embodied in the system, and
+shows the extent to which it has been possible to resolve conflicting goals
+of simplicity, small size, portability and high performance."}
+
+@ARTICLE{Norton:80,
+ AUTHOR = "Lewis M. Norton",
+ TITLE = "A Note About {Laplace} Transform Tables for Computer Use",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1980, VOLUME = 14, NUMBER = 2, PAGES = "30-31", MONTH = "May"}
+
+@TECHREPORT{Nucci:90,
+ AUTHOR = "M. C. Nucci",
+ TITLE = "Interactive {REDUCE} Programs for Calculating Classical,
+Non-Classical and {Lie-B{\"a}cklund} Symmetries of Differential Equations",
+ INSTITUTION = "Georgia Institute of Technology, School of Mathematics",
+ YEAR = 1990, TYPE = "Preprint", NUMBER = "Math: 062090-051"}
+
+@BOOK{Ochiai:90,
+ AUTHOR = "Mitsuyuki Ochiai and Kiyokazu Nagatomo",
+ TITLE = "Linear Algebra using {REDUCE}",
+ PUBLISHER = "Kindai Kagaku sha, Tokyo", MONTH = "January", YEAR = 1990,
+ COMMENT = {In Japanese.}}
+
+@ARTICLE{Ogilvie:82,
+ AUTHOR = "J. F. Ogilvie",
+ TITLE = "Applications of Computer Algebra in Physical Chemistry",
+ JOURNAL = "Computers in Chemistry",
+ YEAR = 1982, VOLUME = 6, NUMBER = 4, PAGES = "169-172",
+ COMMENT = {After distinguishing between algebraic and numerical
+computing, the author outlines the facilities of some
+algebraic or symbolic processors and provides some
+instances of how some important features can be applied
+to problems in physical chemistry.}}
+
+@ARTICLE{Ogilvie:89,
+ AUTHOR = "J. F. Ogilvie",
+ TITLE = "Computer algebra in modern physics",
+ JOURNAL = "Computers in Physics",
+ YEAR = 1989, MONTH = "January/February", PAGES = "66-74"}
+
+@TECHREPORT{Ono:1979,
+ AUTHOR = "Kiyoshi Ono",
+ TITLE = "{BFORT} -- A {Fortran} System with Arbitrary
+Precision Integer and Real Arithmetic",
+ INSTITUTION = "Department of Physics, University of Tokyo",
+ YEAR = 1979, MONTH = "January"}
+
+@TECHREPORT{Ozieblo,
+ AUTHOR = "A. Ozieblo",
+ TITLE = "Application of {REDUCE 2} in General Theory of Relativity",
+ INSTITUTION = "Cyfronet - Krakow, Poland",
+ COMMENT = {Application of {REDUCE 2} in all calculations typical for
+General Theory of Relativity is shown here.  The most
+spectacular usage of {REDUCE 2} appears to be in various
+aspects of tensor calculus including differentiation
+operations.}}
+
+%                          REDUCE BIBLIOGRAPHY
+
+%                              Part 4:  P-Z
+
+% Copyright (c) 1993 RAND.  All Rights Reserved.
+
+% Additions and corrections are solicited.  Please send them, in the
+% same format as these entries if possible, to reduce at rand.org.
+
+
+@InProceedings{Padget90,
+  author =      "Julian Padget and Alan Barnes",
+  title =       "Univariate Power Series Expansions in {REDUCE}",
+  booktitle =   "Proceedings of the International Symposium on
+                 Symbolic and Algebraic Computation",
+  year =        "1990",
+  editor =      "S. Watanabe and Morio Nagata",
+  pages =       "82-87",
+  organization =        "ACM",
+  publisher =   "Addison-Wesley"
+}
+
+@ARTICLE{Pankau:73,
+ AUTHOR = "E. Pankau and W. Nakel",
+ TITLE = "Measurement of the Absolute Cross Section of the
+Elementary Process of Electron-Electron Bremsstrahlung at 300 {keV}",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1973, VOLUME = "44A", PAGES = "65-67"}
+
+@ARTICLE{Pankau:73a,
+ AUTHOR = "E. Pankau and W. Nakel",
+ TITLE = "Eine {Koinzidenzmessung} zum {Elementarprozess}
+der {Elektron-Elektron-Bremsstrahlung} bei 300 {keV}",
+ JOURNAL = "Z. Physik",
+ YEAR = 1973, VOLUME = 264, PAGES = "139-153"}
+
+@ARTICLE{Parsons:68,
+ AUTHOR = "R. G. Parsons",
+ TITLE = "An Estimate of the Sixth Order Contribution to the
+Anomalous Magnetic Moment of the Electron",
+ JOURNAL = "Phys. Rev.",
+ YEAR = 1968, VOLUME = 168, PAGES = "1562-1567"}
+
+@TECHREPORT{Parsons:71,
+ AUTHOR = "R. G. Parsons",
+ TITLE = "S-Channel Transformation Matrices for Helicity and
+Invariant Amplitudes for lambda + N to O + B",
+ INSTITUTION = "Center for Particle Theory, University of Texas",
+ YEAR = 1971, TYPE = "Memo", NUMBER = "CPT-88", MONTH = "January"}
+
+@ARTICLE{Pasini:91,
+ AUTHOR = "P. Pasini and F. Semeria and C. Zannoni",
+ TITLE = "Symbolic computation of orientational correlation function
+moments",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1991, VOLUME = 12, NUMBER = 2, PAGES = "221-231", MONTH = "August"}
+ COMMENTS = {Symbolic manipulation (REDUCE and SCHOONSCHIP) has been
+applied to the analytic evaluation of the coefficients in the Taylor series
+expansion of time-correlation functions.  These expressions are derived
+for cylindrically and biaxially symmetric particles reorienting in a
+uniaxial fluid.  The possibility of using computer algebra to determine
+correlation-function moments should make it applicable to various problems
+in statistical physics.}}
+
+@ARTICLE{Pattnaik:83,
+ AUTHOR = "P. C. Pattnaik and G. Fletcher and J. L. Fry",
+ TITLE = "Improved Numerical Stability for Norm-Conserving ion-{Ure}
+Pseudopotentials",
+ JOURNAL = "Phys. Rev. B",
+ YEAR = 1983, VOLUME = 28, NUMBER = 6, PAGES = "3364-3365",
+ COMMENT = {{REDUCE} and {FORTRAN}; inverting a matrix algebraically would
+be more accurate than a numerical inverse, and used {REDUCE} for this part of
+their work.}}
+
+@ARTICLE{Pearce:81,
+ AUTHOR = "P. D. Pearce and R. J. Hicks",
+ TITLE = "The Application of Algebraic Optimisation Techniques to
+Algebraic Mode Programs for {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1981, VOLUME = 15, NUMBER = 4, PAGES = "15-22",
+ MONTH = "November"}
+
+@ARTICLE{Pearce:83,
+ AUTHOR = "P. D. Pearce and R. J. Hicks",
+ TITLE = "Data Structures and Execution Times of Algebraic Mode
+Programs for {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "31-37", MONTH = "February"}
+
+@ARTICLE{Perjes:84,
+ AUTHOR = "Z. Perj{\'e}s",
+ TITLE = "Stationary Vacuum Fields with a Conformally Flat
+Three-Space.  {III}. {Complete} Solution",
+ JOURNAL = "General Relativity and Gravitation",
+ YEAR = 1984, VOLUME = 18, PAGES = "531-547",
+ COMMENT = {{REDUCE} used to perform the necessary calculations.}}
+
+@ARTICLE{Perjes:84a,
+ AUTHOR = "Z. Perj{\'e}s and B. Luk{\'a}cs and A. Sebesty{\'e}n
+and A. Valentini",
+ TITLE = "Solution of the Stationary Vacuum Equations of
+Relativity for Conformally Flat 3-Spaces",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1984, VOLUME = {100A}, NUMBER = 8, PAGES = "405-406",
+ MONTH = "February"}
+
+@TECHREPORT{Perjes:84b,
+ AUTHOR = "Z. Perj{\'e}s",
+ TITLE = "Improved Characterization of the {Kerr} Metric",
+ INSTITUTION = "Hungarian Academy of Sciences, Central
+Research Institute for Physics",
+ YEAR = 1984, NUMBER = "KFKI-1984-115"}
+
+@TECHREPORT{Perjes:84c,
+ AUTHOR = "Z. Perj{\'e}s",
+ TITLE= "Stationary Vacuum Fields with a Conformally Flat Three-Space.
