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% REDUCE BIBLIOGRAPHY % Part 1: A-F % Copyright (c) 1990 The RAND Corporation. 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{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 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 = "563-584", 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. Zhydkov and I. E. Zhydkova", 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"} @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{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, ed.", 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.}} @TECHREPORT{Bajla:78, AUTHOR = "I. Bajla and G. A. Ososkov and A. C. Hearn", TITLE = "The Orthogonalization Program of Polynomials in Two Variables in {REDUCE}-2 Language", INSTITUTION = "J.I.N.R., Dubna", YEAR = 1978, TYPE = "Report", NUMBER = "P10-11944", ABSTRACT = {The analytical algorithm for constructing orthogonal polynomials in two variables, based on the {Gram-Schmidt} orthogonalization method, is proposed.}} @INPROCEEDINGS{Balian:78, AUTHOR = "R. Balian and G. Parisi and A. Voros", TITLE = "Quartic Oscillator", YEAR = 1978, MONTH = "May", BOOKTITLE = "Proc. of the Colloq. on Mathematical Problems in {Feynman} Path Integrals, Marseille", ABSTRACT = {On the example of the semi-classical expansion for the levels of the quartic oscillator -(d**2/dq**2)+q**4, we show how the complex WKB method provides information about the singularities of the Borel transform of the semi-classical series.}} @ARTICLE{Baker:81, AUTHOR = "G. A. Baker and L. P. Benofy and M. Fortes and M. de Llano and S. M. Peltier and A. Plastino", TITLE = "Hard-Core Square-Well Fermion", JOURNAL = "Phys. Rev. A", YEAR = 1982, VOLUME = 26, PAGES = "3575-3588", COMMENT = {The mixed use of {FORTRAN} and {REDUCE}, various derivative were calculated algebraically, but the double series was evaluated numerically.}} @ARTICLE{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}"}} @TECHREPORT{Bennett, 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"} @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"} @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.}} @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"} @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{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.}} @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"} @INPROCEEDINGS{Bradford:86, AUTHOR = "R. J. Bradford and A. C. Hearn and J. A. Padget and E. Schr{\"u}fer", TITLE = "Enlarging the {REDUCE} Domain of Computation", BOOKTITLE = "Proc. of {SYMSAC} '86", YEAR = 1986, PAGES = "100-106"} @INPROCEEDINGS{Bradford:88, AUTHOR = "R. J. Bradford and J. H. Davenport", TITLE = "Effective Tests for Cyclotomic Polynomials", BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag", YEAR = 1988, VOLUME = 358, PAGES = "244-251"} @InProceedings{Bradford90, author = "Russell Bradford", title = "A parallelization of the Buchberger Algorithm", booktitle = "Proceedings of the International Symposium on Symbolic and Algebraic Computation", year = "1990", editor = "S. Watanabe and Morio Nagata", pages = "296", organization = "ACM", publisher = "Addison-Wesley" } @ARTICLE{Broadhurst:85, 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{Brodsky:62, AUTHOR = "S. J. Brodsky and A. C. Hearn and R. G. Parsons", TITLE = "Determination of the Real Part of the {Compton} Amplitude at a Nucleon Resonance", JOURNAL = "Phys. Rev.", YEAR = 1962, VOLUME = 187, PAGES = "1899-1904"} @ARTICLE{Brodsky:67, AUTHOR = "S. J. Brodsky and J. D. Sullivan", TITLE = "W-Boson Contribution to the Anomalous Magnetic Moment of the Muon", JOURNAL = "Phys. Rev.", YEAR = 1967, VOLUME = 156, PAGES = "1644-1647"} @INPROCEEDINGS{Brodsky:69, AUTHOR = "S. J. Brodsky", TITLE = "Status of Quantum Electrodynamics", YEAR = 1969, BOOKTITLE = "Proc. International Symposium on Electron and Photon Interactions at High Energies, Liverpool, England"} @TECHREPORT{Brodsky:70, AUTHOR = "S. J. Brodsky", TITLE = "Quantum Electrodynamic Theory: Its Relation to Precision Low Energy Experiments", INSTITUTION = "SLAC", YEAR = 1970, TYPE = "Report", NUMBER = "SLAC-PUB-795", MONTH = "August"} @INPROCEEDINGS{Brodsky:71, AUTHOR = "S. J. Brodsky", TITLE = "Algebraic Computation Techniques in Quantum Electrodynamics", YEAR = 1971, VOLUME = "II", PAGES = "IV-1 to IV-27", BOOKTITLE = "Proc. {2nd} Computing Methods in Theoretical Physics, Marseilles"} @TECHREPORT{Brodsky:72, AUTHOR = "S. J. Brodsky", TITLE = "Atomic Physics and Quantum Electrodynamics in the Infinite Momentum Frame", INSTITUTION = "SLAC", YEAR = 1972, TYPE = "Report", NUMBER = "SLAC-PUB-1118", MONTH = "August", COMMENT = {Presented at the Third International Conference on Atomic Physics.}} @ARTICLE{Brodsky:72a, AUTHOR = "S. J. Brodsky and J. F. Gunion and R. L. Jaffe", TITLE = "Test for Fractionally Charged Partons from Deep-Inelastic Bremsstrahlung in the Scaling Region", JOURNAL = "Phys. Rev. D", YEAR = 1972, VOLUME = 6, PAGES = "2487-2494"} @ARTICLE{Brodsky:72b, AUTHOR = "S. J. Brodsky and R. Roskies", TITLE = "Quantum Electrodynamics and Renormalization Theory in The Infinite Momentum Frame", JOURNAL = "Phys. Lett.", YEAR = 1972, VOLUME = "41B", PAGES = "517-520"} @ARTICLE{Brodsky:73, AUTHOR = "S. J. Brodsky and R. Roskies and R. Suaya", TITLE = "Quantum Electrodynamics and Renormalization Theory in the Infinite-Momentum Frame", JOURNAL = "Phys. Rev. D", YEAR = 1973, VOLUME = 8, PAGES = "4574-4594"} @ARTICLE{Broughan:82, AUTHOR = "K. A. Broughan", TITLE = "{Grad-Fokker-Planck} Plasma Equations. Part 1. {Collision} Moments", JOURNAL = "J. Plasma Phys.", YEAR = 1982, VOLUME = 27, PAGES = "437-452", COMMENT = {{REDUCE} used in collaboration with hand calculation. {REDUCE} did the substitutions, with hand integrations. "Thirteen moments are taken of the collision term in Boltzmann-Fokker-Planck equation{\ldots}plasma{\ldots}"}} @ARTICLE{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{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}.}} @TECHREPORT{Caprasse:90a, 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", INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin", YEAR = 1990, TYPE = "Preprint", NUMBER = "SC 90-18", MONTH = "November"} ABSTRACT = {We study the {power-law} type solutions of the fourth order field equations derived from a generic quadratic {Lagrangian} density in the case of multidimensional {Bianchi I} cosmological models. All the solutions of the system of algebraic equations have been found, using computer algebra, from a search of the {Groebner} bases associated to it. 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 {Lagrangian} density. In the case of a pure {Riemann-squared} contribution (suggested by a recent calculation of the effective action for the heterotic string), the possibility exists to realize a splitting of the {d-dimensional} space into a {(d-3)-dimensional} internal space and a physical {3-dimensional} space, the latter expanding in time as a power bigger than 2 (about 4.5 when d = 9).}} @ARTICLE{Carlson:80, AUTHOR = "P. Carlson", TITLE = "Coordinate Free Relativity", JOURNAL = "J. Math. Phys.", YEAR = 1980, VOLUME = 21, PAGES = "1149-1154", COMMENT = {{REDUCE} programs for tetrad formulation of GR.}} @PHDTHESIS{Carroll:73, AUTHOR = "R. Carroll", TITLE = "The Anomalous Magnetic Moment of the Electron in the Mass Operator Formalism", SCHOOL = "University of Michigan", YEAR = 1973} @ARTICLE{Carroll:75, AUTHOR = "R. Carroll", TITLE = "Mass-Operator Calculation of the Electron g-Factor", JOURNAL = "Phys. Rev. D", YEAR = 1975, VOLUME = 8, PAGES = "2344-2354"} @TECHREPORT{Cejchan, AUTHOR = "A. Cejchan and J. Nadrchal", TITLE = "Application of {REDUCE}-2 and Analytic Integration Program in the Theoretical Solid State Physics", INSTITUTION = "Institute of Physics, CSAV, Prague"} @INPROCEEDINGS{Chaffy:88, AUTHOR = "C. Chaffy-Camus", TITLE = "An Application of {REDUCE} to the Approximation of {f(x,y)}", BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag", YEAR = 1988, VOLUME = 358, PAGES = "73-84"} @ARTICLE{Chinnick:86, AUTHOR = "K. Chinnick and C. Gibson and J. F. Griffiths and W. Kordylewski", TITLE = "Isothermal Interpretations of Oscillatory Ignition During Hydrogen Oxidation in an Open System. {I}. {Analytical} Predictions and Experimental Measurements of Periodicity", JOURNAL = "Proc. Royal Soc. Lond.", YEAR = 1986, VOLUME = "A405", PAGES = "117-128", COMMENT = {Used {REDUCE} to solve Jacobian, but answer too complicated to be of any use.