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%                          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"}

@ARTICLE{AskeyWilson:85,
 AUTHOR = "R. Askey and J. Wilson",
 TITLE = "Some Basic Hypergeometric Orthogonal Polynomials that
		  Generalize Jacobi Polynomials",
 JOURNAL = "Memoirs Amer. Math. Soc. 319",
 ADDRESS = "Providence, RI",
 YEAR = "1985"}

@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.}}

@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.}}

@BOOK{Baker:81a,
 AUTHOR= "Baker(Jr.), George A. and Graves-Morris, Peter",
 TITLE = "Pad\'{e} Approximants, Part I: Basic Theory",
 PUBLISHER = "Addison-Wesley Publishing Company",
 ADDRESS = "Reading, Massachusetts",
 YEAR = "1981"}

@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{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{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"
}

@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"}

@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"}

@BOOK{Bronstein:97,
 AUTHOR = "Manuel Bronstein",
 TITLE = "Symbolic Integration I: Transcendental Functions",
 PUBLISHER = "Springer-Verlag",
 ADDRESS = "Heidelberg",
 YEAR = "1997"}

@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.}}

@MANUAL{CALI,
  AUTHOR = {H.-G. Gr\"abe},
  TITLE = "CALI -- A Reduce package for commutative algebra.
           Version 2.2.1",
  ORGANIZATION = "Uni Leipzig",
  YEAR = "June 1995",
  ADDRESS = "Available from\\ {\tt
             http://www.informatik.uni-leipzig.de/\~{}compalg}"}

@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.}}

@INCOLLECTION{Chou:84,
  AUTHOR = "Chou, S.-C.",
  TITLE =  "Proving elementary geometry theorems using {Wu's}
                  algorithm", 
  BOOKTITLE = "Contemp. Math.",
  PUBLISHER = "AMS, Providence, Rhode Island",
  YEAR =      "1984",
  VOLUME =    "19",
  PAGES =     "243 - 286"}

@BOOK{Chou:88,
  AUTHOR = "Chou, S.-C.",
  TITLE =  "Mechanical geometry theorem proving",
  PUBLISHER = "Reidel, Dortrecht",
  YEAR = "1988"}

@INPROCEEDINGS{Chou:90,
  AUTHOR = "Chou, S.-C.",
  TITLE =  "Automated reasoning in geometries using the
            characteristic set method and {Gr\"obner} basis
            method", 
  BOOKTITLE = "Proc. ISSAC-90",
  PUBLISHER = "ACM Press",
  YEAR =      "1990",
  PAGES =     "255-260",
}

@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.}}

@BOOK{Coxeter:67,
  AUTHOR = "Coxeter, H.S.M. and Greitzer, S.L.",
  TITLE =  "Geometry revisted",
  PUBLISHER = "Random House, The L.W. Singer Comp., New York",
  YEAR = "1967",
}

@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}

@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}").}}

@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.}}

@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{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.}}

@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.}}

@Article{DolzmannSturm:97a,
  AUTHOR =       {Dolzmann, Andreas and Sturm, Thomas},
  TITLE =        {Redlog: Computer Algebra Meets Computer Logic},
  JOURNAL =      {ACM SIGSAM Bulletin},
  YEAR =         1997,
  VOLUME =       31,
  NUMBER =       2,
  MONTH =        Jun,
  PAGES =        {2-9}
}

@TechReport{DolzmannSturm:96a,
  AUTHOR =       {Dolzmann, Andreas and Sturm, Thomas},
  TITLE =        {Redlog User Manual},
  institution =  {FMI, Universit\"at Passau},
  YEAR =         1996,
  TYPE =         {Technical Report},
  NUMBER =       {MIP-9616},
  ADDRESS =      {D-94030 Passau, Germany},
  MONTH =        oct,
  NOTE =         {Edition 1.0 for Version 1.0}
}

@Manual{DolzmannSturm:99,
  TITLE =        {Redlog User Manual},
  AUTHOR =       {Dolzmann, Andreas and Sturm, Thomas},
  ORGANIZATION = {FMI, Universit\"at Passau},
  ADDRESS =      {D-94030 Passau, Germany},
  NOTE =         {Edition 2.0 for Version 2.0},
  YEAR =         1999,
  MONTH =        apr
}

@Article{DolzmannSturm:97c,
  AUTHOR =       {Dolzmann, Andreas and Sturm, Thomas},
  TITLE =        {Simplification of Quantifier-free Formulae over
                  Ordered Fields},
  JOURNAL =      {Journal of Symbolic Computation},
  YEAR =         1997,
  VOLUME =       24,
  NUMBER =       2,
  MONTH =        aug,
  PAGES =        {209-231}
}

@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.}}

@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.}}

@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: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"}

@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{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: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{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.}}

@UNPUBLISHED{Gasper:95,
 AUTHOR = "G. Gasper",
 TITLE = "Lecture Notes for an Introductory Minicourse on q-Series",
 YEAR = "1995",
 NOTE = "To obtain from ftp://unvie6.un.or.at/siam/opsf_new/00index_by_author.html"}

@BOOK{GasperRahman:90,
 AUTHOR = "G. Gasper and M. Rahman",
 TITLE = "Basic Hypergeometric Series",
 SERIES = "Encyclopedia of Mathematics and its Applications",
 NUMBER = "35",
 PUBLISHER = "Cambridge University Press",
 ADDRESS = "London and New York",
 YEAR = "1990"}