+{IV}. {Complete} Solution",
+ INSTITUTE = "Institute for Nuclear Study, University of Tokyo",
+ YEAR = 1984,  NUMBER = "INS-REP.-487", MONTH = "January"}
+
+@TECHREPORT{Perjes:86,
+ AUTHOR = "Z. Perj{\'e}s",
+ TITLE = "Ernst Coordinates",
+ INSTITUTION = "Hungarian Academy of Sciences, Central
+Research Institute for Physics",
+ YEAR = 1986, TYPE = "Preprint", NUMBER = "KFKI-1986-33/B"} ,
+
+@ARTICLE{Perjes:86a,
+ AUTHOR = "Z. Perj{\'e}s",
+ TITLE = "Stationary Vacuum Fields with a Conformally
+Flat Three-Space.  {II}. {Proof} of Axial Symmetry",
+ JOURNAL = "General Relativity and Gravitation",
+ YEAR = 1986, VOLUME = 18, NUMBER = 5, PAGES = "511-530",
+ MONTH = "May"}
+
+@ARTICLE{Perjes:88,
+ AUTHOR = "Z. Perj{\'e}s",
+ TITLE  = "Approaches to  Axisymmetry by  Man and  Machine",
+ JOURNAL = "Relativity Today",
+ YEAR = 1988, EDITOR = "Z. Perjes", PUBLISHER = "World Scientific,
+ Singapore"}
+
+@ARTICLE{Perlt:90,
+ AUTHOR = "H. Perlt and J. Ranft and J. Heinrich",
+ TITLE = "Calculation of {QED} graphs with the {Spinor} technique",
+ JOURNAL = "Comp. Phys. Commun.",
+ YEAR = 1990, VOLUME = 56, NUMBER = 3, PAGES = "385-390", MONTH = "January"}
+
+@TECHREPORT{Perrottet:78,
+ AUTHOR = "M. Perrottet",
+ TITLE = "Signature for {W} Boson Production From Jet Analysis
+In e+e- $\rightarrow$ {W+W-} $\rightarrow$ Hadrons",
+ INSTITUTION = "CPT 2, CNRS, Marseille", YEAR = 1978,
+ TYPE = "Preprint", NUMBER = "78/P.1019", MONTH = "June",
+ ABSTRACT = {We have computed the ratio
+o(e+e- $\rightarrow$ W+W- $\rightarrow$ Hadrons)/ o(e+e- $\rightarrow$
+G,Z $\rightarrow$ Hadrons) as a function of the {CM} energy in the
+Weinberg-Salam model.}}
+
+@TECHREPORT{Pesic:73,
+ AUTHOR = "P. D. Pesic",
+ TITLE = "Two-Photon Cross Section for {W}-Pair Production
+by Colliding Beams",
+ INSTITUTION = "Stanford University", YEAR = 1973, TYPE = "Report",
+NUMBER = "SLAC-PUB-1188",
+ COMMENT = {Stanford University Linear Accelerator Report.}}
+
+@PHDTHESIS{Pictiaw:69,
+ AUTHOR = "Chen Pictiaw",
+ TITLE = "An Analytical Investigation of Infinitesimal Spatial
+Motion Theory and its Application to Three-Dimensional Linkages",
+ SCHOOL = "Dept. of Mech. Eng., Stanford University",
+ YEAR = 1969, MONTH = "March"}
+
+@ARTICLE{Piessens:84,
+ AUTHOR = "R. Piessens",
+ TITLE = "A Series Expansion for the First Positive Zero of the {Bessel}
+Function",
+ JOURNAL = "Math. Comp.",
+ YEAR = 1984, VOLUME = 42, PAGES = "195-197",
+ COMMENT = {Gives explicit series for first positive zero for 4 terms, using
+{REDUCE}.}}
+
+@ARTICLE{Piessens:86,
+ AUTHOR = "R. Piessens and S. Ahmed",
+ TITLE = "Note on Approximation for the Turning Points of {Bessel}
+Functions",
+ JOURNAL = "J. Comp. Phys.",
+ YEAR = 1986, VOLUME = 64, PAGES = "253-257",
+ COMMENT = {{REDUCE} used to differentiate and give expansions.}}
+
+@ARTICLE{Pignataro:85,
+ AUTHOR = "M. Pignataro and A. Luongo and N. Rizzi",
+ TITLE = "On the Effect of the Local Overall Interaction on the
+Postbuckling of Uniformly Compressed Channels",
+ JOURNAL = "Thin-Walled Structures",
+ YEAR = 1985, VOLUME = 3, PAGES = "292-321",
+ COMMENT = {{REDUCE} generating {FORTRAN}, but also used to investigate the
+form of the solutions.}}
+
+@MASTERSTHESIS{Podgorzak:84,
+ AUTHOR = "E. Podg{\'o}rak and I. Romanowska",
+ TITLE = "Application of {REDUCE} 2 to the Construction of
+Recurrence Relations",
+ SCHOOL = "Institute of Computer Science, University of Wroclaw",
+ YEAR = "1984"}
+
+@ARTICLE{Price:84,
+ AUTHOR = "S. L. Price and A. J. Stone and M. Alderton",
+ TITLE = "Explicit Formulae for the Electrostatic Energy, Forces and
+Torques Between a Pair of Molecules of Arbitrary Symmetry",
+ JOURNAL = "Molecular Phys.",
+ YEAR = 1984, VOLUME = 52, PAGES = "987-1001",
+ COMMENT = {"The substitution of the complex multipoles and the S
+functions into the expression for the electrostatic energy was
+facilitated by the use of the symbolic algebraic manipulation program
+{REDUCE}."  Involves heavy calculations.}}
+
+@TECHREPORT{Quarton,
+ AUTHOR = "D. C. Quarton and A. D. Garrad",
+ TITLE = "Some Comments on the Stability Analysis of Horizontal
+Axis Wind Turbines",
+ INSTITUTION = "Wind Energy Group, Taylor Woodrow Construction Ltd."}
+
+@TECHREPORT{Quarton:84,
+ AUTHOR = "D. C. Quarton and A. D. Garrad",
+ TITLE = "Symbolic Computing as a Tool in Wind Turbine Dynamics",
+ INSTITUTION = "Wind Energy Group, Taylor Woodrow Construction Ltd.",
+ YEAR = 1984,
+ COMMENT = {Presented at the European Wind Energy Conference and Exhibition
+22-26 Oct 1984, Hamburg.}}
+
+@MASTERSTHESIS{Rao:85,
+ AUTHOR = "R. H. Rao",
+ TITLE = "Deformation of a Fluid-Filled Cylindrical Membrane by a
+Slow Viscous Shear Flow",
+ SCHOOL = "Washington University",
+ ADDRESS = "Dept. of Mech. Eng., Washington University, St. Louis",
+ YEAR = "1985",
+ COMMENT = {Draws attention to the use of classical perturbation
+techniques combined with computer algebra as an alternative to
+numerical calculation.}}
+
+@BOOK{Rayna:87,
+ AUTHOR = "G. Rayna",
+ TITLE = "{REDUCE}:  A System for Computer Algebra",
+ PUBLISHER = "Springer-Verlag",
+ YEAR = 1987}
+
+@INPROCEEDINGS{Renner:91,
+ AUTHOR = "Friedrich Renner",
+ TITLE = "Nonlinear Evolution Equations and the {Painlev{\'e}} Analysis:
+A constructive Approach with {REDUCE}",
+ YEAR = 1991, MONTH = "July",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
+ PAGES = "289-294",
+ ABSTRACT = {A number of necessary conditions for a class of nonlinear
+partial differential equations to pass the Painlev{\'e} test with the
+Kruskal ansatz is given.  Using these we can (theoretically) construct all
+evolution equations of certain form and this property with a computer algebra
+package based on {REDUCE}.}}
+
+@ARTICLE{Renner:92,
+ AUTHOR = "Friedrich Renner",
+ TITLE = "A constructive {REDUCE} package based upon the {Painlev{\'e}}
+analysis of nonlinear evolutions equations in Hamiltonian and/or normal
+form",
+ JOURNAL = "Computer Physics Communications",
+ YEAR = 1992, VOLUME = 70, NUMBER = 2, PAGES = "409-416", MONTH = "June",
+ ABSTRACT = {A number of necessary conditions for scalar nonlinear evolution
+equations of normal or certain Hamiltonian form to pass the {Painlev{\'e}}
+test in one (or two) branches with the Kruskal ansatz is used to write a
+{REDUCE} package able to construct (theoretically) all equations with this
+property.  Starting with a given leading order, a degree of homogeneity
+and (in the Hamiltonian case) a skew-adjoint differential operator, the
+system generates al admissible resonance patterns, adapts (if possible)
+the free parameters of the equation according to the chosen pattern and the
+constraints of the compatibility conditions.  In the {Painlev{\'e}} case,
+the general inhomogeneous equation is generated and also examined.  For
+help and further investigations a set of utility procedures is supplied.}}
+
+@ARTICLE{Reusch:86,
+ AUTHOR = "M. F. Reusch and G. H. Neilson",
+ TITLE = "Torodially Symmetric Polynomial Multipole Solutions
+of the Vector {Laplace} Equation",
+ JOURNAL = "J. Comp. Phys.",
+ YEAR = 1986, VOLUME = 64, PAGES = "416-432",
+ COMMENT = {{REDUCE} (plasma MHD) algebraic form of multipoles, then
+numerical.}}
+
+Marcelo Ribeiro
+Departamento de Astrofisica
+Observatorio Nacional - CNPq
+Rua General Jose Cristino 77
+Rio de Janeiro, RJ 20921-400
+BRAZIL
+;N arpa mbr obsn.on.br
+
+@PHDTHESIS{Rink:71,
+ AUTHOR = "R. A. Rink",
+ TITLE = "Application of a Digital Computer to Solve Analytically
+Special Classes of Linear and Nonlinear Differential Equations",
+ SCHOOL = "Stanford University",
+ YEAR = 1971}
+
+@ARTICLE{Rizzi:85,
+ AUTHOR = "N. Rizzi and A. Tatone",
+ TITLE = "Symbolic Manipulation in Buckling and Postbuckling Analysis",
+ JOURNAL = "Computers and Structures",
+ YEAR = 1985, VOLUME = 21, PAGES = "691-700",
+ COMMENT = {Gives {REDUCE} program and output for generating {FORTRAN}.}}
+
+@ARTICLE{Rodionov:84,
+ AUTHOR = "A. Ya. Rodionov",
+ TITLE = "Work with {non-commutative} variables in the {REDUCE-2}
+system for analytical calculations",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1984, VOLUME = 18, NUMBER = 3, PAGES = "16-19", MONTH = "August"}
+
+@ARTICLE{Rodionov:87,
+ AUTHOR = "A. Ya. Rodionov and A. Yu. Taranov",
+ TITLE = "Computation of Covariant Derivatives of the Geodetic
+Interval within the Coincident Arguments",
+ JOURNAL = "Class. Quantum Grav.",
+ YEAR = 1987, VOLUME = 4, PAGES = "1767-1775",
+ COMMENT = {Used {REDUCE} to calculate the geodetic interval of the
+Riemannian manifold by calculating the multiple covariant derivatives of