}} @ARTICLE{Cline:90, AUTHOR = "Terry Cline and Harold Abelson and Warren Harris", TITLE = "Symbolic Computing in Engineering Design", JOURNAL = "AI EDAM", YEAR = 1990, MONTH = "February"} @TECHREPORT{Cohen:76, AUTHOR = "H. I. Cohen and O. Leringe and Y. Sundblad", TITLE = "The Use of Algebraic Computing in General Relativity", INSTITUTION = "The Royal Institute of Technology Department of Mechanics", YEAR = 1976, NUMBER = "TRITA-MEK-76-02"} @TECHREPORT{Cohen:76a, AUTHOR = "I. Cohen and F. Bark", TITLE = "Perturbation Calculations for the Spin Up Problem Using {REDUCE}", INSTITUTION = "The Royal Institute of Technology, Department of Mechanics", YEAR = 1976, NUMBER = "TRITA-MEK-76-03"} @TECHREPORT{Cohen:77, AUTHOR = "I. Cohen and S. Yu. Slavyanov", TITLE = "Smooth Perturbations of the Schr{\"o}dinger Equation with a Linear Potential Related to the Charmonium Models", INSTITUTION = "University of Stockholm Institute of Physics", YEAR = 1977, TYPE = "USIP Report", NUMBER = "77-17"} @ARTICLE{Cohen:79, AUTHOR = "J. P. Fitch and H. I. Cohen", TITLE = "Using {CAMAL} for Algebraic Calculations in General Relativity", JOURNAL = "General Relativity and Gravitation", VOLUME = 11, YEAR = 1979, PAGES = "411-418"} @ARTICLE{Cohen:84, AUTHOR = "H. I. Cohen and I. B. Frick and J. E. {\AA}man", TITLE = "Algebraic Computing in General Relativity", JOURNAL = "General Relativity and Gravitation, ed.", YEAR = 1984, PAGES = "139-162", COMMENT = {General relativity review.}} @INPROCEEDINGS{Cohen:89, AUTHOR = "Joel S. Cohen", TITLE = "The Effective Use of Computer Algebra Systems", YEAR = 1989, PAGES = "677-698", BOOKTITLE = "Transactions of the Sixth Army Conference on Applied Mathematics and Computing", COMMENT = {Review of author's experience with four computer algebra systems.}} @ARTICLE{Connor:84, AUTHOR = "J. N. L. Connor and P. R. Curtis and D. Farrelly", TITLE = "The Uniform Asymptotic Swallowtail Approximation: Practical Methods for Oscillating Integrals with Four Coalescing Saddle Points", JOURNAL = "J. Phys. A", YEAR = 1984, VOLUME = 17, PAGES = "283-310", COMMENT = {Used {REDUCE} and {SCHOONSCHIP} for some algebraic manipulations, and then checked the results with {MACSYMA}; this is the most distrustful reference we have found.}} @ARTICLE{Connor:84a, AUTHOR = "J. N. L. Connor and P. R. Curtis and C. J. Edge and A. Lagan{`a}", TITLE = "The Uniform Asymptotic Swallowtail Approximation: Application to the Collinear $H+F_{2}$", JOURNAL = "J. Chem. Phys.", YEAR = 1984, VOLUME = 80, NUMBER = 3, PAGES = "1362-1363", MONTH = "February"} @ARTICLE{Conwell:84, AUTHOR = "P. R. Conwell and P. W. Barber and C. K. Rushworth", TITLE = "Resonant Spectra of Dielectric Sphere", JOURNAL = "J. Opt. Soc. Am. A", YEAR = 1984, VOLUME = 1, PAGES = "62-67", COMMENT = {{REDUCE} used to confirm independently convergence and accuracy of {Numerical Bessel} function routine, expanding series by {REDUCE} and using bigfloats. Described as slow but worthwhile.}} @INPROCEEDINGS{Cowan:79, AUTHOR = "Richard M. Cowan and Martin L. Griss", TITLE = "Hashing -- The Key to Rapid Pattern Matching", BOOKTITLE = "Proc. {EUROSAM} 1979, Lecture Notes in Computer Science", YEAR = 1979, VOLUME = 72, PAGES = "266-278", PUBLISHER = "Springer-Verlag"} @ARTICLE{Cung:75, AUTHOR = "V. K. Cung", TITLE = "Differential Cross Section of e+ + e- to e+ + mu- + nubar(mu) + nubar(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", 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", PRINTING = "2nd", YEAR = 1989} @TECHREPORT{Della-Dora:81, AUTHOR = "J. Della Dora and E. Tournier", TITLE = "Solutions Formelles {D'Equations} Differentielles au Voisinage de Points Singuliers Reguliers", INSTITUTION = "Centre National de la Recherche Scientifique", YEAR = 1981, TYPE = "Report", NUMBER = 239} @INPROCEEDINGS{Della-Dora:84, AUTHOR = "J. Della Dora and E. Tournier", TITLE = "Homogeneous Linear Difference Equation {(Frobenius-Boole Method)}", BOOKTITLE = "Proc. {EUROSAM} 1984, Lecture Notes in Computer Science", YEAR = 1984, VOLUME = 174, PAGES = "2-12", PUBLISHER = "Springer-Verlag"} @TECHREPORT{Della-Dora:85, AUTHOR = "Jean Della-Dora and Claire Dicrescenzo and Dominique Duval", TITLE = "About a New Method for Computing in Algebraic Number Fields", INSTITUTION = "Universit{\'e} de Grenoble, Institut Fourier, France", YEAR = 1985, MONTH = "November"} @ARTICLE{Demaret:89, AUTHOR = "J. Demaret and H. Caprasse and A. Moussiaux and Ph. Tombal and D. Papadopoulos", TITLE = "{Ten-dimensional Lovelock-type Space-Times}", JOURNAL = "{To appear} Phys. Rev. D", YEAR = 1989, MONTH = "July"} @ARTICLE{DeMenna:87, AUTHOR = "L. De Menna and G. Miano and G. Rubinacci", TITLE = "Volterra's Series Solutions of Free Boundary Plasma Equilibria", JOURNAL = "Phys. Fluids", YEAR = 1987, VOLUME = 30, PAGES = "409-416", COMMENT = {Magnetohydrodynamics. "We have carried out the computations up to the fourth order, (the fourth order has been obtained by means of the symbolic program {REDUCE}").}} @ARTICLE{Demichev:85, AUTHOR = "A. P. Demichev and A. Ya. Rodionov", TITLE = "A {REDUCE} Program for the Calculation of Geometrical Characteristics of Compactified Multidimensional {Riemannian} Space", JOURNAL = "Comp. Phys. Comm.", YEAR = 1985, VOLUME = 38, PAGES = "441-448", COMMENT = {Covariant theories in N dimensional ($N \geq 4$) space-time. {REDUCE} programs to calculate {Ricci, Einstein and Yang-Mills} curvature and energy-momentum tensor.}} @TECHREPORT{Demichev:86, AUTHOR = "A. P. Demichev and A. Ya. Rodionov", TITLE = "Freund-{Rubin} Type Solutions for Different Compactifications of the Eleven-Dimensional Space", INSTITUTION = "Institute for High Energy Physics", YEAR = 1986, TYPE = "Preprint", NUMBER = "86-85", ABSTRACT = {The results of calculating geometrical characteristics of seven-dimensional quotient spaces are represented. These quantities are necessary for the construction of compactifying solutions of the eleven-dimensional supergravity.}} @ARTICLE{deRop:88, AUTHOR = "Y. de Rop and J. Demaret", TITLE = "Using {EXCALC} to Study Nondiagonal Multidimensional Spatially Homogeneous Cosmologies", JOURNAL = "Gen. Rel. Grav.", YEAR = 1988, VOLUME = 20, PAGES = "1127-1139"} @TECHREPORT{DeVos:89, AUTHOR = "Alexis De Vos", TITLE = "The use of {Reduce} in solar energy conversion theory", INSTITUTION = "State University of Gent, {CAGe} Computer Algebra Group", YEAR = 1989, TYPE = "Reports of the {CAGe} Project", NUMBER = 4, MONTH = "August"} @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", 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", TITLE = "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 = "Internal Report", NUMBER = "GUTPA 88/04-01", MONTH = "July", COMMENT = {Presented at 15th {UK} Plasma Physics Conference, {UMIST}.}} @ARTICLE{Diver:91, AUTHOR = "D. A. Diver", TITLE = "Modelling Waves with Computer Algebra", JOURNAL = "J. Symbolic Computation", YEAR = 1991, VOLUME = 11, NUMBER = 3, PAGES = "275-289", MONTH = "March", ABSTRACT = {A sophisticated model for linear waves in an inhomogeneous plasma is tackled completely using the computer algebra system {REDUCE}. The algebra code mirrors the mathematics, and is structured in a simple and straightforward manner. In so doing, the solution technique is made obvious, and the overall philosophy of the approach is intuitive to the {non-specialist} computer algebra user.