@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.}}

@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"
}

@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"}

@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"}

@BOOK{Geddes:92,
 AUTHOR = "K.O. Geddes et. al.",
 TITLE = "Algorithms for Computer Algebra",
 PUBLISHER = "Klewer Academic Publishers",
 YEAR = "1992"}

@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"}

@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: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.}}

@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"}

@INPROCEEDINGS{Gosper:78,
 AUTHOR = "R. W. Gosper Jr.",
 TITLE = "Decision Procedure for Indefinite Hypergeometric Summation",
 BOOKTITLE = "Proc. Natl. Acad. Sci. USA",
 YEAR = "1978",
 NUMBER = "75",
 PAGES = "40-42"}

@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.}}

@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"}

@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"}

@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.}}

@MISC{IMO,
  KEY= "IMO",
  TITLE = "International Mathematics Olympiad (IMO)",
  HOWPUBLISHED = "Available from\\ {\tt
                  http://olympiads.win.tue.nl/imo}"}

@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.}}

@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{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"}

@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: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.}}

@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.}}

@BOOK{Knuth:81,
 AUTHOR = "D. E. Knuth",
 TITLE = "The Art of Computer Programming, Seminumerical Algorithms",
 EDITION = "second",
 PUBLISHER = "Addison-Wesley Publishing Company",
 YEAR = "1981"}

@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"}

@TECHREPORT{KoekoekSwarttouw:94,
 AUTHOR = "R. Koekoek and R. F. Swarttouw",
 TITLE = "The Askey-scheme of Hypergeometric Orthogonal Polynomials
		  and its $q$-analogue",
 INSTITUTION = "Faculty of Technical Mathematics and Informatics",
 YEAR = "1994",
 TYPE = "Report",
 NUMBER = "94-05",
 ADDRESS = "Technische Universiteit Delft, Delft"}

@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{Koepf:95b,
 AUTHOR = "W. Koepf",
 TITLE = "Algorithms for $m$-fold hypergeometric Summation",
 JOURNAL = "Journal of Symbolic Computation",
 YEAR = "1995",
 VOLUME = "20",
 PAGES = "399-417"}

@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{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.}}

@ARTICLE{Koornwinder:93,
 AUTHOR = "T. H. Koornwinder",
 TITLE = "On {Zeilberger's} algorithm and its $q$-analogue: a rigorous
          description",
 JOURNAL = "J. of Comput. and Appl. Math.",
 VOLUME = "48",
 PAGES = "91-111",
 YEAR = "1993"}

@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}

@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"
}

@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{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{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"}

@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{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.}}

@ARTICLE{Muroa:91,
 AUTHOR = "Hirokazu Murao",
 TITLE = "Vectorization of symbolic determinant calculation",
 JOURNAL = "Supercomputer",
 YEAR = 1991, VOLUME = "43,VIII-3", PAGES = "36-48"}

@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{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: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{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.}}

@INPROCEEDINGS{PauleRiese:95,
 AUTHOR = "P. Paule and A. Riese",
 TITLE = "A Mathematica $q$-analogue of Zeilberger's algorithm based
		  on an algebraically motivated approach to
		  $q$-hypergeometric telescoping",
 BOOKTITLE = "Fields Proceedings of the Workshop 'Special Functions,
		  $q$-Series and Related Topics",
 ORGANIZATION = "Fields Institute for Research in Mathematical
		  Sciences at University College",
 PAGES = "179-210",
 ADDRESS = "Toronto, Ontario",
 MONTH = "12-23 June",
 YEAR = "1995"}

@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{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"}

@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.}}

@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"}

@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.}}

@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"}

@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{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}."}}

@Article{Weispfenning:92,
  author =       {Weispfenning, Volker},
  title =        {Comprehensive {G}r\"obner Bases},
  journal =      {Journal of Symbolic Computation},
  year =         1992,
  month =        jul,
  volume =       14,
  pages =        {1-29}
}

@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}

@INCOLLECTION{Wu:84a,
  AUTHOR = "Wu, W.-T.",
  TITLE =  "On the decision problem and the mechanization of
            theorem-proving in elementary geometry",   
  BOOKTITLE = "Contemp. Math.",
  PUBLISHER = "AMS, Providence, Rhode Island",
  YEAR = "1984",
  VOLUME = "19",
  PAGES = "213 - 234"}

@INCOLLECTION{Wu:84b,
  AUTHOR = "Wu, W.-T.",
  TITLE =  "Some recent advances in mechanical theorem proving
            of geometry",  
  BOOKTITLE = "Contemp. Math.",
  PUBLISHER = "AMS, Providence, Rhode Island",
  YEAR = "1984",
  VOLUME = "19",
  PAGES = "235 - 241"}

@Book{Wu:94,
  AUTHOR = "Wu, W.-T.",
  TITLE =  "Mechanical Theorem Proving in Geometries",
  NUMBER = "1",
  SERIES = "Texts and Monographs in Symbolic Computation",
  PUBLISHER = "Springer, Wien",
  YEAR = "1994"}

@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{Zeilberger:90,
 AUTHOR = "D. Zeilberger",
 TITLE = "A fast algorithm for proving terminating hypergeometric
		  identities",
 JOURNAL = "Discrete Math.",
 VOLUME = "80", PAGES = "207-211", YEAR = "1990"}

@ARTICLE{Zeilberger:91,
 AUTHOR = "D. Zeilberger",
 TITLE = "The method of creative telescoping",
 JOURNAL = "J. Symbolic Computation",
 VOLUME = "11", PAGES = "195-204", YEAR = "1991"}

@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.}}
@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{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"}

@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."}

@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"}

@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"}