+orders 7 and 8.  Direct use of {REDUCE} was not sufficient, but some
+investigations of the structure of the problem produced some
+recurrence relations.}}
+
+@INPROCEEDINGS{Rodionov:87a,
+ AUTHOR = "A. Ya. Rodionov and A. Yu. Taranov",
+ TITLE = "Combinatorial Aspects of Simplification of Algebraic Expressions",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "192-201",
+ PUBLISHER = "Springer-Verlag"}
+
+@TECHREPORT{Rodionov:88,
+ AUTHOR = "A. Ya. Rodionov and A. Yu. Taranov",
+ TITLE = "{RTENSOR - Packet} for work with tensoric expressions",
+ INSTITUTION = "Moscow State University, Scientific Research Institute
+of Nuclear Physics", YEAR = 1988, TYPE = "Preprint", NUMBER = "88-29/50"}
+
+@INPROCEEDINGS{Roelofs:91,
+ AUTHOR = "Marcel Roelofs and Peter K.H. Gragert",
+ TITLE = "Implementation of multilinear operators in {REDUCE} and
+applications in mathematics",
+ YEAR = 1991, MONTH = "July",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
+ PAGES = "390-396",
+ ABSTRACT = {In this paper we introduce and implement a concept for dealing
+with mathematical bases of linear spaces and mappings (multi)linear with
+respect to such bases, in {REDUCE}.  Using this concept we give some
+examples how to implement some well known (multi)linear mappings in
+mathematics with very little effort.  Moreover we implement a procedure
+operatorcoeff similar to the standard {REDUCE} procedure coeff, but now
+for linear spaces instead of polynomial rings.}}
+
+@BOOK{Rogers:89,
+ AUTHOR = "C. Rogers and W. F. Ames",
+ TITLE = "Nonlinear Boundary Value Problems in Science and Engineering",
+ PUBLISHER = "Academic Press, Inc.",
+ YEAR = 1989}
+
+@ARTICLE{Roque:88,
+ AUTHOR = "Waldir L. Roque and Renato P. dos Santos",
+ TITLE = "Computa\c{c}\~{a}o alg\'{e}brica: ``um assistente matem\~{a}tico''",
+ JOURNAL = "Ci\^{e}ncia e Cultura",
+ YEAR = 1988, VOLUME = 40, NUMBER = 9, PAGES = "843-852", MONTH =
+"September",
+ ABSTRACT = {In this paper we discuss in a simple and
+informative way the theme ``algebraic computing'' in an attempt to encourage
+the Brasilian scientific community to make use of this new tool{\ldots}. Many
+algebraic computing systems have been developed in a variety of research
+fields. Some of these systems, their main characteristics and applications
+will be discussed.},
+ COMMENT = {In Portuguese}}
+
+@ARTICLE{Roque:91,
+ AUTHOR = "Waldir L. Roque and Renato P. dos Santos",
+ TITLE = "Computer algebra in spacetime embedding",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1991, VOLUME = 12, NUMBER = 3, PAGES = "381-389", MONTH =
+"September",
+ ABSTRACT = {In this paper we describe an algorithm to determine the vectors
+normal to a space-time ${V}_{4}$ embedded in a pseudo-Euclidean manifold
+${M}_{4+N}$.  An application of this algorithm is given considering the
+Schwarzchild spacetime geometry embedded in a 6 dimensional pseudo-Euclidean
+manifold, using the algebraic computing system REDUCE.}}
+
+@ARTICLE{Ronveaux:88,
+ AUTHOR = "A. Ronveaux and G. Thiry",
+ TITLE = "Polynomial Solution of Recurrence Relation and Differential
+Equation",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1988, VOLUME = 22, NUMBER = 4, PAGES = "9-19", MONTH = "October"}
+
+@ARTICLE{Ronveaux:89,
+ AUTHOR = "A. Ronveaux and G. Thiry",
+ TITLE = "Differential Equations of Some Orthogonal Families in {REDUCE}",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1989, VOLUME = 8, NUMBER = 5, PAGES = "537-541", MONTH = "November"}
+
+@INPROCEEDINGS{Rudenko:91,
+ AUTHOR = "V.M. Rudenko and V.V. Leonov and A.F. Bragazin and
+I.P Shmyglevsky",
+ TITLE = "Application of Computer Algebra to the Investigation of the
+Orbital Satellite Motion",
+ YEAR = 1991, MONTH = "July",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
+ PAGES = "450-451"}
+
+@ARTICLE{Saez:83,
+ AUTHOR = "A. E. Saez and B. J. McCoy",
+ TITLE = "Transient Analysis of Packed-Bed Thermal Storage Systems",
+ JOURNAL = "Int. J. Heat Mass Transfer",
+ YEAR = 1983, VOLUME = 26, NUMBER = 1, PAGES = "49-54"}
+
+@ARTICLE{Sage:88,
+ AUTHOR = "Martin L. Sage",
+ TITLE = "An Algebraic Treatment of Quantum Vibrations",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1988, VOLUME = 5, NUMBER = 3, PAGES = "377-384", MONTH = "June"}
+
+@ARTICLE{Sarlet:92,
+ AUTHOR = "W. Sarlet and J. Vanden Bonne",
+ TITLE = "{REDUCE-}procedures for the study of adjoint symmetries of
+second-order differential equations",
+ JOURNAL = "J. Symbolic Computation",
+ VOLUME = 13, NUMBER = 6, YEAR = 1992, MONTH = "June", PAGES = "683-693",
+ ABSTRACT = {Two {REDUCE} programs are presented which should be of
+assistance in computing and studying so-called adjoint symmetries of
+second-order ordinary differential equations.  The first program essentially
+serves to construct the determining equations for adjoint symmetries,
+whose leading coefficients are allowed to be polynomial functions of the
+velocities.  The second program runs various tests concerning the possible
+construction of a first integral or a lagrangian for the given system.}}
+
+@INPROCEEDINGS{Sasaki:79,
+ AUTHOR = "Tateaki Sasaki",
+ TITLE = "An Arbitrary Precision Real Arithmetic Package in {REDUCE}",
+ BOOKTITLE = "Proc. {EUROSAM} 1979, Lecture Notes
+in Computer Science", YEAR = 1979, VOLUME = 72, PAGES = "358-368",
+ PUBLISHER = "Springer-Verlag",
+ ABSTRACT = {A {REDUCE} arbitrary precision real arithmetic package is
+described which will become a part of the kernel of an algebraic-numeric
+system being developed for {REDUCE}.}}
+
+@ARTICLE{Savage:90,
+ AUTHOR = "Stuart B. Savage",
+ TITLE = "Symbolic computation of the flow of granular avalanches",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1990, VOLUME = 9, NUMBER = 4, PAGES = "515-530", MONTH = "April"}
+
+@ARTICLE{Sayers:87,
+ AUTHOR = "C. M. Sayers",
+ TITLE = "The Elastic Anisotropy of Polycrystalline Aggregates
+of Zirconium and Its Alloys",
+ JOURNAL = "J. Nuclear Materials",
+ YEAR = 1987, VOLUME = 144, PAGES = "211-213",
+ COMMENT = {Used {REDUCE} for calculations of tensor products.}}
+
+@ARTICLE{Sayers:87a,
+ AUTHOR = "C. M. Sayers",
+ TITLE = "Elastic Wave Anisotropy in the Upper Mantle",
+ JOURNAL = "Geophysical J. R. Ast. Soc.",
+ YEAR = 1987, VOLUME = 88, PAGES = "417-424",
+ COMMENT = {Used {REDUCE} in calculations.  "Theoretical expressions for
+angular dependence of the longitudinal and shear wave velocities in an
+axially symmetric aggregate{\ldots}"}}
+
+@INPROCEEDINGS{Schlegel:91,
+ AUTHOR = "H. Schlegel",
+ TITLE = "Determination of the Root System of Semisimple {Lie} Algbras from
+the {Dynkin} Diagram",
+ YEAR = 1991, MONTH = "July",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
+ PAGES = "239-240"}
+
+@INPROCEEDINGS{Schmuck:77,
+ AUTHOR = "P. Schmuck",
+ TITLE = "Verification of the Transient, Two Phase Fluid
+Flow Program {Kachina} using Computerized Similarity Analysis",
+ YEAR = 1977, MONTH = "October",
+ BOOKTITLE = "Second {GAMM} Conference on Numerical Methods
+in Fluid Mechanics, k{\"o}ln"}
+
+@TECHREPORT{Schoebel:92,
+ AUTHOR = "Franziska Schoebel",
+ TITLE = "The Symbolic Classification of Real Four-Dimensional
+   Lie Algebras", NUMBER = "Preprint 27/92", YEAR = 1992,
+ INSTITUTION = "Naturwissenschaftlich-Theoretisches Zentrum, Universitaet
+    Leipzig, Germany"}
+
+@TECHREPORT{Schoepf:91,
+ AUTHOR = "Rainer Sch{\"o}pf and Peter Deuflhard",
+ TITLE = "{OCCAL} A mixed symbolic-numeric {Optimal Control CALculator}",
+ INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin",
+ YEAR = 1991, TYPE = "Preprint", NUMBER = "SC 91-13", MONTH = "December",
+ ABSTRACT = {The numerical solution of optimal control problems by indirect
+methods (such as multiple shooting or collocation) requires a considerable
+amount of analytic calculation to establish a numerically tractable system.
+These analytic calculations, though being rather tedious in realistic
+examples, are nowadays mostly still done by hand--and thus prone to
+calculation errors.  The paper aims at automating this analytic processing
+to a reasonable extent by means of a modern symbolic manipulation language
+(here:  REDUCE).  In its present stage of development the package OCCAL
+(mnemotechnically for Optimal Control CALculator) permits an interactive
+use, covering tasks like automatic determination of control and, in case of a
+singular control, of its order.  In simpler problems, the present version of
+OCCAL automatically produces the full subroutine input for a MULtiple
+shooting code (MULCON) with adaptive numerical CONtinuation.