}} @TECHREPORT{Dorfi:85, AUTHOR = "E. A. Dorfi and L. O'C. Drury", TITLE = "Simple Adaptive Grids for {1D} Initial Value Problems", INSTITUTION = "Max-Plack-Institut fuer Kernphysik, Heidelberg, West Germany", YEAR = 1985, NUMBER = "MPI H-1985-V21"} @ARTICLE{Dorizzi:86, AUTHOR = "B. Dorizzi and B. Grammaticos and J. Hietarinta and A. Ramani and F. Schwarz", TITLE = "New integrable three dimensional quartic potentials", JOURNAL = "Phys. Lett.", YEAR = 1986, VOLUME = "116A", PAGES = "432-436", COMMENT = {{REDUCE} is used to construct and verify constants of motion.}} @TECHREPORT{dosSantos:85, AUTHOR = "R. P. dos Santos and P. P. Srivastava", TITLE = "Two-loop Effective Potential for Wess-Zumino Model using Superfields", INSTITUTION = "International Centre for Theoretical Physics", YEAR = 1985, NUMBER = "IC/85/205", MONTH = "October", ABSTRACT = {For the case of several interacting chiral superfields the propagators for the unconstrained superfield potentials in the 'shifted' theory, where the supersymmetry is explicitly broken, are derived in a compact form. They are used to compute one-loop effective potential in the general case, while a superfield calculation of renormalized effective potential to two loops for the Wess-Zumino model is performed.}} @ARTICLE{dosSantos:87, AUTHOR = "Renato P. dos Santos", TITLE = "Using {REDUCE} in Supersymmetry", JOURNAL = "J. Symb. Comp.", YEAR = 1989, VOLUME = 7, PAGES = "523-525"} @PHDTHESIS{dosSantos:87a, AUTHOR = "R. P. dos Santos", TITLE = "O M{\'e}todo de Supercampos para o C{\'a}lculo de Potencial Efetivo em Modelos com Supercampos Quirais: Os Modelos de Wess e Zumino e de O'Raifeartaigh", SCHOOL = "Centro Brasileiro de Pesquisas F{\'i}sicas", YEAR = 1987, COMMENT = {{(In Portuguese)} Using the method of {Superfields}, the effective potential for supersymmetric models of {Wess-Zumino} and of {O'Raifeartaigh} is evaluated up to two-loop order. The spontaneous supersymmetry breaking is discussed. {REDUCE} plays very important role in evaluation of the {Feynman} superdiagrams and in renormalization.}} @TECHREPORT{dosSantos:88a, AUTHOR = "Renato P. dos Santos", TITLE = "Introdu\c{c}\~{a}o ao Sistema {REDUCE} de C\'{a}lculo Alg\'{e}brico", INSTITUTION = "CBPF, Rio de Janeiro, Brazil", YEAR = 1988, NUMBER = "CBPF-NT-001/88", COMMENT = {{(In Portuguese)} Lecture notes of a course on {REDUCE}.}} @ARTICLE{dosSantos:90, AUTHOR = "R. P. dos Santos and W. L. Roque", TITLE = "On the Design of an Expert Help System for Computer Algebra Systems", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1990, VOLUME = 24, NUMBER = 4, PAGES = "22-25", MONTH = "October"} @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, NUMBER = "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} @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"} @ARTICLE{Falck:89, AUTHOR = "N. K. Falck and D. Graudenz and G. Kramer", TITLE = "Cross section for {five-parton} production in $e^{+} e^{-}$ annihilation", JOURNAL = "Comp. Phys. Comm.", YEAR = 1989, VOLUME = 56, PAGES = "181-198", NUMBER = 2, MONTH = "December"} @ARTICLE{Fazio:84, AUTHOR = "P. M. Fazio and G. E. Copeland", TITLE = "Cooper-Type Minima in Multipole Cross Sections of Atomic Hydrogen", JOURNAL = "Phys. Rev. Lett.", YEAR = 1984, VOLUME = 53, NUMBER = "2", MONTH = "July"} @INPROCEEDINGS{Fedorova:87, AUTHOR = "R. N. Fedorova and V. P. Gerdt and N. N. Govorun and V. P. Shirikov", TITLE = "Computer Algebra in Physical Research of {Joint Institute} for {Nuclear Research}", BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "1-10", PUBLISHER = "Springer-Verlag"} @INPROCEEDINGS{Fedorova:87a, AUTHOR = "R. N. Fedorova and V. V. Kornyak", TITLE = "Computer Algebra Application for Determining Local Symmetries of Differential Equations", BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "174-175", PUBLISHER = "Springer-Verlag"} @ARTICLE{Feldmar:86, AUTHOR = "E. Feldmar and K. S. K{\"o}lbig", TITLE = "{REDUCE} Procedures for the Manipulation of Generalized Power Series", JOURNAL = "Comp. Phys. Comm.", YEAR = 1986, VOLUME = 39, PAGES = "267-284"} @ARTICLE{Feuillebois:84, AUTHOR = "F. Feuillebois", TITLE = "Sedimentation in a Dispersion with Vertical Inhomogenieties", JOURNAL = "Journ. Fluid Mech.", YEAR = 1984, VOLUME = 139, PAGES = "145-171", COMMENT = {Uses {REDUCE} and {INT} to evaluate some integrals in the expansion of 1/s, a small quantity.}} @ARTICLE{Fitch:73, AUTHOR = "John Fitch", TITLE = "Problems \#3 and \#4 in {REDUCE} and {MACSYMA}", JOURNAL = "SIGSAM Bulletin", YEAR = 1973, PAGES = "10-11", ABSTRACT = {The algebra systems {REDUCE} and {MACSYMA} are used to solve {SIGSAM} Problem \#3, the Reversion of a Double Series, and {SIGSAM} Problem \#4, the Lie Transform Solution of the Harmonic Oscillator.}} @INPROCEEDINGS{Fitch:81, AUTHOR = "J. P. Fitch", TITLE = "User-based Integration Software", BOOKTITLE = "Proc. 1981 {ACM} Symposium on Symbolic and Algebraic Computation", YEAR = 1981, PAGES = "245-248"} @INPROCEEDINGS{Fitch:83, AUTHOR = "J. P. Fitch", TITLE = "Implementing {REDUCE} on a Microprocessor", BOOKTITLE = "Proc. {EUROCAL} 1983, Lecture Notes in Computer Science", YEAR = 1983, VOLUME = 162, PAGES = "128-136", PUBLISHER = "Springer-Verlag"} @ARTICLE{Fitch:85, AUTHOR = "J. P. Fitch", TITLE = "Solving Algebraic Problems with {REDUCE}", JOURNAL = "J. of Symbolic Computation", YEAR = 1985, VOLUME = 1, NUMBER = 2, PAGES = "211-227", MONTH = "June"} @INPROCEEDINGS{Fitch:85a, AUTHOR = "J. P. Fitch", TITLE = "Applying Computer Algebra", BOOKTITLE = "International Conference on Computer Algebra and its Application in Theory", YEAR = 1985, PAGES = "262-275"} @INPROCEEDINGS{Fitch:87, AUTHOR = "J. P. Fitch", TITLE = "Utilisation du Calcul Formel", BOOKTITLE = "Calcul Formel et Automatique", EDITOR = "P. Chenin", PUBLISHER = "Editions du {CNRS}", YEAR = 1987, PAGES = "119-136"} @INPROCEEDINGS{Fitch:87a, AUTHOR = "J. P. Fitch and R. G. Hall", TITLE = "Symbolic Computation and the Finite Element Method", BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "95-96", PUBLISHER = "Springer-Verlag"} @INPROCEEDINGS{Fitch:89, AUTHOR = "J. P. Fitch", TITLE = "Can {REDUCE} be run in parallel?", BOOKTITLE = "Proc. of {ISSAC} '89", PUBLISHER = "{ACM} Press, New York", YEAR = 1989, PAGES = "155-162"} @ARTICLE{Fitch:89a, AUTHOR = "J. Fitch", TITLE = "Compiling for Parallelism", JOURNAL = "Computer Algebra and Parallelism", EDITOR = "J. Della Dora and J. Fitch", YEAR = 1989, PAGES = "19-31", PUBLISHER = "Academic Press, London"} @InProceedings{Fitch90, author = "J. P. Fitch", title = "A delivery system for {REDUCE}", booktitle = "Proceedings of the International Symposium on Symbolic and Algebraic Computation", year = "1990", editor = "S. Watanabe and Morio Nagata", pages = "76-81", organization = "ACM", publisher = "Addison-Wesley" } @ARTICLE{Fitch:90a, AUTHOR = "John Fitch", TITLE = "The symbolic-numeric interface", JOURNAL = "Comp. Phys. Comm.", YEAR = 1990, VOLUME = 61, NUMBER = "1-2", MONTH = "November", PAGES = "22-33", ABSTRACT = {Algebraic computation can be of great assistance in the preparation of numerical programs. The paper considers some of these, from simple to complex, and describes work currently in progress to produce a true integrated symbolic-numeric computing system.}} @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.}} % REDUCE BIBLIOGRAPHY % Part 2: G-L % Copyright (c) 1990 The RAND Corporation. 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{Gaemers, AUTHOR = "K. J. F. Gaemers and R. Gastmans and F. M. Renard", TITLE = "Neutrino Counting in e+ e- Collisions", INSTITUTION = "NIKHEF-H, Amsterdam", TYPE = "Preprint", ABSTRACT = {The possibility of counting the number of neutrino types in e+ e- $\rightarrow$ gamma nu nubar is re-examined by taking into account effects of the Z-pole.