+
+In more complicated problems where singular sub-arcs may occur or where the
+sequence of sub-arcs of the optimal trajectory is unclear OCCAL is a
+significant help in reducing analytic pre-processing.  Examples illustrate
+the performance of OCCAL/MULCON.}}
+
+@ARTICLE{Schruefer:81,
+ AUTHOR = "E. Schr{\"u}fer and H. Heintzmann",
+ TITLE = "Lorentz-Covariant Eikonal Method in Magnetohydrodynamics
+{II} - The Determination of the Wave Amplitude",
+ JOURNAL = "Phys. Lett.",
+ YEAR = 1981, VOLUME = {81A}, NUMBER = 9, PAGES = "501-506",
+ MONTH = "February",
+ COMMENT = {Used {REDUCE} for "rather tedious algebra."}}
+
+@ARTICLE{Schruefer:82,
+ AUTHOR = "E. Schr{\"u}fer",
+ TITLE = "An Implementation of the Exterior Calculus in {REDUCE:}
+A Status Report",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1982, VOLUME = 16, NUMBER = 4, PAGES = "27-31", MONTH = "November"}
+
+@ARTICLE{Schruefer:87,
+ AUTHOR = "E. Schr{\"u}fer and F. W. Hehl and J. D. McCrea",
+ TITLE = "Exterior Calculus on the Computer:  The {REDUCE}-Package
+{EXCALC} Applied to General Relativity and to the {Poincar{\'e}}
+Gauge Theory",
+ JOURNAL = "General Relativity and Gravitation",
+ YEAR = 1987, VOLUME = 19, NUMBER = 2, PAGES = "197-218",
+ MONTH = "February",
+ COMMENT = {Application of {EXCALC/REDUCE}, including review of other
+systems, and description of {EXCALC}.}}
+
+@ARTICLE{Schruefer:88,
+ AUTHOR = "E. Schr{\"u}fer",
+ TITLE = "A Note on {Einstein} Metrics",
+ JOURNAL = "SIGSAM Bulletin",
+ YEAR = 1988, VOLUME = 22, NUMBER = 3, PAGES = "22-26", MONTH = "July"}
+
+@ARTICLE{Schwarz:80,
+ AUTHOR = "F. Schwarz",
+ TITLE = "An Approximation Scheme for Constructing $\pi_{0}\pi$
+Amplitudes from {ACU} Requirements",
+ JOURNAL = "Fortschritte der Physik",
+ YEAR = 1980, VOLUME = 28, PAGES = "201-235",
+ COMMENT = {"To derive the equations expressing the threshold and the
+asymptotic behaviour one relies heavily on the programming system
+{REDUCE}."}}
+
+@ARTICLE{Schwarz:82,
+ AUTHOR = "F. Schwarz",
+ TITLE = "Symmetries of the Two Dimensional {Korteweg-De Vries} Equation",
+ JOURNAL = "J. Phys. S. Japan",
+ YEAR = 1982, VOLUME = 51, NUMBER = 8, PAGES = "2387-2388",
+ COMMENT = {{REDUCE} used in the {SPDE} package.}}
+
+@ARTICLE{Schwarz:82a,
+ AUTHOR = "F. Schwarz",
+ TITLE = "A {REDUCE} Package for Determining {Lie} Symmetries of
+Ordinary and Partial Differential Equations",
+ JOURNAL = "Computer Physics Communications",
+ YEAR = 1982,  VOLUME = 27, PAGES = "179-186",
+ COMMENT = {Preliminary description of {REDUCE} packages {SODE} and
+{SPDE}.}}
+
+@ARTICLE{Schwarz:83,
+ AUTHOR = "Fritz Schwarz",
+ TITLE = "A {REDUCE} Package for Series Analysis by {Hadamard's}
+Theorem and {QD} Schemes",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "38-44", MONTH = "February"}
+
+@INPROCEEDINGS{Schwarz:83a,
+ AUTHOR = "Fritz Schwarz",
+ TITLE = "Automatically Determining Symmetries of Ordinary Differential
+Equations",
+ BOOKTITLE = "Proc. {EUROCAL} 1983, Lecture Notes
+in Computer Science", YEAR = 1983, VOLUME = 162, PAGES = "45-54",
+ PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{Schwarz:84,
+ AUTHOR = "F. Schwarz",
+ TITLE = "The {Riquier-Janet} Theory and Its Application to Nonlinear
+Evolution Equations",
+ JOURNAL = "Physica",
+ YEAR = 1984, VOLUME = "11D", PAGES = "243-251",
+ COMMENT = {Prologation methods in {REDUCE}.  Points to existence of
+{REDUCE} system.}}
+
+@ARTICLE{Schwarz:84a,
+ AUTHOR = "F. Schwarz and W. H. Steeb",
+ TITLE = "Symmetries and First Integrals for Dissipative Systems",
+ JOURNAL = "J. Phys. {A:}  Math. Gen.",
+ YEAR = 1984, VOLUME = 17, PAGES = "L819-L823"}
+
+@ARTICLE{Schwarz:85,
+ AUTHOR = "F. Schwarz",
+ TITLE = "Automatically Determining Symmetries of Partial Differential
+Equations",
+ JOURNAL = "Computing",
+ YEAR = 1985, VOLUME = 34, PAGES = "91-106",
+ COMMENT = {Describes the {SPDE} package for {REDUCE}.}}
+
+@ARTICLE{Schwarz:85a,
+ AUTHOR = "Fritz Schwarz",
+ TITLE = "An Algorithm for Determining Polynomial First Integrals of
+Autonomous Systems of Ordinary Differential Equations",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1985, VOLUME = 1, NUMBER = 2, PAGES = "229-233", MONTH = "June"}
+
+@ARTICLE{Schwarz:86,
+ AUTHOR = "F. Schwarz",
+ TITLE = "A {REDUCE} Package for Determining First Integrals of
+Autonomous Systems of Ordinary Differential Equations",
+ JOURNAL = "Computer Physics Communications",
+ YEAR = 1986, VOLUME = 39, PAGES = "285-296",
+ COMMENT = {Description of package {DISSYS} in {REDUCE}.}}
+
+@INPROCEEDINGS{Schwarz:87,
+ AUTHOR = "F. Schwarz",
+ TITLE = "Symmetries and Involution Systems: Some Experiments in
+Computer Algebra",
+ YEAR = 1987, MONTH = "August",
+ BOOKTITLE = "Topics in Soliton Theory and Exactly Solvable Nonlinear
+Equations", PUBLISHER = "World Science Press", ADDRESS = "Singapore",
+ COMMENT = {Description of algorithm {INVSYS} and applications.}}
+
+@ARTICLE{Schwarz:88,
+ AUTHOR = "F. Schwarz",
+ TITLE = "Symmetries of Differential Equations: From {Sophus Lie} to
+Computer Algebra",
+ JOURNAL = "Siam Review",
+ YEAR = 1988, VOLUME = 30, PAGES = "450-481",
+ COMMENT = {Review article on applying the {REDUCE} package {SPDE}.}}
+
+@ARTICLE{Schwarz:94,
+ AUTHOR = "F. Schwarz",
+ TITLE = "Efficient Factorization of Linear {ODE's}",
+ JOURNAL = "Sigsam Bulletin",
+ YEAR = 1994, VOLUME = 28, NUMBER = 1, PAGES = "9-17",
+ ABSTRACT = {Factorization and testing for irreducibility has turned out to
+be one of the most important algorithms for handling linear ode's.  The
+main hindrance for applying it is its trmendous complexity originating to a
+large extent from solving certain Riccati equations which occur during the
+factorization.  The solution procedure for these Riccati equations is much
+more manageable if it is subdivided into two major parts.  At first so
+called solution candidates are determined each of which depends only on the
+parameters of a single irreducible denominator or the behavior at infinity.
+In a second step it is tried to complete each candidate into a genuine
+solution of the Riccati equation, possibly including an unspecified number
+of additional first order poles.  Furthermore a scheme is proposed for
+running the factorization procedure in parallel on a two-processor machine
+in which possible factors are searched for both from the right and the left
+at the same time.}}
+
+@ARTICLE{Seiler:91,
+ AUTHOR = "Werner M. Seiler",
+ TITLE = "{SUPERCALC-} a {REDUCE} package for commutator calculations",
+ JOURNAL = "Computer Physics Communications",
+ YEAR = 1991, VOLUME = 66, PAGES = "363-376",
+ COMMENT = {A {REDUCE} package for commutator calculations in sypersymmetric
+theories (including ordered products) and for infinite sums is presented
+and an application to the computation of anomalies in string theory is
+given.}}
+
+@INPROCEEDINGS{Shablygin:87,
+ AUTHOR = "E. Shablygin",
+ TITLE = "Integral Equation with Hidden Eigenparameter Solver:
+{REDUCE} and {FORTRAN} in Tandem",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "186-191",
+ PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{Shmueli:83,
+ AUTHOR = "U. Shmueli and A. J. C. Wilson",
+ TITLE = "Generalized Intensity Studies:  The Subcentric Distribution
+and Effects of Dispersion",
+ JOURNAL = "Acta Cryst.",
+ YEAR = 1983, VOLUME = "A39", PAGES = "225-233",
+ COMMENT = {Uses {REDUCE} for series expansion to high order as convergence
+is slow.}}
+
+@ARTICLE{Shmueli:83a,
+ AUTHOR = "U. Shmueli and U. Kaldor",
+ TITLE = "Moments of the Trigonometric Structure Factor",
+ JOURNAL = "Acta Cryst.",
+ YEAR = 1983, VOLUME = "A39", PAGES = "615-621",
+ COMMENT = {Eight moment of magnitude of trigonometric structure factor.
+Used {REDUCE}.  Description of {REDUCE} in appendix.}}
+
+@TECHREPORT{Shtokhamer:75,
+ AUTHOR = "R. Shtokhamer",
+ TITLE = "Canonical Form of Polynomials in the Presence of
+Side Relations",
+ INSTITUTION = "Technion",
+ YEAR = 1975, NUMBER = "Technion-PH-76-25"}
+
+@TECHREPORT{Shtokhamer:77,
+ AUTHOR = "R. Shtokhamer",
+ TITLE = "The Use of {``LET''} Statements in Producing Short
+Comprehended Outputs",
+ INSTITUTION = "Department of Physics, Technion-Israel
+Institute of Technology, Haifa, Israel",
+ YEAR = 1977, NUMBER = "Technion-PH-77-36",
+ ABSTRACT = {It is shown that an algebraic implementation of {"LET"}
+statements may be useful in producing comprehended outputs.
+The suggested algorithm is based on solving large set of
+linear equations over a field.}}
+
+@INPROCEEDINGS{Smit:79,
+ AUTHOR = "J. Smit",
+ TITLE = "New Recursive Minor Expansion Algorithms, A Presentation in
+a Comparative Context",
+ BOOKTITLE = "Proc. {EUROSAM} 1979, Lecture Notes
+in Computer Science", YEAR = 1979, VOLUME = 72, PAGES = "74-87",
+PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{Smit:81,
+ AUTHOR = "J. Smit and J. A. van Hulzen and B. J. A. Hulshof",
+ TITLE = "{NETFORM} and Code Optimizer Manual",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1981, VOLUME = 15, NUMBER = 4, PAGES = "23-32",
+ MONTH = "November"}
+
+@INPROCEEDINGS{Smit:82,
+ AUTHOR = "J. Smit and J. A. van Hulzen",
+ TITLE = "Symbolic Numeric Methods in Microwave Technology",
+ BOOKTITLE = "Proc. {EUROCAM} 1982, Lecture Notes
+in Computer Science", YEAR = 1982, VOLUME = 144, PAGES = "281-288",
+ PUBLISHER = "Springer-Verlag"}
+
+@INPROCEEDINGS{Smit:87,
+ AUTHOR = "J. Smit and S. H Gerez and R. Mulder",
+ TITLE = "Application of a Structured {LISP} System to Computer Algebra",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "149-160",
+ PUBLISHER = "Springer-Verlag"}
+
+@TECHREPORT{Soderstrand:72,
+ AUTHOR = "M. A. Soderstrand and D. C. Huey",
+ TITLE = "Sensitivities of Fourth-Order Filters Obtained by a
+Low-Pass to Band-Pass Transformation",
+ INSTITUTION = "University of California, Davis",
+ YEAR = 1972, TYPE = "Report"}
+
+@INPROCEEDINGS{Soderstrand:72a,
+ AUTHOR = "M. A. Soderstrand and S. K. Mitra",
+ TITLE = "Computer-aided Sensitivity Analysis of Higher Filters",
+ YEAR = 1972, MONTH = "July",
+ BOOKTITLE = "Proc. Second Symposium on Network Theory,
+Herzegnovia, Yugoslavia"}
+
+@TECHREPORT{Soderstrand:74,
+ AUTHOR = "M. A. Soderstrand and J. F. Lathrop",
+ TITLE = "Two Computer Programs for the Sensitivity Analysis
+of Higher Order Filters",
+ INSTITUTION = "Sandia Laboratories", YEAR = 1974,
+ TYPE = "Report", NUMBER = "SLL-73-0225", MONTH = "January"}
+
+@ARTICLE{Soma:77,
+ AUTHOR = "T. Soma",
+ TITLE = "Relativistic Aberration Formulas for Combined
+Electric-Magnetic Focusing-Deflection System",
+ JOURNAL = "Optik",
+ YEAR = 1977, VOLUME = 49, PAGES = "255-262",
+ COMMENT = {Existence of a vertical landing electron beam deflecting
+system free of all deflection induced aberrations is
+presented analytically.}}
+
+@INPROCEEDINGS{Soma:85,
+ AUTHOR = "Takashi Soma",
+ TITLE = "Recent Applications of {REDUCE} in {RIKEN}",
+ YEAR = 1985,
+ BOOKTITLE = "Proc. of the Second {RIKEN} International
+Symposium on Symbolic and Algebraic Computation by Computers",
+ PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "181-182"}
+
+@INPROCEEDINGS{Spiridonova:87,
+ AUTHOR = "M. Spiridonova",
+ TITLE = "Some extensions and Applications of {REDUCE} System",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "136-137",
+ PUBLISHER = "Springer-Verlag"}
+
+@TECHREPORT{Squire,
+ AUTHOR = "W. Squire",
+ TITLE = "Some Applications of Symbolic Matrix Inversion",
+ INSTITUTION = "Dept. of Mechanical and Aerospace Engineering,
+West Virginia University"}
+
+@BOOK{Steeb:92b,
+ AUTHOR = "Willi-Hans Steeb and Dirk Lewien",
+ TITLE = "Algorithms and Computation with {REDUCE}",
+ PUBLISHER = "BI-Wissenschaftsverlag, Mannheim", YEAR = 1992,
+ ABSTRACT ={This book gives a collection of 75 standard methods
+ in mathematics, physics and engineering together with their
+ programs in {REDUCE} 3.4. Each item consists of a one page mathematical
+ description and one page {REDUCE} algebraic source text (in most cases
+ a few lines only). The book is an introduction by example
+ to algebraic programming in {REDUCE} and a collection of
+ ready to use solutions for many mathematical subtasks}}
+
+@BOOK{Steeb:92c,
+ AUTHOR = "Willi-Hans Steeb",
+ TITLE = "Chaos and Fractals: Algorithms and Computations",
+ PUBLISHER = "BI-Wissenschaftsverlag, Mannheim",
+ YEAR = 1992,
+ COMMENT = "This book includes 26 Turbo C and C++, 47 Turbo PASCAL
+and 23 REDUCE programs"}
+
+@ARTICLE{Steeb:92d,
+ AUTHOR = "W-H Steeb",
+ TITLE = "Computer Algebra and Its Applications in Physics",
+ JOURNAL = "International Journal of Modern Physics C",
+ YEAR = 1992, VOLUME = 3, NUMBER = 6, PAGES = "1333-1350",
+ COMMENT = {Computer algebra is a powerful tool in the study of a wide
+class of problems in mathematics, physics, and engineering.  The primary
+domain of computer algebra is the solution of large scale formal problems.
+We give an introduction and survey on computer algebra.  In particular we
+show with examples how problems in physics can be solved.  We also show
+with an example how object-oriented programming can be used in such
+problems.}}
+
+@ARTICLE{Steeb:93,
+ AUTHOR = "W-H Steeb",
+ TITLE = "Fermi Systems and Computer Algebra",
+ JOURNAL = "International Journal of Modern Physics C",
+ YEAR = 1993, VOLUME = 4, NUMBER = 4, PAGES = "841-846",
+ COMMENT = {Computer algebra is a helpful tool in studying Fermi systems.
+We show how the anticommutation relations can be implemented with computer
+algebra.  Then we give an application to the Hubbard model.}}
+
+@BOOK{Steeb:93a,
+ AUTHOR = "W.-H Steeb",
+ TITLE = "Invertible Point Transformations and Nonlinear Differential
+Equations",
+ PUBLISHER = "World Scientific Publishing",
+ YEAR = 1993}
+
+@BOOK{Steeb:94,
+ AUTHOR = "W.-H Steeb",
+ TITLE = "Chaos und Quantenchaos in dynamischen Systemen",
+ PUBLISHER = "Bi-Wissenschaftsverlag, Mannheim",
+ YEAR = 1994}
+
+@BOOK{Steeb:94a,
+ AUTHOR = "W.-H Steeb",
+ TITLE = "Quantum Mechanics using Computer Algebra",
+ PUBLISHER = "World Scientific Publishing, Singapore",
+ YEAR = 1994}
+
+@ARTICLE{Steeb:94b,
+ AUTHOR = "W-H Steeb",
+ TITLE = "Applications of Computer Algebra in Quantum Groups",
+ JOURNAL = "International Journal of Modern Physics C",
+ YEAR = 1994, VOLUME = 6, PAGES = "701-706"}
+
+@ARTICLE{Steeb:94c,
+ AUTHOR = "W-H Steeb",
+ TITLE = "Extended {Lorenz} Models and Time Dependent First Integrals",
+ JOURNAL = "Zeitschrift fuer Naturforschung",
+ YEAR = 1994, VOLUME = "49a", PAGES = "751-753"}
+
+@ARTICLE{Steeb:95,
+ AUTHOR = "W-H Steeb",
+ TITLE = "{Bose-Fermi} Systems and Computer Algebra",
+ JOURNAL = "Foundations of Physics Letters", YEAR = 1995}
+
+@ARTICLE{Steinberg:82,
+ AUTHOR = "Stanly Steinberg",
+ TITLE = "Mathematics and Symbol Manipulation",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1982, VOLUME = 16, NUMBER = 3, PAGES = "11-15", MONTH = "August"}
+
+@InProceedings{Steinberg:93,
+  author =      "S. Steinberg and R. Liska",
+  title =       "Stability Analysis and Quantifier Elimination",
+  booktitle =   "Proceedings of the 1993 International IMACS Symposium on
+                 Symbolic Computation",
+  year =        "1993",
+  editor =      "G. Jacob and N. E. Oussous and S. Steinberg",
+  pages =       "62-67",
+  organization ="IMACS",
+  publisher =   "Laboratoire d'Informatique Fondamentale de Lille, France",
+  comment =     {Stability of time-stepping numerical schemes for partial
+                 differential equations based on the {REDUCE} package FIDE
+                 and the SACLIB package QEPCAD.}
+}
+
+@ARTICLE{Steuerwald,
+ AUTHOR = "J. Steuerwald and W. Kerner",
+ TITLE = "A Contribution to the Efficient Solution of
+Extensive Symbolic Computations",
+ JOURNAL = "Comp. Phys. Comm."}
+
+@ARTICLE{Stoutemyer:74,
+ AUTHOR = "D. Stoutemyer",
+ TITLE = "Automatic Error Analysis Using the Computer Symbolic
+Manipulation Language",
+ JOURNAL = "TOMS 3",
+ YEAR = 1977, VOLUME = 3, NUMBER = 1, PAGES = "26-43",
+ MONTH = "March",
+ ABSTRACT = {This paper shows how the inherent error and the fixed-point
+or floating-point roundoff of chopoff error of an expression can be
+determined automatically using a computer algebra language such as
+{REDUCE}.}}
+
+@TECHREPORT{Stoutemyer:75,
+ AUTHOR = "David R. Stoutemyer",
+ TITLE = "Symbolic Computer Solution of an Equation in Finite Terms",
+ INSTITUTION = "Dept. of Comp. Science, Univ. of Utah",
+ TYPE = "Report", YEAR = 1975, NUMBER = "UCP-33",
+ ABSTRACT = {This report contains a program listing together with
+documentation, a demonstration, and discussion of a {REDUCE} program for the
+exact solution of an equation in finite terms.  Capable of treating certain
+equations involving elementary transcendental functions, radicals,
+and polynomials, the program incorporates several solution techniques
+not implemented in existing analogous programs written in other
+computer algebra languages.  The program is also capable of solving
+linear or linear fractional in the unknowns.  In this case it simply
+used the built-in matrix equation solver, but permitting input as
+lists of expressions rather than matrices, which is convenient for
+sparse or small linear systems.}}
+
+@ARTICLE{Stoutemyer:77,
+ AUTHOR = "David R. Stoutemyer",
+ TITLE = "Analytically Solving Integral Equations by Using Computer
+Algebra",
+ JOURNAL = "TOMS",
+ YEAR = 1977, VOLUME = 3, NUMBER = 2, PAGES = "128-146",
+ MONTH = "June",
+ ABSTRACT = {This report describes how a computer algebra language, such as
+{REDUCE}, may be used to automatically construct closed-form and series
+analytical solutions of integral equations.}}
+
+@ARTICLE{Stroscio:74,
+ AUTHOR = "M. A. Stroscio and J. M. Holt",
+ TITLE = "Radiative Corrections to the Decay Rate of Orthopositronium",
+ JOURNAL = "Phys. Rev. A",
+ YEAR = 1974, MONTH = "September", VOLUME = 10, PAGES = "749-755"}
+
+@ARTICLE{Stuart:88,
+ AUTHOR = "Robin G. Stuart",
+ TITLE = "Algebraic Reduction of one-loop {Feynman} Diagrams to
+Scalar Integrals",
+ JOURNAL = "Comp. Phys. Commun.",
+ YEAR = 1988, VOLUME = 48, NUMBER = 3, PAGES = "367-389", MONTH = "March"}
+
+@ARTICLE{Stuart:90,
+ AUTHOR = "Robin G. Stuart and A. G{\'o}ngora-T",
+ TITLE = "Algebraic Reduction of one-loop {Feynman} Diagrams to
+Scalar Integrals II",
+ JOURNAL = "Comp. Phys. Commun.",
+ YEAR = 1990, VOLUME = 56, NUMBER = 3, PAGES = "337-350", MONTH = "January"}
+
+@ARTICLE{Suppes:89,
+ AUTHOR = "Patrick Suppes and Shuzo Takahashi",
+ TITLE = "An Interactive Calculus Theorem-prover for Continuity
+Properties",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1989, VOLUME = 7, NUMBER = 6, PAGES = "573-590", MONTH = "June"}
+
+@ARTICLE{Surguladze:89,
+ AUTHOR = "L.R. Surguladze and F.V. Tkachov",
+ TITLE = "{LOOPS:} Procedures for Multiloop Calculations in Quantum Field
+Theory for the {REDUCE} System",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1989, VOLUME = 55, NUMBER = 2, PAGES = "205-215",
+ MONTH = "September", PUBLISHER = "North Holland Publishing Company"}
+
+@INPROCEEDINGS{Surguladze:91,
+ AUTHOR = "Levan R. Surguladze and Mark A. Samuel",
+ TITLE = "Algebraic Perturbative Calculations in High Energy Physics
+Methods, algorithms, computer programs and physical applications",
+ YEAR = 1991, MONTH = "July",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
+ PAGES = "439-447",
+ ABSTRACT = {The methods and algorithms for high order algebraic
+perturbative calculations in theoretical high energy physics are briefly
+reviewed.  The {SCHOONSCHIP} program {MINCER} and the {REDUCE} program
+{LOOPS} for analytical computation of arbitrary massless, one-, two-
+and three-loop Feynman diagrams of the propagator type are described.