}} @TECHREPORT{Gaemers:78, AUTHOR = "K. J. F. Gaemers and G. J. Gounaris", TITLE = "Polarization Amplitudes For e+e- $\rightarrow$ W+W- $\rightarrow$ ZZ", INSTITUTION = "CERN", YEAR = 1978, TYPE = "Preprint", NUMBER = "TH.2548-CERN", MONTH = "August", ABSTRACT = {The main purpose of this work is to study the three weak boson vertex. We give explicit formulae for all polarization amplitudes of the processes e+e- $\rightarrow$ W+W- and e+e- $\rightarrow$ ZZ, with arbitrary couplings between the various intermediate vector bosons.}} @INPROCEEDINGS{Ganzha:89, AUTHOR = "V. Ganzha and R. Liska", TITLE = "Application of the {REDUCE} Computer Algebra System to Stability Analysis of Difference Schemes", BOOKTITLE = "Proc. Computers and Mathematics '89", EDITOR = "E. Kaltofen and S. M. Watt", YEAR = 1989, PAGES = "119-129", PUBLISHER = "Springer-Verlag, New York"} @InProceedings{Ganzha90, author = "Victor G. Ganzha and Michail Yu. Shaskov", title = "Local Approximation Study of Difference Operators by means of {REDUCE} System", booktitle = "Proceedings of the International Symposium on Symbolic and Algebraic Computation", year = "1990", editor = "S. Watanabe and Morio Nagata", pages = "185-192", organization = "ACM", publisher = "Addison-Wesley" } @InProceedings{Ganzha90a, author = "V. G. Ganzha and S. V. Meleshko and V. P. Shelest", title = "Application of {REDUCE} System for Analyzing Consistency of Systems of {P.D.E.'s}", booktitle = "Proceedings of the International Symposium on Symbolic and Algebraic Computation", year = "1990", editor = "S. Watanabe and Morio Nagata", pages = "301", organization = "ACM", publisher = "Addison-Wesley" } @TECHREPORT{Garavaglia, AUTHOR = "Theodore Garavaglia", TITLE = "Polarized Electron Scattering on Spin Zero and Polarized Spin $\frac{1}{2}$ Targets: Deep Inelastic Scattering, Elastic Electron-muon Scattering, and Elastic Electron-Nucleon Scattering", INSTITUTION = "Inst. Teich. Bhaile Atha Cliath, Eire", TYPE = "Preprint", ABSTRACT = {A covariant formulation is developed and used to derive cross-sections for the analysis of experiments in which polarized electrons(muons) are scattered from spin zero and from polarized spin 1/2 targets.}} @ARTICLE{Garavaglia:80, AUTHOR = "T. Garavaglia", TITLE = "A Covariant Formulation for Polarized Electron (Muon) Scattering on Spin-Zero and Polarized Spin-$\frac{1}{2}$ Targets", JOURNAL = "Il Nuovo Cimento", YEAR = 1980, VOLUME = "56A", PAGES = "121-128", COMMENT = {{REDUCE} used in quantum mechanics.}} @ARTICLE{Garavaglia:84, AUTHOR = "Theodore Garavaglia", TITLE = "{Dirac-} and {Majorana-neutrino-mass} effects in {neutrino-electron} elastic scattering", JOURNAL = "Physical Review {D}", YEAR = 1984, VOLUME = 29, NUMBER = 3, PAGES = "387-392", MONTH = "February"} @ARTICLE{Garcia:86, AUTHOR = "Arnaldo Garcia and Paulo Viana", TITLE = "Weierstrass Points on Certain Non-Classical Curves", JOURNAL = "Arch. Math.", YEAR = 1986, VOLUME = 46, PAGES = "315-322"} @ARTICLE{Garrad:86, AUTHOR = "A. D. Garrad and D. C. Quarton", TITLE = "Symbolic Computing as a Tool in Wind Turbine Dynamics", JOURNAL = "Journ. of Sound and Vibration", YEAR = 1986, VOLUME = 109, NUMBER = 1, PAGES = "65-78", COMMENT = {{REDUCE} as a tool in turbine design, in particular present a program for part of a stability analysis for a turbine tower.}} @ARTICLE{Gastmans:79, AUTHOR = "R. Gastmans and A. van Proeyen and P. Verbaeten", TITLE = "Symbolic Evaluations of Dimensionally Regularized {Feynman} Diagrams", JOURNAL = "Comp. Phys. Comm.", YEAR = 1979, VOLUME = 18, PAGES = "201-203", ABSTRACT = {A modification of the symbolic and algebraic manipulation program {REDUCE} is reported which allows the treatment of vector and gamma algebra in an arbitrary number of dimensions.}} @TECHREPORT{Gatermann:90, AUTHOR = "Karin Gatermann", TITLE = "Gruppentheoretische konstruktion von symmetrischen kubaturformeln", INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin", YEAR = 1990, TYPE = "Preprint", NUMBER = "TR 90-1", MONTH = "January"} @InProceedings{Gatermann90a, author = "Karin Gatermann", title = "Symbolic solution of polynomial equation systems with symmetry", booktitle = "Proceedings of the 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:90b, AUTHOR = "Karin Gatermann and Andreas Hohmann", TITLE = "Symbolic Exploitation of Symmetry in Numerical Pathfollowing", INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin", YEAR = 1990, TYPE = "Preprint", NUMBER = "SC 90-11", MONTH = "November", 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{Gates:85, AUTHOR = "Barbara L. Gates and J. A. van Hulzen", TITLE = "Automatic Generation of Optimized Programs", BOOKTITLE = "Proc. {EUROCAL} '85", YEAR = 1985, MONTH = "April"} @ARTICLE{Gates:85a, AUTHOR = "Barbara L. Gates", TITLE = "Gentran: An Automatic Code Generation Facility for {REDUCE}", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1985, VOLUME = 19, NUMBER = 3, PAGES = "24-42", MONTH = "August"} @TECHREPORT{Gates:85b, AUTHOR = "Barbara L. Gates", TITLE = "Gentran User's Manual - {REDUCE} Version", INSTITUTION = "Twente University of Technology, Department of Computer Science, The Netherlands", TYPE = "Memorandum", YEAR = 1985, NUMBER = "INF-85-11", MONTH = "June"} @TECHREPORT{Gates:85c, AUTHOR = "Barbara L. Gates", TITLE = "Gentran Design and Implementation, {REDUCE} Version", INSTITUTION = "Twente University of Technology, Department of Computer Science, The Netherlands", YEAR = 1985, TYPE = "Memorandum", NUMBER = "INF-85-12", MONTH = "August"} @INPROCEEDINGS{Gates:86, AUTHOR = "Barbara L. Gates", TITLE = "A Numerical Code Generation Facility for {REDUCE}", BOOKTITLE = "Proc. {SYMSAC} '86", YEAR = 1986, PAGES = "94-99", MONTH = "July"} @TECHREPORT{Gebauer:85, AUTHOR = "R{\"u}diger Gebauer and H. Michael M{\"o}ller", TITLE = "A Fast Variant of {Buchberger's} Algorithm", INSTITUTION = "Universit{\"a}t Heidelberg and Fernuniversit{\"a}t {Hagen}", YEAR = 1985, MONTH = "October"} @ARTICLE{Gebauer:88, AUTHOR = "R{\"u}diger Gebauer and H. Michael M{\"o}ller", TITLE = "On an Installation of {Buchberger's} Algorithm", JOURNAL = "J. Symbolic Computation", YEAR = 1988, VOLUME = 6, NUMBER = "2 and 3", PAGES = "275-286"} @ARTICLE{George:68, AUTHOR = "D. J. George", TITLE = "A Covariant Theory of the Disintegration of the Deuteron by Pions and Photons at High Energy", JOURNAL = "Phys. Rev.", YEAR = 1968, VOLUME = 167, PAGES = "1357-1364"} @ARTICLE{Gerdt:80, AUTHOR = "V. P. Gerdt", TITLE = "Analytical Calculations in High Energy Physics by Computer", JOURNAL = "Comp. Phys. Comm.", YEAR = 1980, VOLUME = 20, PAGES = "85-90", COMMENT = {A review, comparing {SCHOONSCHIP, ASHMEDAI and REDUCE-2}.}} @ARTICLE{Gerdt:80a, AUTHOR = "V. P. Gerdt and O. V. Tarasov and D. V. Shirkov", TITLE = "Analytical Calculations on Digital Computers for Applications in Physics and Mathematics", JOURNAL = "Sov. Phys. USP", YEAR = 1980, VOLUME = 23, PAGES = "59-77", COMMENT = {General review of applications in many languages.}} @TECHREPORT{Gerdt:80b, AUTHOR = "V. P. Gerdt", TITLE = "On Global Structure of the General Solution of the {Chew-Low} Equations", INSTITUTION = "J.I.N.R., Dubna", YEAR = 1980, TYPE = "Preprint", NUMBER = "P2-80-436"} @ARTICLE{Gerdt:85, AUTHOR = "V. P. Gerdt and A. B. Shvachka and A. Yu. Zharkov", TITLE = "Computer Algebra Application for Classification of Integrable Non-Linear Evolution Equations", JOURNAL = "J. Symb. Comp.", YEAR = 1985, VOLUME = 1, PAGES = "101-107"} @TECHREPORT{Gerdt:85a, AUTHOR = "V. P. Gerdt and N. A. Kostov and P. P. Raychev and R. P. Roussev", TITLE = "Calculation of the Matrix Elements of the {Hamiltonian} of the Interacting Vector Boson Model Using Computer Algebra - Basic Concepts of the Interacting Vector Boson Model and Matrix Elements of the {SU(3)-Quadrupole} Operator", INSTITUTION = "Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria", YEAR = 1985, NUMBER = "E4-85-262"} @TECHREPORT{Gerdt:85b, AUTHOR = "V. P. Gerdt and N. A. Kostov and P. P. Raychev", TITLE = "Calculation of the Matrix Elements of the {Hamiltonian} of the Interacting Vector Boson Model Using Computer Algebra - Matrix Elements of the {Hamiltonian} and Some {U(6)-Clebsch-Gordon} Coefficients", INSTITUTION = "Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria", YEAR = 1985, NUMBER = "E4-85-263"} @TECHREPORT{Gerdt:85c, AUTHOR = "V. P. Gerdt and N. A. Kostov and P. P. Raychev and R. P. Roussev", TITLE = "Calculation of the Matrix Elements of the {Hamiltonian} of the Interacting Vector Boson Model Using Computer Algebra - Matrix Elements of the {Hamiltonian} - Analytical Results", INSTITUTION = "Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria", YEAR = 1985, NUMBER = "E4-85-264"} @TECHREPORT{Gerdt:86, AUTHOR = "V. P. Gerdt and M. G. Meshcheryakov and D. V. Shirkov", TITLE = "Computers in Theoretical Physics", INSTITUTION = "J.I.N.R., Dubna", YEAR = 1986, NUMBER = "P2-86-848", ABSTRACT = {The paper is written on the basis of the report presented by two authors ({M.G. Meshcheryakov} and {D.V. Shirkov}) at the 60th session of the JINR Scientific Council, June 5, 1986. It reviews the usage of computer mathematics in theoretical and mathematical investigations carried out in the Joint Institute. Recommendations are given on further development of the JINR Computer Center in accordance with the program of theoretical researches in nearest Five-Year Plan.}} @INPROCEEDINGS{Gerdt:87, AUTHOR = "V. P. Gerdt and A. B. Shabat and S. I. Svinolupov and A. Yu. Zharkov", TITLE = "Computer Algebra Application for Investigating Integrability of Nonlinear Evolution Systems", BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "81-92", PUBLISHER = "Springer-Verlag"} @INPROCEEDINGS{Gerdt:87a, AUTHOR = "V. P. Gerdt and N. A. Kostov and Z. T. Kostova", TITLE = "Computer Algebra and Computation of {Puiseux} Expansions of Algebraic Functions", BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "206-207", PUBLISHER = "Springer-Verlag"} @INPROCEEDINGS{Gerdt:89, AUTHOR = "V. P. Gerdt and N. A. Kostov", TITLE = "Computer Algebra in the theory of Ordinary Differential Equations of Halphen type", BOOKTITLE = "Proc. Computers and Mathematics '89", EDITOR = "E. Kaltofen and S. M. Watt", YEAR = 1989, PAGES = "279-288", PUBLISHER = "Springer-Verlag, New York"} @TECHREPORT{Gerdt:89a, AUTHOR = "V. P. Gerdt and Z. T. Kostova and N. A. Kostov and I. P. Yudin", TITLE = "Algebraic-Numeric Calculations of Proton Trajectories in Bending Magnets of Synchrotron Accelerator", INSTITUTION = "J.I.N.R., Dubna", YEAR = 1989, TYPE = "Preprint", NUMBER = "E11-89-755", ABSTRACT = {We study a solution of nonlinear differential equation of the second degree which describes the trajectories of the charged particles in the fully inhomogeneous field of cyclic accelerator. We give the clear mathematical statement of the problem and algorithm of solving it. We realize this algorithm on the Computer Algebra System {REDUCE 3.2}. Our algorithm is based both on the existence of exact solution in terms of hyperelliptic integral and on the existence of power series solution of specific inversion problem. We use the known {REDUCE} procedures of operation on generalized power series. Using the {FORTRAN} code we give the numerical analysis of these series in the close relation to the concrete physical situation. We apply our results to the beam dynamics modeling of the protons in the bending magnets in synchrotron accelerator.}} @TECHREPORT{Gerdt:89b, AUTHOR = "V. P. Gerdt and A. Yu. Zharkov", TITLE = "Solving the Polynomial System Arising in Classification of Integrable Coupled {KdV-like} Systems", INSTITUTION = "J.I.N.R., Dubna", YEAR = 1989, TYPE = "Preprint", NUMBER = "P5-89-231", ABSTRACT = {A system of algebraic equations which follows from the necessary integrability conditions for the {ten-parametric} family of coupled {KdV-like} nonlinear evolution systems is considered. The method for solving this system based on the structure of the canonical local conservation laws densities is described. Computer algebra system {REDUCE} was used to find all the solutions. As a result we obtain the complete list of integrable coupled {KdV-like} systems.}} @InProceedings{Gerdt90, author = "V. P. Gerdt and A. Yu. Zharkov", title = "Computer Generation of Necessary Integrability Conditions for Polynomial-Nonlinear Evolution Systems", booktitle = "Proceedings of the International Symposium on Symbolic and Algebraic Computation", year = "1990", editor = "S. Watanabe and Morio Nagata", pages = "250-254", organization = "ACM", publisher = "Addison-Wesley" } @InProceedings{Gerdt90a, author = "Vladimar P. Gerdt and Nikolai V. Khutornoy and Alexey Yu. Zharkov", title = "Solving Algebraic Systems which arise as Necessary Integrability Conditions for Polynomial-Nonlinear evolution Equations", booktitle = "Proceedings of the International Symposium on Symbolic and Algebraic Computation", year = "1990", editor = "S. Watanabe and Morio Nagata", pages = "299", organization = "ACM", publisher = "Addison-Wesley" } @ARTICLE{Gerdt:90b, AUTHOR = "V. P. Gerdt and A. Yu. Zharkov", TITLE = "Computer Classification of Integrable Coupled {KdV-Like} Systems", JOURNAL = "J. Symb. Comp.", YEAR = 1990, VOLUME = 10, PAGES = "203-207", ABSTRACT = {The foundations of the symmetry approach to the classification problem of integrable {non-linear} evolution systems are briefly described. Within the framework of the symmetry approach the {ten-parametric} family of the third order {non-linear} evolution coupled {KdV-like} systems is investigated. The necessary integrability conditions lead to an {over-determined} {non-linear} algebraic system. To solve that system an effective method based on its structure has been used. This allows us to obtain the complete list of integrable systems of a given type. All computation has been completed on the basis of computer algebra systems {FORMAC} and {REDUCE}.}} @INPROCEEDINGS{Gerdt:90c, AUTHOR = "V. P. Gerdt and N. A. Kostov and A. Yu. Zharkov", TITLE = "Nonlinear Evolution Equations and Solving Algebraic Systems: The Importance of Computer Algebra", YEAR = 1990, BOOKTITLE = "International Conference 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.}} @ARTICLE{Gervois:74, AUTHOR = "A Gervois and Y. Pomeau", TITLE = "Logarithmic Divergence in the Virial Expansion of Transport Coefficients of Hard Spheres", JOURNAL = "Phys. Rev. A", YEAR = 1974, VOLUME = 9, PAGES = "2196-2213"} @TECHREPORT{Gladd:82, AUTHOR = "N. T. Gladd", TITLE = "Computational Aspects of Research on the Relativistic Whistler Instability", INSTITUTION = "Jaycor", YEAR = 1982, NUMBER = "J530-82-020", MONTH = "June"} @INPROCEEDINGS{Gladkih:83, AUTHOR = "I. Gladkih and E. Lovas", TITLE = "On the Application of Computer Algebra Languages in the {Central Research Institute for Physics}", BOOKTITLE = "Proceedings of the International Conference on Systems and Techniques of Analytical Computing and Their Applications in Theoretical Physics, {D11-83-511, Dubna}", YEAR = 1983} @INPROCEEDINGS{Gladkih:84, AUTHOR = "I. Gladkih and M. Zimanyi", TITLE = "Comparison of systems for Symbolic Computing in use in the {Central Research Institute for Physics} (in {Russian})", BOOKTITLE = "Proceedings of the International Conference on {Computer-Based} Scientific Research, Plovdiv", YEAR = 1984} @ARTICLE{Goldman:89, AUTHOR = "V. V. Goldman and J. A. van Hulzen", TITLE = "Automatic Code Vectorization of Arithmetic Expressions by Bottom-Up Structure Recognition", JOURNAL = "Computer Algebra and Parallelism", EDITOR = "J. Della Dora and J. Fitch", YEAR = 1989, PAGES = "119-132", PUBLISHER = "Academic Press, London"} @INPROCEEDINGS{Golley, AUTHOR = "Bruce W. Golley and Joseph Petrolito", TITLE = "An Alternative Finite Strip Technique for the Static Analysis of Single-Span, Multi-Span and Continuous Plates", YEAR = 1982, BOOKTITLE = "Proc. International Conference on Finite Element Methods"} @ARTICLE{Good:75, AUTHOR = "D. Good and R. L. London and W. W. Bledsoe", TITLE = "An Interactive Program Verification System", JOURNAL = "Sigplan Notices", YEAR = 1975, VOLUME = 10, NUMBER = 6, PAGES = "482-492"} @ARTICLE{Goto:77, AUTHOR = "E. Goto and T. Soma", TITLE = "{MOL} (Moving Objective Lens) Formulation of Deflective Aberration Free System", JOURNAL = "Optik", YEAR = 1977, VOLUME = 48, PAGES = "255-270"} @INPROCEEDINGS{Goto:78, AUTHOR = "E. Goto and T. Soma", TITLE = "Electron Beam Lithography for Advanced {LSI} Fabrication", YEAR = 1978, PAGES = "1223-1228", BOOKTITLE = "Proc. 1978 National Computer Conference, {AFIPS} Press, New Jersey"} @ARTICLE{Gould:84, AUTHOR = "H. W. Gould and M. E. Mays", TITLE = "Series Expansions of Means", JOURNAL = "Journ. of Mathematical Analysis and Applications", YEAR = 1984, VOLUME = 101, NUMBER = 2, PAGES = "611-621", MONTH = "July"} @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{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.}} @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).}} @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{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", BOOKTITLE = "Interactive Systems for Experimental Applied Mathematics", PUBLISHER = "Academic Press"} @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:71, 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:71a, 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. of {AAECC}-3, Lecture Notes on Comp. Science", YEAR = 1986, VOLUME = 229, PAGES = "392-403"} @TECHREPORT{Hearn:87, AUTHOR = "Anthony C. Hearn", TITLE = "{REDUCE} User's Manual, {Version} 3.3", INSTITUTION = "The RAND Corporation", YEAR = 1987, TYPE = "Report", NUMBER = "CP 78", MONTH = "July"} @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.}} @BOOK{Hirota:89, AUTHOR = "Ryogo Hirota and Masaaki Ito", TITLE = "Introduction to {REDUCE --- Doing} Symbolic Computation on {PC}", PUBLISHER = "Science sha, Tokyo", MONTH = "June", YEAR = 1989, COMMENT = {(In Japanese).}} @TECHREPORT{Horowitz:75, AUTHOR = "E. Horowitz and D. R. Musser", TITLE = "The Synthesis and Use of Algebraic Specifications of Data Structures", INSTITUTION = "University of Southern California", YEAR = 1975, TYPE = "Preprint"} @ARTICLE{Horwitz:83, AUTHOR = "B. Horwitz", TITLE = "Unequal Diameters and Their Effects on Time Varying Voltages in Branched Neurons", JOURNAL = "BioPhys. J.", YEAR = 1983, VOLUME = 41, PAGES = "51-66", COMMENT = {Theoretical biophysics. Much algebra, and used {REDUCE} to decrease mental labor. "Crucial point is that the existence of such computer techniques allows higher-order correction terms to be used."}} @ARTICLE{Hughes:90, AUTHOR = "D. I. Hughes", TITLE = "Symbolic Computation with Fermions", JOURNAL = "J. Symbolic Computation", YEAR = 1990, VOLUME = 10, NUMBER = 6, PAGES = "657-664", MONTH = "December", ABSTRACT = {A set of {REDUCE} routines for manipulating operators which anticommute amongst themselves is described. These routines have applications in theories such as supergravity where anticommuting operators are used to represent fermions. The Dirac bracket of the supersymmetry constraints arising in a quantum cosmological model based on N = 1 supergravtiy coupled to a massless scalar multiplet is calculated as an example.}} @INPROCEEDINGS{Hulshof:84, AUTHOR = "B. J. A. Hulshof and J. A. van Hulzen", TITLE = "Automatic Error Cumulation Control", BOOKTITLE = "Proc. {EUROSAM} 1984, Lecture Notes in Computer Science", YEAR = 1984, VOLUME = 174, PAGES = "260-271", PUBLISHER = "Springer-Verlag"} @INPROCEEDINGS{Hulshof:85, AUTHOR = "B. J. A. Hulshof and J. A. van Hulzen", TITLE = "An Expression Compression Package for {REDUCE} based on Factorization and Controlled Expansion", BOOKTITLE = "Proc. {EUROCAL} 1985, Lecture Notes in Computer Science", YEAR = 1985, VOLUME = 204, PAGES = "315-316", PUBLISHER = "Springer-Verlag"} @TECHREPORT{Hulshof:81, AUTHOR = "B. J. A. Hulshof and J. A. van Hulzen and J. Smit", TITLE = "Code Optimization Facilities Applied in the {Netform} Context", INSTITUTION = "Department of Applied Mathematics, Twente University of Technology, The Netherlands", YEAR = 1981, TYPE = "Memorandum", NUMBER = 368, MONTH = "December"} @ARTICLE{Hulshof:83, AUTHOR = "B. J. A. Hulshof and J. A. van Hulzen", TITLE = "Some {REDUCE} Facilities for Pretty Printing Subscripts and Formal Derivatives", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "16-20", MONTH = "February"} @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"} @TECHREPORT{Idesawa:77, AUTHOR = "M. Idesawa and T. Yatagai", TITLE = "General Theory of Projection-Type Moir{\'e} Topography", INSTITUTION = "Institute of Physical and Chemical Research, Wako-Shi, Saitama", YEAR = 1977, TYPE = "Scientific Papers", NUMBER = 71, ABSTRACT = {The configuration of equi-order surfaces in the projection-type {Moire} topography is described in terms of system parameters without any restrictions on the measurement condition.}} @INPROCEEDINGS{Ilyin:87, AUTHOR = "V. A. Ilyin and A. P. Kryukov", TITLE = "{DIMREG} - The Package for Calculations in the Dimensional Regularization with {4-dimensional} $\gamma^{5}$ -matrix in Quantum Field Theory", BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "225-232", PUBLISHER = "Springer-Verlag"} @ARTICLE{Ilyin:89, AUTHOR = "V. A. Ilyin and A. P. Kryukov and A. Ya. Rodioniov and A. Yu. Taranov", TITLE = "Fast Algorithm for Calculation of {Dirac's Gamma-Matrices} Traces", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1989, VOLUME = 23, NUMBER = 4, PAGES = "15-24", MONTH = "October"} @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{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"} @ARTICLE{Kagan:85, AUTHOR = "Y. Y. Kagan and L. Knopoff", TITLE = "The First-Order Statistical Moment of the Seismic Moment Tensor", JOURNAL = "Geophys. J. R. Astron. Soc.", YEAR = 1985, VOLUME = 81, PAGES = "429-444"} @ARTICLE{Kagan:88, AUTHOR = "Y. Y. Kagan", TITLE = "Static Sources of Elastic Deformation in a Homogeneous Half-Space", JOURNAL = "J. Geophys. Res.", YEAR = 1988, VOLUME = 93, NUMBER = "B9", PAGES = "10,560-10,574", MONTH = "September"} @TECHREPORT{Kahn:69, AUTHOR = "M. E. Kahn", TITLE = "The Near-Minimum-Time Control of Open Loop Articulated Kinematic Chains", INSTITUTION = "Stanford University, Computer Science Dept.", YEAR = 1969, TYPE = "Report", NUMBER = "AIM-106"} @TECHREPORT{Kamal:81, AUTHOR = "A. N. Kamal and J. Kodaira and T. Muta", TITLE = "Gluon Jets From Heavy Paraquarkonium", INSTITUTION = "University of Alberta, Canada and Stanford University, California and Fermi National Accelerator Laboratory, Illinois", YEAR = 1981, NUMBER = "SLAC-PUB-2725", MONTH = "April"} @TECHREPORT{Kamel:69, AUTHOR = "A. A. Kamel", TITLE = "Perturbation Method in the Theory of Non-Linear Oscillations", INSTITUTION = "Stanford University, Dept. of Aeronautics and Astronautics", YEAR = 1969, TYPE = "Report"} @TECHREPORT{Kamel:69a, AUTHOR = "A. A. Kamel", TITLE = "Perturbation Theory Based on {Lie} Transforms and Its Application to the Stability of Motion Near {Sun}-Perturbed {Earth-Moon} Triangular Libration Points", INSTITUTION = "Stanford University, Dept. of Aeronautics and Astronautics", YEAR = 1969, TYPE = "Report", NUMBER = "391"} @INPROCEEDINGS{Kamel:78, AUTHOR = "A. A. Kamel", TITLE = "Synchronous Satellite Ephemeris Due to Earth's Triaxiality and Luni-Solar Effects", YEAR = 1978, MONTH = "August", BOOKTITLE = "{AIAA/AAS} Astrodynamics Conference, Palo Alto, CA", COMMENT = {Synchronous satellite ephemeris is developed in terms of non-singular orbital elements.}} @ARTICLE{Kanada:81, AUTHOR = "Yasumasa Kanada and Tateaki Sasaki", TITLE = "{LISP-based} {big-float} system is not slow", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1981, VOLUME = 15, NUMBER = 2, PAGES = "13-19", MONTH = "May"} @TECHREPORT{Kanada:75, AUTHOR = "Y. Kanada", TITLE = "Implementation of {HLISP} and Algebraic Manipulation Language {REDUCE} 2", INSTITUTION = "University of Tokyo Information Science Lab", YEAR = 1975, TYPE = "Report", NUMBER = "75-01"} @ARTICLE{Kaneko:89, AUTHOR = "Toshiaki Kaneko and Setsuya Kawabata", TITLE = "A Preprocessor for Fortran Source Code Produced by {REDUCE}", JOURNAL = "Comp. Phys. Comm.", YEAR = 1989, VOLUME = 55, NUMBER = 2, PAGES = "141-147", MONTH = "September", PUBLISHER = "North Holland Publishing Company"} @ARTICLE{Kaps:85, AUTHOR = "P. Kaps and S. W. H. Poon and T. D. Bui", TITLE = "Rosenbrock Methods for Stiff {ODEs}: A Comparison of {Richardson} Extrapolation and Embedding Techniques", JOURNAL = "Computing", YEAR = 1985, VOLUME = 34, PAGES = "17-40", COMMENT = {Reference to {REDUCE} but not in text.