+The version of the program {LOOPS} for personal computers and the extended
+version of the program {MINCER} for four-loop renormalization group
+calculations are presented.  The new program for algebraic perturbative
+calculations is also discussed.  This program is written on the new
+algebraic programming system {FORM}.  Some recent results of application
+to the high energy physics are given.}}
+
+@ARTICLE{Tallents:84,
+ AUTHOR = "G. J. Tallents",
+ TITLE = "The Relative Intensities of Hydrogen-Like Fine Structure",
+ JOURNAL = "J. Phys. B",
+ YEAR = 1984, VOLUME = 17, PAGES = "3677-3691",
+ COMMENT = {{REDUCE} used to check a formula; also checked numerically.}}
+
+@InProceedings{Tao90,
+  author =      "Qingsheng Tao",
+  title =       "Symbolic and Algebraic manipulation for Formulae of
+                 Interpolation and Quadrature",
+  booktitle =   "Proceedings of the 1990 International Symposium on
+                 Symbolic and Algebraic Computation",
+  year =        "1990",
+  editor =      "S. Watanabe and Morio Nagata",
+  pages =       "306",
+  organization =        "ACM",
+  publisher =   "Addison-Wesley"
+}
+
+@TECHREPORT{Tasso:76,
+ AUTHOR = "H. Tasso and J. Steuerwald",
+ TITLE = "Subroutine for Series Solutions of Linear Differential Equations",
+ INSTITUTION = "Max Planck Institut for Plasmaphysik",
+ YEAR = 1976, NUMBER = "IPP 6/143"}
+
+@TECHREPORT{Thas:89,
+ AUTHOR = "C. Thas",
+ TITLE = "A collection of {REDUCE} and {MACSYMA} programs about college
+geometry.  Part 1",
+ INSTITUTION = "State University of Gent",
+ YEAR = 1989, NUMBER = 5, MONTH = "September"}
+
+@TECHREPORT{Thas:89a,
+ AUTHOR = "C. Thas",
+ TITLE = "A collection of {REDUCE} and {MACSYMA} programs about college
+geometry.  Part 2",
+ INSTITUTION = "State University of Gent",
+ YEAR = 1989, NUMBER = 5, MONTH = "September"}
+
+@INPROCEEDINGS{Todd:88,
+ AUTHOR = "P. H. Todd and G. W. Cherry",
+ TITLE = "Symbolic Analysis of Planar Drawings",
+ BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag",
+ YEAR = 1988, VOLUME = 358, PAGES = "344-355"}
+
+@ARTICLE{Toth:86,
+ AUTHOR = "K. T{\'o}th and K. Szeg{\"o} and A. Margaritis",
+ TITLE =  "Radiative Corrections for Semileptonic Decays of {Hyperons:
+`Model-Independent' Part}",
+ JOURNAL = "Physical Review D", YEAR = 1986, VOLUME = 33, NUMBER = 11,
+ PAGES = "3306-3315", MONTH ="June"}
+
+@INPROCEEDINGS{Tournier:79,
+ AUTHOR = "Evelyne Tournier",
+ TITLE = "An Algebraic Form of a Solution of a System
+of Linear Differential Equations with Constant Coefficients",
+ BOOKTITLE = "Proc. {EUROSAM} 1979, Lecture Notes
+in Computer Science", YEAR = 1979, VOLUME = 72, PAGES = "153-163",
+ PUBLISHER = "Springer-Verlag",
+ ABSTRACT = {In this paper we describe an algorithm for finding an
+algebraic form for the solution of a system of linear differential
+equations with constant coefficients, using the properties of elementary
+divisors of a polynomial matrix.}}
+
+@PHDTHESIS{Tournier:87,
+ AUTHOR = "Evelyne Tournier",
+ TITLE = "Solutions Formelles D'Equations Differentielles,
+le Logiciel de Calcul Formel:  {DESIR} Etude Theorique
+et Realisation",
+ SCHOOL = "L'Universit{\'e} Scientifique, Technologique et
+Medicale de Grenoble",
+ YEAR = 1987, MONTH = "April"}
+
+@INPROCEEDINGS{Trenkov:91,
+ AUTHOR = "I. Trenkov and M. Spiridonova and M. Daskalova",
+ TITLE = "An Application of the {REDUCE} System for Solving a Mathematical
+Geodesy Problem",
+ YEAR = 1991, MONTH = "July",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
+ PAGES = "448-449"}
+
+@INPROCEEDINGS{Trotter:89,
+ AUTHOR = "H. F. Trotter",
+ TITLE = "Use of Symbolic Methods in Analyzing an Integral Operator",
+ BOOKTITLE = "Proc. of Computers and Mathematics '89",
+ EDITOR = "E. Kaltofen and S. M. Watt",
+ YEAR = 1989, PAGES = "82-90", PUBLISHER = "Springer-Verlag, New York"}
+
+@ARTICLE{Tsai:65,
+ AUTHOR = "Y. S. Tsai and A. C. Hearn",
+ TITLE = "Differential Cross-Section for e+ + e- $\rightarrow$ {W+} +
+{W-} $\rightarrow$ e- + $\overline{\nu}_{e} + \mu + \nu_{\mu}$",
+ JOURNAL = "Phys. Rev.",
+ YEAR = 1965, VOLUME = 140, PAGES = "B721-B729"}
+
+@ARTICLE{Tsai:74,
+ AUTHOR = "Y. S. Tsai",
+ TITLE = "Pair Production and Bremsstrahlung of Charged Leptons",
+ JOURNAL = "Rev. Mod. Phys.",
+ YEAR = 1974, VOLUME = 46, PAGES = "815-851"}
+
+@ARTICLE{Ucoluk:82,
+ AUTHOR = "G. {\"U}\c{c}oluk and A. Hacinliyan",
+ TITLE = "A Proposal for Extensions to {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1982, VOLUME = 16, NUMBER = 2, PAGES = "4-14", MONTH = "May",
+ ABSTRACT = {Three classes of extensions are proposed for {REDUCE}:  A
+facility  for evaluating arbitrary functions of matrices; a facility for
+grouping, modifying or restoring the status of various flags
+in {REDUCE}; further extensions and modifications for separating
+terms, coefficients of expressions, concatenation, and non-
+commuting algebra.}}
+
+@BOOK{Ueberberg:92,
+ AUTHOR = "Johannes Ueberberg",
+ TITLE = "Einf{\"u}hrung in die computeralgebra mit {REDUCE}",
+ PUBLISHER = "BI-Wissenschaftsverlag, Mannheim",
+ YEAR = 1992}
+
+@ARTICLE{Umeno:89,
+ AUTHOR = "Takaji Umeno and Syuichi Yamashita and Osami Saito and
+Kenichi Abe",
+ TITLE = "Symbolic Computation Application for the Design of Linear
+Multivariable Control Systems",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1989, VOLUME = 8, NUMBER = 6, PAGES = "581-588", MONTH = "December"}
+
+@INPROCEEDINGS{Urintsev:91,
+ AUTHOR = "A.L. Urintsev and A.V. Samoilov",
+ TITLE = "Complex Reduce-programs for analytic solution of some problems of
+beam transport systems",
+ YEAR = 1991,
+ BOOKTITLE = "In:  4th International Conference on Computer Algebra in
+Physical Research",
+ EDITOR = "D.V. Shirkov and V.A. Rostovtsev and V.P. Gerdt",
+ PUBLISHER = "World Scientific", ADDRESS = "Singapore, New Jersey, London,
+Hong Kong", PAGES = "438-442"}
+
+@ARTICLE{vandenHeuvel:86,
+ AUTHOR = "Pim van den Heuvel",
+ TITLE = "Adding Statements to {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1986, VOLUME = 20, NUMBER = "1 and 2", PAGES = "8-14",
+ MONTH = "February and May"}
+
+@TECHREPORT{vandenHeuvel:86a,
+ AUTHOR = "Pim van den Heuvel",
+ TITLE = "Some Experiments in {REDUCE} Related to the
+Calculation of {Groebner} Bases",
+ INSTITUTION = "Department of Computer Science, Twente
+University of Technology, The Netherlands",
+ YEAR = 1986, MONTH = "June"}
+
+@INPROCEEDINGS{vandenHeuvel:87,
+ AUTHOR = "P. van den Heuvel and J. A. van Hulzen and V. V. Goldman",
+ TITLE = "Automatic Generation of {FORTRAN}-Coded {Jacobians} and
+{Hessians}",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "120-131",
+ PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{vandenHeuvel:87a,
+ AUTHOR = "P. van den Heuvel and B. J. A. Hulshof and J. A. van Hulzen",
+ TITLE = "Some Simple Pretty-Print Facilities for {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1987, VOLUME = 21, NUMBER = 1, PAGES = "14-17", MONTH = "February"}
+
+@TECHREPORT{vanHeerwaarden,
+ AUTHOR = "M. C. van Heerwaarden and J. A. van Hulzen",
+ TITLE = "Pretty Print Facilities for {REDUCE}",
+ INSTITUTION = "Department of Computer Science, University
+of Twente, The Netherlands",
+ YEAR = 1988, TYPE = "Memorandum",
+ NUMBER = "INF-88-36", MONTH = "August"}
+
+@ARTICLE{vanHulzen:80,
+ AUTHOR = "J. A. van Hulzen",
+ TITLE = "Computational Problems in Producing {Taylor} Coefficients
+for the Rotating Disk Problem",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1980, VOLUME = 14, NUMBER = 2, PAGES = "36-49", MONTH = "May"}
+
+@TECHREPORT{vanHulzen:81,
+ AUTHOR = "J. A. van Hulzen",
+ TITLE = "Breuer's Grow Factor Algorithm in Computer Algebra",
+ INSTITUTION = "Department of Applied Mathematics, Twente University
+of Technology, The Netherlands",
+ YEAR = 1981, TYPE = "Memorandum", NUMBER = 332, MONTH = "April",
+ COMMENT = {A shorter version appears in: Proceedings SYMSAC 81
+ (Paul S. Wang, ed.) ACM, August 1981.}}
+
+@ARTICLE{vanHulzen:82,
+ AUTHOR = "J. A. van Hulzen and B. J. A. Hulshof",
+ TITLE = "An Expression Analysis Package for {REDUCE}",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1982, VOLUME = 16, NUMBER = 4, PAGES = "32-44", MONTH = "November"}
+
+@INPROCEEDINGS{vanHulzen:82a,
+ AUTHOR = "J. A. van Hulzen",
+ TITLE = "Computer Algebra Systems Viewed by a Notorious User",
+ BOOKTITLE = "Proc. {EUROCAM} 1982, Lecture Notes
+in Computer Science", YEAR = 1982, VOLUME = 144, PAGES = "166-180"}
+
+@INCOLLECTION{vanHulzen:83,
+ AUTHOR = "J. A. van Hulzen and J. Calmet",
+ TITLE = "Computer Algebra Systems",
+ EDITOR = "B. Buchberger and G. E. Collins and R. Loos and R. Albrecht",
+ BOOKTITLE = "Computer Algebra and Symbolic and Algebraic Computation",
+ EDITION = "2nd", PUBLISHER = "Springer-Verlag", YEAR = 1983}
+
+@INPROCEEDINGS{vanHulzen:83a,
+ AUTHOR = "J. A. van Hulzen",
+ TITLE = "Code Optimization of Multivariate Polynomial Schemes:  A
+Pragmatic Approach",
+ BOOKTITLE = "Proc. {EUROCAL} 1983, Lecture Notes
+in Computer Science", YEAR = 1983, VOLUME = 162, PAGES = "286-300",
+ PUBLISHER = "Springer-Verlag"}
+
+@INPROCEEDINGS{vanHulzen:87,
+ AUTHOR = "J. A. van Hulzen",
+ TITLE = "Program Generation Aspects of the Symbolic-Numeric Interface",
+ BOOKTITLE = "Proc. Third Intern. Conf. on Computer Algebra and its
+applications in Theor. Phys, 1985", YEAR = 1987, PAGES = "104-113",
+ PUBLISHER = "{J.I.N.R., Dubna, USSR}"}
+
+@TECHREPORT{vanHulzen:88,
+ AUTHOR = "J. A. van Hulzen",
+ TITLE = "Formule Manipulatie m.b.v. {REDUCE} (in {Dutch})",
+ INSTITUTION = "Department of Computer Science, Twente University
+of Technology, The Netherlands",
+ YEAR = 1988, MONTH = "October"}
+
+@INPROCEEDINGS{vanHulzen:89,
+ AUTHOR = "J. A. van Hulzen and B. J. A. Hulshof and B. L. Gates and
+M. C. Van Heerwaarden",
+ TITLE = "A Code Optimization Package for {REDUCE}",
+ BOOKTITLE = "Proc. of {ISSAC} '89", PUBLISHER = "{ACM} Press, New York",
+ YEAR = 1989, PAGES = "163-170",
+ COMMENT = {Lecture Notes.}}
+
+@TECHREPORT{vanHulzen:89a,
+ AUTHOR = "J. A. van Hulzen",
+ TITLE = "Computer Algebra and Numerical Mathematics:  The Odd Couple?",
+ INSTITUTION = "Department of Computer Science, Twente University
+of Technology, The Netherlands",
+ NUMBER = "Informatica 89-40",
+ YEAR = 1989, MONTH = "June"}
+
+@TECHREPORT{VanProeyan:76,
+ AUTHOR = "A. Van Proeyen",
+ TITLE = "Quantum Gravity Corrections on the Anomalous
+Magnetic and Quadrupole Moments of a Spin-1 Particle",
+ INSTITUTION = "Instituut voor Theor. Fys., Leuven",
+ YEAR = 1976, MONTH = "October"}
+
+@TECHREPORT{VanProeyan:79,
+ AUTHOR = "A. Van Proeyan",
+ TITLE = "Gravitational Divergences of the Electromagnetic
+Interactions of Massive Vectorparticles",
+ INSTITUTION = "Universiteit Leuven",
+ YEAR = 1979, TYPE = "Preprint", NUMBER = "KUL-TF-79/032",
+ MONTH = "October",
+ ABSTRACT = {In a search for the explanation of the finite quantum
+gravity corrections to anomalous moments we examined a
+spontaneous broken 0(3) model with Yang-Mills particles
+and Higgs scalars coupled to gravitons.}}
+
+@INPROCEEDINGS{Vega:91,
+ AUTHOR = "Laureano Gonz{\'a}lez Vega",
+ TITLE = "Working with Real Algebraic Plane Curves in {REDUCE:} the
+{GCUR} package",
+ YEAR = 1991, MONTH = "July",
+ BOOKTITLE = "Proc. of the 1991 International Symposium on Symbolic and
+Algebraic Computation",
+ EDITOR = "Stephen M. Watt", PUBLISHER = "ACM Press", ADDRESS = "Maryland",
+ PAGES = "397-402"}
+
+@TECHREPORT{Vinitsky:87,
+ AUTHOR = "S. I. Vinitsky and V. A. Rostovtsev",
+ TITLE = "A Use of {REDUCE} System in Problems of
+Hydrogen Atom in an Electric Field",
+ INSTITUTION = "J.I.N.R., Dubna", TYPE = "Preprint",
+ YEAR = 1987, NUMBER = "P11-87-303"}
+
+@ARTICLE{Viry:93,
+ AUTHOR = "Guy Viry",
+ TITLE = "Factorization of Multivariate Polynomials with Coefficients in
+$F_{p}$",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1993, VOLUME = 15, NUMBER = 4, PAGES = "371-391", MONTH = "November",
+ COMMENT = {The ring of polynomials in $X,X_{1}, \1dots ,X_{m}$ are denoted
+by $F_{p}[X,X_{1}, \1dots ,X_{m}]$ in $F_{p}$, that is the field of
+integers defined modulo $p$. In the usual factorization algorithm defined
+by Wang, the given polynolmial $P$ is first factorized modulo $\Delta^{n}$,
+where $\Delta^{n}$ is an ideal.  This algorithm uses a generalization of
+Hensel's Lemma.  If there are no extraneous factors, then the factors
+defined modulo $\delta^[{n}$ correspond to the factors of $P$ in
+$F_{p}[X,X_{1}, \1dots ,X_{m}]$ or else the defined factors must be
+regrouped to find the factors of $P$ in $F_{p}[X,X_{1}, \1dots ,X_{m}]$.
+In this paper, a mapping that transforms the product of the factors into a
+sum is defined.  A theorem that determines whether a subproduct of the
+factors of $P$ corresponds to a factor of $P$ in $F_{p}[X,X_{1}, \1dots
+,X_{m}]$ is given.  Therefore the regrouping of the factors of $P$ reduces
+to solving a system of linear equations, as in the univariate case, with
+Berlekamp's algorithm.}}
+
+@ARTICLE{Voros:77,
+ AUTHOR = "A. Voros",
+ TITLE = "Asymptotic K-Expansions of Stationary Quantum States",
+ JOURNAL = "Ann. Inst. H. Poincare",
+ YEAR = 1977, VOLUME = "26A", PAGE = "343"}
+
+@TECHREPORT{Wanas,
+ AUTHOR = "M. I. Wanas",
+ TITLE = "The Third Face of Computer -- Computer Solution
+of Symbolic Problems",
+ INSTITUTION = "Military Technical College, Cairo, Egypt",
+ NUMBER = "CAP-3 837"}
+
+@INPROCEEDINGS{Wanas:85,
+ AUTHOR = "M. I. Wanas",
+ TITLE = "Manipulation of Parameters Indicating the
+Physical Significance of any Absolute Parallelism
+Space Using {REDUCE} 2",
+ YEAR = 1985,
+ BOOKTITLE = "Tenth International Congress for Statistics,
+Computer Science, Social and Demographic Research"}
+
+@INPROCEEDINGS{Wang:84,
+ AUTHOR = "Paul S. Wang and T. Y. P. Chang and J. A. van Hulzen",
+ TITLE = "Code Generation and Optimization for Finite Element Analysis",
+ BOOKTITLE = "Proc. {EUROSAM} 1984, Lecture Notes
+in Computer Science", YEAR = 1984, VOLUME = 174, PAGES = "237-247",
+ PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{Wang:93,
+ AUTHOR = "Jian-Xiong Wang",
+ TITLE = "Automatic calculation of {Feynman loop-diagrams}, I.  Generation
+of a simplified form of the amplitude",
+ YEAR = 1993, VOLUME = 77, NUMBER = 2, PAGES = "263-285", MONTH = "October"}
+ ABSTRACT = {In order to develop an automatic system to calculate loop
+diagrams in renormalizable theories, we present the first part of a
+complete system written in {REDUCE} and {RLISP}.  It can generate the tensor
+and gamma matrix basis which is able to cast the total amplitude into a
+simpler form with the help of gauge invariance and symmetry among identical
+particles.}
+
+@ARTICLE{Wassam:87,
+ AUTHOR = "W. A. {Wassam, Jr.} and Go. Torres-Vega",
+ TITLE = "Dual {Lanczos} Transformation Theory:  Closed Set of Algebraic
+Equations Connecting {Lanczos} Parameters with Moments in Moment
+Expansions of Time-Dependent Quantities",
+ JOURNAL = "Chemical Phys. Lett.",
+ YEAR = 1987, VOLUME = 134, NUMBER = 4, PAGES = "355-360",
+ COMMENT = {"The utility of this set of equations is illustrated by using
+them with the aid of symbolic manipulation on a computer to construct a
+previously unknown exact continued fraction for the spectral density
+of the incoherent scattering function{\ldots}" The system used is {REDUCE}
+on a Burroughs.  Appear enthusiastic about the possibilities for
+computer algebra in related fields.}}
+
+@ARTICLE{Wassam:87a,
+ AUTHOR = "W. A. {Wassam, Jr.} and Go. Torres-Vega and J. Neito-Frausto",
+ TITLE = "Dual {Lanczos} Transformation Theory:  Exact Continued
+Fraction Expression for Resonant $\gamma$-ray Absorption Spectrum of a
+Harmonically Bound Atom Executing Classical Motion Described by
+{Smoluchowski} Dynamics",
+ JOURNAL = "Chemical Phys. Lett.",
+ YEAR = 1987, VOLUME = 136, NUMBER = 1, PAGES = "26-30",
+ COMMENT = {"{\ldots}with the aid of symbolic manipulation techniques, we
+construct a previously unknown exact continued fraction for the resonance
+$\gamma$-ray absorption spectrum{\dots}"  The system used is {REDUCE}
+on a Burroughs.}}
+
+@TECHREPORT{Watanabe:85,
+ AUTHOR = "Yoichi Watanabe",
+ TITLE = "Symbolic Manipulation of Structure Functions
+in Availability Analysis",
+ INSTITUTION = "Fusion Technology Institute, University of
+Wisconsin, Madison, Wisconsin",
+ YEAR = 1985, NUMBER = "UWFDM-658", MONTH = "November"}
+
+@ARTICLE{Watanabe:76,
+ AUTHOR = "Shunro Watanabe",
+ TITLE = "Formula Manipulations Solving Linear Ordinary
+Differential Equations {II}",
+ JOURNAL = "Publications of the Research Institute for
+Mathematical Sciences, Kyoto University",
+ YEAR = 1976, VOLUME = 11, NUMBER = 2, PAGES = "297-337"}
+
+@ARTICLE{Watanabe:79,
+ AUTHOR = "Shunro Watanabe",
+ TITLE = "A Verification for Non-existence of Movable Branch Points of Six
+Painlev{\'e} Transcendents by Formula Manipulations",
+ JOURNAL = "Tokyo Journal of Mathematics",
+ YEAR = 1979, VOLUME = 2, NUMBER = 2, PAGES = "285-291"}
+
+@ARTICLE{Weber:79,
+ AUTHOR = "Lawrence A. Weber and Gerhard Rayna",
+ TITLE = "Problem \#11 Solved in {REDUCE:}  A Case Study in Program
+Translation",
+ JOURNAL = "{SIGSAM} Bulletin",
+ YEAR = 1979, VOLUME = 13, NUMBER = 4, PAGES = "21-24", MONTH = "November"}
+
+@ARTICLE{Wehner:86,
+ AUTHOR = "M. F. Wehner and W. G. Wolfer",
+ TITLE = "The Pressure of a Hard Sphere Fluid on a Curved Surface",
+ JOURNAL = "J. Statistical Phys.",
+ YEAR = 1986, VOLUME = 42, PAGES = "509-521",
+ COMMENT = {Integral equation approach and perturbation expansions in
+{REDUCE}.  "Therefore, in order to avoid errors, the integrations have been
+done in closed form with the algebraic manipulation routine {REDUCE}."}}
+
+@InProceedings{Weispfenning:94,
+  author =       {Volker Weispfenning},
+  title =        {Quantifier elimination for real algebra -- the cubic case},
+  booktitle =    {Symbolic and Algebraic Computation},
+  editor =       {},
+  series =       {ISSAC},
+  year =         {1994},
+  organization = {SIGSAM},
+  publisher =    {ACM},
+  pages =        {258--263}
+}
+
+@INCOLLECTION{Winkelmann:89,
+ AUTHOR = "Volker Winkelmann and Friedrich W. Hehl",
+ TITLE = "{REDUCE} for Beginners. Six Lectures on the
+Application of Computer Algebra",
+ EDITOR = "D. Stauffer and F. W. Hehl and V. Winkelmann and
+J. G. Zabolitzky",
+ BOOKTITLE = "Computer Simulation and Computer Algebra.