}} @INPROCEEDINGS{Karr:85, AUTHOR = "Michael Karr", TITLE = "Canonical Form for Rational Exponential Expressions", BOOKTITLE = "Proc. {EUROCAL} 1985, Lecture Notes in Computer Science", YEAR = 1985, VOLUME = 204, PAGES = "585-594", PUBLISHER = "Springer-Verlag"} @INPROCEEDINGS{Katsura:85, AUTHOR = "Shigetoshi Katsura", TITLE = "Application of the Formula Manipulating System to Statistical Mechanics", YEAR = 1985, BOOKTITLE = "Proc. of the Second {RIKEN} International Symposium on Symbolic and Algebraic Computation by Computers", PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "155-180"} @PHDTHESIS{Kauffman:73, AUTHOR = "S. K. Kauffman", TITLE = "Ortho-Positronium Annihilation: Steps Toward Computing the First Order Radiative Corrections", SCHOOL = "California Institute of Technology", YEAR = 1973} @INPROCEEDINGS{Kazasov:87, AUTHOR = "C. Kazasov", TITLE = "Laplace Transformations in {REDUCE} 3", BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "132-133", PUBLISHER = "Springer-Verlag"} @ARTICLE{Keady:85, AUTHOR = "Grant Keady", TITLE = "The Power Concavity of Solutions of Some Semilinear Elliptic {Boundary-Value} Problems", JOURNAL = "Bull. Austral. Math. Soc.", YEAR = 1985, VOLUME = 31, PAGES = "181-184"} @ARTICLE{Keener:83, AUTHOR = "James P. Keener", TITLE = "Oscillatory coexistence in the {chemostat:} a codimension two unfolding", JOURNAL = "{SIAM} J. Appl. Math.", YEAR = 1983, VOLUME = 43, NUMBER = 5, PAGES = "1005-1018"} @ARTICLE{Keener:85, AUTHOR = "James P. Keener", TITLE = "Oscillatory coexistence in a food chain model with competing predators", JOURNAL = "J. Math. Biology", YEAR = 1985, VOLUME = 22, PAGES = "123-135"} @ARTICLE{Keener:89, AUTHOR = "James P. Keener", TITLE = "Knotted scroll wave filaments in excitable media", JOURNAL = "Physica D 34", YEAR = 1989, PAGES = "378-390"} @ARTICLE{Keener:90, AUTHOR = "James P. Keener", TITLE = "Knotted vortex filaments in an ideal fluid", JOURNAL = "J. Fluid Mech.", YEAR = 1990, VOLUME = 211, PAGES = "629-651"} @ARTICLE{Kendall:88, AUTHOR = "W. S. Kendall", TITLE = "Symbolic Computation and the Diffusion of Shapes of Triads", JOURNAL = "Adv. Appl. Prob.", YEAR = 1988, VOLUME = 20, PAGES = "775-797"} @TECHREPORT{Kendall:89, AUTHOR = "W. S. Kendall", TITLE = "The Diffusion of {Euclidean} Shape", INSTITUTION = "University of Warwick, Dept. of Statistics", YEAR = 1989, TYPE = "Research Report", NUMBER = 161} @TECHREPORT{Kendall:89a, AUTHOR = "W. S. Kendall", TITLE = "Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence", INSTITUTION = "University of Warwick, Dept. of Statistics", YEAR = 1989, TYPE = "Research Report", NUMBER = 162} @ARTICLE{Kendall:90, AUTHOR = "W. S. Kendall", TITLE = "Computer Algebra and Stochastic Calculus", JOURNAL = "Notices A.M.S.", YEAR = 1990, VOLUME = 37, PAGES = "1254-1256"} @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{\"a}cklund 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.}} @TECHREPORT{Kobayashi:84, AUTHOR = "Hidestune Kobayashi", TITLE = "Weierstrass Points on a Curve, $X^{7}_{0}+X^{7}_{1} +X^{7}_{2}=0$", INSTITUTION = "Research Institute of Science and Technology, Nihon University", YEAR = 1984, TYPE = "Preprint", NUMBER = 28, MONTH = "March"} @INPROCEEDINGS{Kobayashi:88, AUTHOR = "H. Kobayashi and S. Moritsugu and R. W. Hogan", TITLE = "Solving Systems of Algebraic Equations", BOOKTITLE = "Proc. of {ISSAC} '88", PUBLISHER = "Springer-Verlag", YEAR = 1988, VOLUME = 358, PAGES = "139-149"} @INPROCEEDINGS{Kodaira:85, AUTHOR = "Hiroshi Kodaira and Hiroshi Toshima", TITLE = "Gini Coefficient of Wealth in Life Cycle Model", YEAR = 1985, BOOKTITLE = "Proc. of the Second {RIKEN} International Symposium on Symbolic and Algebraic Computation by Computers", PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "119-151"} @ARTICLE{Koh:82, AUTHOR = "I. G. Koh and Y. D. Kim and Y. J. Park and C. H. Kim and Y. S. Kim", TITLE = "Complete Set of {SU(5)} Monopole Solution", JOURNAL = "J. Math. Phys.", YEAR = 1982, VOLUME = 23, PAGES = "1210-1212", COMMENT = {Calculation checked by {REDUCE} after hand calculation.}} @ARTICLE{Koelbig:81, AUTHOR = "K. S. K{\"o}lbig and F. Schwarz", TITLE = "On Positive Function Series", JOURNAL = "Computing", YEAR = 1981, VOLUME = 27, PAGES = "319-337", COMMENT = {{REDUCE} for algebra on constraints on a functional form and Jacobi polynomials.}} @ARTICLE{Koelbig:81b, AUTHOR = "K. S. K{\"o}lbig", TITLE = "A Program for Computing the Conical functions of the First Kind ${P}^{m}_{-1/2+i\tau}(x)$ for $m = 0$ and $m = 1$", JOURNAL = "Comp. Phys. Comm.", YEAR = 1981, VOLUME = 23, PAGES = "51-61", PUBLISHER = "North Holland Publishing Company"} @ARTICLE{Koelbig:82, AUTHOR = "K. S. K{\"o}lbig", TITLE = "Closed Expressions for $\int_{0}^{1} t^{-1} $log$^{n-1}t\, $log$^{p}(1 - t) dt$", JOURNAL = "Math. Comp.", YEAR = 1982, VOLUME = 39, NUMBER = 160, PAGES = "647-654", MONTH = "October", COMMENT = {Closed form of integral for easy calculation. Used {REDUCE} for manipulations. This class includes dilog, Spence functions etc. Remarks that {REDUCE} is easier than {FORTRAN}.}} @ARTICLE{Koelbig:82a, AUTHOR = "K. S. K{\"o}lbig and W. R{\"u}hl", TITLE = "Complex Zeros of the Partition Function for Two-Dimensional {U(N)} Lattice Gauge Theories", JOURNAL = "Z. Phys. C - Particles and Fields", YEAR = 1982, VOLUME = 12, PAGES = "135-143", COMMENT = {The Complex Zeros of the Partition Function for Two-Dimensional U(N) Lattice Gauge Theories.}} @ARTICLE{Koelbig:83, AUTHOR = "K. S. K{\"o}lbig", TITLE = "On the Integral $\int_{0}^{\pi/2} $log$^{n}$cos$\,x\,$ log$^{p}$sin$\,x\,dx$", JOURNAL = "Math. Comp.", MONTH = "April", YEAR = 1983, VOLUME = 40, PAGES = "565-570", COMMENT = {A formula is derived for the integral in the title which allows easy evaluation by formula manipulation on a computer.}} @ARTICLE{Koelbig:83a, AUTHOR = "K. S. K{\"o}lbig", TITLE = "On the Integral $\int_{0}^{\infty} e^{-\mu t} t^{\nu -1} $log$^{m} t dt$", JOURNAL = "Math. Comp.", YEAR = 1983, VOLUME = 41, PAGES = "171-182", COMMENT = {A recurrence relation is given for the integral in the title.}} @ARTICLE{Koelbig:84, AUTHOR = "K. S. K{\"o}lbig and B. Schorr", TITLE = "Asymptotic Expansions for the {Landau} Density and Distribution Function", JOURNAL = "Comp. Phys. Comm.", YEAR = 1984, VOLUME = 32, PAGES = "121-131"} @ARTICLE{Koelbig:84a, AUTHOR = "K. S. K{\"o}lbig and B. Schorr", TITLE = "A Program Package for the {Landau} Distribution", JOURNAL = "Comp. Phys. Comm.", YEAR = 1984, VOLUME = 31, PAGES = "97-111"} @TECHREPORT{Koelbig:84b, AUTHOR = "K. S. K{\"o}lbig", TITLE = "Some Problems Involving Special Functions Arising From Physics at {CERN}", INSTITUTION = "CERN, Data Handling Division", YEAR = 1984, NUMBER = "DD 84-14", MONTH = "September"} @TECHREPORT{Koelbig:85, AUTHOR = "K. S. K{\"o}lbig", TITLE = "On the Integral $\int_{0}^{1} x^{\nu -1} (1 - x)^{-\lambda} $ln$^{m} x dx$", INSTITUTION = "CERN, Data Handling Division", YEAR = 1985, NUMBER = "DD/85/18", MONTH = "September"} @ARTICLE{Koelbig:85a, AUTHOR = "K. S. K{\"o}lbig", TITLE = "Explicit Evaluation of Certain Definite Integrals Involving Powers of Logarithms", JOURNAL = "J. Symbolic Computation", YEAR = 1985, VOLUME = 1, NUMBER = 1, PAGES = "109-114", MONTH = "March"} @ARTICLE{Koelbig:86, AUTHOR = "K. S. K{\"o}lbig", TITLE = "On the Integral $\int_{0}^{\infty} x^{\nu -1} (1 + \beta x)^{-\lambda} $ln$^{m} x dx$", JOURNAL = "Journal of Comp. and Appl. Math.", YEAR = 1986, VOLUME = 14, PAGES = "319-344"} @ARTICLE{Kolar:90, AUTHOR = "M. Kol{\'a}\u{r} and