+Lectures for Beginners",
+ CHAPTER = 3, EDITION = "2nd", PUBLISHER = "Springer-Verlag",
+ YEAR= 1989}
+
+@TECHREPORT{Winkler:88,
+ AUTHOR = "F. Winkler and B. Kutzler and F. Lichtenberger",
+ TITLE = "Computeralgebrasysteme (in {German})",
+ INSTITUTION = "RISC - LINZ, Austria", TYPE = "Report",
+ YEAR = 1988, NUMBER = "88-10"}
+
+@ARTICLE {Witham:77,
+ AUTHOR = "C. R. Witham and S. Dubowsky",
+ TITLE = "An Improved Symbolic Manipulation Technique for
+the Simulation of Nonlinear Dynamic Systems With Mixed
+Time-Varying and Constant Terms",
+ JOURNAL = "Journal of Dynamic Systems, Measurement, and Control",
+ YEAR = 1977, MONTH = "September", PAGES = "157-165",
+ ABSTRACT = {The time domain behavior of nonlinear dynamic systems
+often is obtained by numerical integration on the digital
+computer.  These solutions are usually expensive and limit
+the scope of the dynamic study.  The proposed improved
+technique results in a substantial increase in the computational
+efficiency by using automatic symbolic manipulation to generate
+explicit equations of motion algebraically prior to numerical
+integration.}}
+
+@TECHREPORT{Wolf:95,
+ AUTHOR = "Thomas Wolf",
+ TITLE = "Programs for Applying Symmetries of PDEs",
+ INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin",
+ YEAR = 1995, TYPE = "Preprint", NUMBER = "SC 95-5", MONTH = "February",
+ ABSTRACT = {In this paper the programs APPLYSYM, QUASILINPDE and DETRAFO
+are described which aim at the utilization of infinitesimal symmetries of
+differential equations.  The purpose of QUASILINPDE is the general solution
+of quasilinear PDEs.  This procedure is used by APPLYSYM for the
+application of point symmetries for either
+
+calculating similarity variables to perform a point transformation which
+lowers the order of an ODE or effectively reduces the number of explicitly
+occuring independent variables in a PDE(-system) or for
+
+generalizing given special solutions of ODEs/PDEs with new constant
+parameters.
+
+The program DETRAFO performs arbitrary point- and contact transformations
+of ODEs/PDEs and is applied if similarity and symmetry variables have been
+found.  The program APPLYSYM is used in connection with the program LIEPDE
+for formulating and solving the conditions for point- and contact
+symmetries which is described in [4].  The actual problem solving is done
+in all these programs through a call to the package CRACK for solving
+overdetermined PDE-systems.}}
+
+@ARTICLE{Wood:89,
+ AUTHOR = "John C. Wood",
+ TITLE = "Harmonic Two Spheres in the Unitary Group",
+ YEAR = 1989,
+ JOURNAL = "Proc. London Math. Soc.",
+ VOLUME = 3, NUMBER = 58, PAGES = "608-624"}
+
+@TECHREPORT{Wright:84,
+ AUTHOR = "F. J. Wright and G. Dangelmayr",
+ TITLE = "Explicit Iterative Algorithms to Reduce a Univariate Catastrophe
+to Normal Form",
+ INSTITUTION = "Universit{\"a}t T{\"u}bingen",
+ YEAR = 1984}
+
+@TECHREPORT{Wulkow:90,
+ AUTHOR = "Michael Wulkow and Peter Deuflhard",
+ TITLE = "Towards an efficient computational treatment of heterogeneous
+polymer reactions",
+ INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin",
+ YEAR = 1990, TYPE = "Preprint", NUMBER = "SC 90-1", MONTH = "January"}
+
+@INPROCEEDINGS{Yamamoto:87,
+ AUTHOR = "T. Yamamoto and Y. Aoki",
+ TITLE = "{REDUCE} 3.2 on {iAPX 86/286}-based Personal Computers",
+ BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes
+in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "134-135",
+ PUBLISHER = "Springer-Verlag"}
+
+@ARTICLE{Yamartino:91,
+ AUTHOR = "Robert J. Yamartino and Richard Pavelle",
+ TITLE = "An Application of Computer Algebra to a Problem in Stratified
+Fluid Flow",
+ JOURNAL = "J. Symb. Comp.",
+ YEAR = 1991, VOLUME = 12, NUMBER = 6, PAGES = "669-672", MONTH = "December",
+ ABSTRACT = {The computationally tedious problem of considering trial Green's
+function solutions to the fourth-order partial differential equation for a
+stratified atmosphere flowing over a hill is approached using MACSYMA.
+Significance of the problem, solution methodologies and CPU time
+intercomparisons using various computer platforms and other algebra systems
+are discussed.}}
+
+@ARTICLE{Yannouleas:88,
+ AUTHOR = "C. Yannouleas and J. M. Pacheco",
+ TITLE = "An Algebraic Program for the States Associated with the
+${U(5)} \supset {O(5)} \supset {O(3)}$ Chain of Groups",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1988, VOLUME = 52, NUMBER = 1, PAGES = "85-92", MONTH = "December"}
+
+@ARTICLE{Yannouleas:89,
+ AUTHOR = "C. Yannouleas and J. M. Pacheco",
+ TITLE = "Algebraic Manipulation of the States Associated with the
+${U(5)} \supset {O(5)} \supset {O(3)}$ Chain of {groups:}
+Orthonormalization and Matrix Elements",
+ JOURNAL = "Comp. Phys. Comm.",
+ YEAR = 1989, VOLUME = 54, NUMBER = "2 and 3", PAGES = "315-328",
+MONTH = "June and July"}
+
+@ARTICLE{Zacrep:75,
+ AUTHOR = "Douglas Zacrep and Bing-Lin Young",
+ TITLE = "Trace and {Ward-Takahashi} Identity Anomalies
+in an {SU}(3) Current Model with Energy-Momentum Tensor",
+ JOURNAL = "Phys. Rev. D",
+ YEAR = 1975, VOLUME = 12, PAGES = "513-522"}
+
+@ARTICLE{Zahalak:87,
+ AUTHOR = "G. I. Zahalak and P. R. Rao and S. P. Sutera",
+ TITLE = "Large Deformations of a Cylindrical Liquid-Filled Membrane
+by a Viscous Shear Flow",
+ JOURNAL = "J. Fluid Mech.",
+ YEAR = 1987, VOLUME = 179, PAGES = "283-305",
+ COMMENT = {Draws attention to the use of classical perturbation
+techniques combined with computer algebra as an alternative to
+numerical calculation.}}
+
+@ARTICLE{Zeng:84,
+ AUTHOR = "{Wan-zhen} Zeng and {Bail-lin} Hao",
+ TITLE = "Scaling Property of Period-n-Tupling
+Sequences in One-Dimensional Mappings",
+ JOURNAL = "Commun. in Theor. Phys., Beijing, China",
+ YEAR = 1984, VOLUME = 3, NUMBER = 3, PAGES = "283-295"}
+
+@ARTICLE{Zharkov:93,
+ AUTHOR = "A. Yu. Zharkov",
+ TITLE = "Computer Classification of the Integrable Coupled {Kdv}-like
+Systems with Unit Main Matrix",
+ JOURNAL = "J. Symbolic Computation",
+ YEAR = 1993, VOLUME = 15, NUMBER = 1, PAGES = "85-90", MONTH = "January",
+ COMMENT = {The classification of 2-component systems of equations for
+the form $u^{i}_{t}=u^{i}_{xxx}+c_{ij}u^{i}u^{j}_{x}(i,j=1,2)$ which
+possess higher symmetries is given.  A new class of such integrable
+KdV-like systems is obtained.  All the computations have been done using
+the {REDUCE}computer algebra system.}}
+
+@InProceedings{Zharkov:93a,
+  author =      "A. Yu. Zharkov and Yu. A. Blinkov",
+  title =       "Involution Approach to Solving Systems of Algebraic
+Equations",
+  booktitle =   "Proceedings of the 1993 International IMACS Symposium on
+                 Symbolic Computation",
+  year =        "1993",
+  editor =      "G. Jacob and N. E. Oussous and S. Steinberg",
+  pages =       "11-16",
+  organization ="IMACS",
+  publisher =   "Laboratoire d'Informatique Fondamentale de Lille, France",
+
+  comment =     {An "involutive set" is a canonical basis of a 0-dim
+		 polynomial ideal based on Janet division and well suited for
+                 equation solving.  It can be transformed into a
+                 lexicographic Groebner basis by linear algebra tools.
+                 The algorithms for computing involutive sets has been
+		 developed using {REDUCE}.}
+}
+
+@TECHREPORT{Zhidkova:78,
+ AUTHOR = "I. E. Zhidkova and I. P. Nedyalkov and V. A. Rostovtsev",
+ TITLE = "On Applicability Limits of the Experimental Method
+for Investigating Strong Gravitational Fields",
+ INSTITUTION = "J.I.N.R., Dubna",
+ YEAR = 1978, NUMBER = "P2 - 11589",
+ COMMENT = {Mechanical effects of tidal forces on the physical apparatus
+exploring strong gravitational fields are investigated.}}
+