M. K. Ali", TITLE = "Trace maps associated with general {two-letter} substitution rules", JOURNAL = "Physical Review {A}", YEAR = 1990, VOLUME = 42, NUMBER = 12, PAGES = "7112-7124", MONTH = "December", ABSTRACT = {Spectral properties, as determined by trace maps, of the one-dimensional chains (layered structures) constructed according to general two-letter substitution rules are investigated. In all trace maps thus obtained an important role is played by the quantity $I=x^{2}+y^{2}+z^{2}-xyz-4$ However, only a very small fraction of all such trace maps are similar to the Fibonacci golden-mean trace map in that I is their invariant. In addition to the known case of the precious-mean lattices (precious means are ratios of the form $^{1}_{2}[m+(m^{2}+4)^{1/2}]$, m being any positive integer; m=1 gives the golden mean), we have identified two new large clases of substitution rules that give trace maps with invariant I. One of them is a superset of the precious-mean lattices. All other cases represent a vast assortment of different trace maps (and thus the potential for various hitherto unexplored spectral properties) with a unifying feature that the set I=0 plays the role of an attractor in the trace space. In most (but not all) cases, two chains with identical trace maps (and thus identical spectra) are locally isomorphic. Generally, local isomorphism equivalence classes seem to be subsets of identical spectrum equivalence classes.}} @TECHREPORT{Kornyak:87, AUTHOR = "V. V. Kornyak and R. N. Fedorova", TITLE = "A {REDUCE} Program to Calculate Determining Equations of {Lie-Baecklund} Symmetries of Differential Equations", INSTITUTION = "J.I.N.R., Dubna", YEAR = 1987, NUMBER = "P11-87-19"} @ARTICLE{Kotorynski:86, AUTHOR = "W. P. Kotorynski", TITLE = "Steady Laminar Flow Through a Twisted Pipe of Elliptical Cross-Section", JOURNAL = "Computers and Fluids", YEAR = 1986, VOLUME = 14, PAGES = "433-444", COMMENT = {Used {REDUCE} to perform the calculations for steady flow through twisted pipes, but who also remarked that the techniques he developed for this problem are applicable to a variety of other pipe flow tasks.}} @ARTICLE{Krack:82, AUTHOR = "K. Krack", TITLE = "Rechnerunterst{\"u}tzte {Entwicklung} der {Mittelbreitenformeln} und Absch{\"a}tzung ihrer ellipsoidischen {Anteile} zur L{\"o}sung der zweiten geod{\"a}tischen {Hauptaufgabe} auf dem {Rotationsellipsoid}", JOURNAL = "Z. Vermessungswes.", YEAR = 1982, VOLUME = 107, PAGES = "502-513", COMMENT = {(In German) Used {REDUCE} to develop the Gauss mid-latitude formulae for inverse positioning to the 7th order (Geodesy).}} @PHDTHESIS{Kraus:73, AUTHOR = "J. Kraus", TITLE = "Delbr{\"u}ckstreuung und Pr{\"u}fung der Quantenelektrodynamik", SCHOOL = "Ludwig-Maximilians-Universit{\"a}t zu M{\"u}nchen", YEAR = 1973} @ARTICLE{Kredel:88, AUTHOR = "Heinz Kredel", TITLE = "Admissible termorderings used in Computer Algebra Systems", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1988, VOLUME = 22, NUMBER = 1, PAGES = "28-31", MONTH = "January"} @ARTICLE{Kruse:83, AUTHOR = "Hans-Guenther Kruse and Karin Ohlsen", TITLE = "About the Realization of an Extended, but Really Interactive {REDUCE} by Integration of a Small Editing and Executing System", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "21-25", MONTH = "February"} @TECHREPORT{Kryukov, AUTHOR = "A. P. Kryukov and A. Ya. Rodionov", TITLE = "Usage of {REDUCE} for Computations of Group-Theoretical Weight of {Feynman} Diagrams in Non-Abelian Gauge Theories", INSTITUTION = "Institute of Nuclear Physics, Moscow, USSR", YEAR = "TBD"} @ARTICLE{Kryukov:84, AUTHOR = "A. P. Kryukov", TITLE = "An Antitranslator of the {RLISP} Language", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1984, VOLUME = 18, NUMBER = 3, PAGES = "12-15", MONTH = "August"} @ARTICLE{Kryukov:85, AUTHOR = "A. P. Kryukov and A. Ya. Rodionov", TITLE = "Dynamic-Debugging System for the {REDUCE} Programs", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1985, VOLUME = 19, NUMBER = 2, PAGES = "34-37", MONTH = "May"} @ARTICLE{Kryukov:85a, AUTHOR = "A. P. Kryukov and A. Ya. Rodionov", TITLE = "Interactive {REDUCE}", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1985, VOLUME = 19, NUMBER = 3, PAGES = "43-45", MONTH = "August"} @TECHREPORT{Kryukov:87, AUTHOR = "A. P. Kryukov and A. Ya. Rodionov and V. A. Rostovtsev", TITLE = "Pattern Compilation in {REDUCE}", INSTITUTION = "J.I.N.R., Dubna", YEAR = 1987, NUMBER = "P11-87-302"} @INPROCEEDINGS{Kryukov:87a, AUTHOR = "A. P. Kryukov and A. Ya. Rodionov", TITLE = "{CTS} - Algebraic Debugging System for {REDUCE} Programs", BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "233-243", PUBLISHER = "Springer-Verlag"} @TECHREPORT{Kryukov:88, AUTHOR = "A. P. Kryukov and A. Ya. Rodionov and V. A. Rostovtsev", TITLE = "New Programming Tools for Computing Substitution Rules in {REDUCE} System", INSTITUTION = "J.I.N.R., Dubna", YEAR = 1988, NUMBER = "P11-88-402", COMMENT = {New programming tools allowing to compile patterns in {REDUCE} system are described. A guide for using these tools and examples of their working are presented.}} @ARTICLE{Kryukov:88a, AUTHOR = "A. P. Kryukov and A. Ya. Rodionov", TITLE = "Program {``COLOR''} for Computing the Group-Theoretic Weight of {Feynman} Diagrams in {Non-Abelian} Gauge Theories", JOURNAL = "Comp. Phys. Commun.", YEAR = 1988, VOLUME = 48, NUMBER = 2, PAGES = "327-334", MONTH = "February"} @TECHREPORT{Kryukov:88b, AUTHOR = "A. P. Kryukov and D. A. Slavnov", TITLE = "The Role of the $gg \rightarrow c\overline{c}g$ Process in the Cross Section of Production of Charmed Particles (in {Russian})", INSTITUTION = "Moscow State University", YEAR = 1988, NUMBER = "88-49/70", TYPE = "Preprint"} @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 eler and Neil Soiffer", TITLE = "An Interactive Graphical Interface for {REDUCE}", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1985, VOLUME = 19, NUMBER = 3, PAGES = "17-23", MONTH = "August"} @ARTICLE{Lepage:83, AUTHOR = "G. P. Lepage and P. B. Mackenzie and K. H. Streng and P. M. Zernas", TITLE = "Multiphoton Decays of Positronium", JOURNAL = "Phys. Rev. A", YEAR = 1983, VOLUME = 28, PAGES = "3090-3091", COMMENT = {Same as Adkins and Brown (1983) but independent of it.}} @INPROCEEDINGS{Levi:70, AUTHOR = "I. Levi and N. Hoff", TITLE = "Non-Symmetric Creep Buckling of Circular Cylindrical Shells in Axial Compression", YEAR = 1970, MONTH = "August", BOOKTITLE = "Proc. Intern. Symp. in Creep Effect in Structures, Gotenburg, Sweden"} @INPROCEEDINGS{Levi:71, AUTHOR = "I. M. Levi", TITLE = "Symbolic Algebra by Computer - Applications to Structural Mechanics", YEAR = 1971, MONTH = "April", BOOKTITLE = "{AIAA/ASME} 12th Structures, Structural Dynamics and Materials Conference, Anaheim, California"} @ARTICLE{Liebermann:75, AUTHOR = "R. Liebermann", TITLE = "Traces of High Energy Processes in Strong Magnetic Fields", JOURNAL = "J. Comp. Phys.", YEAR = 1975} @ARTICLE{Liska:84, AUTHOR = "R. Liska", TITLE = "Program for Stability and Accuracy Analysis of Finite Difference Methods", JOURNAL = "Comp. Phys. Comm.", YEAR = 1984, VOLUME = 34, PAGES = "175-186"} @INPROCEEDINGS{Liska:87, AUTHOR = "R. Liska and D. Drska", TITLE = "Evaluation of Plasma Fluid Equations Collision Integrals Using {REDUCE}", BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = 178, PUBLISHER = "Springer-Verlag"} @InProceedings{Liska90, author = "R. Liska and L. Drska", title = "{FIDE}: A {REDUCE} package for automation of {FI}nite difference method for solving {pDE}", booktitle = "Proceedings of the International Symposium on Symbolic and Algebraic Computation", year = "1990", editor = "S. Watanabe and Morio Nagata", pages = "169-176", organization = "ACM", publisher = "Addison-Wesley" } @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.}} % REDUCE BIBLIOGRAPHY % Part 3: M-Z % Copyright (c) 1990 The RAND Corporation. 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. @BOOK{MacCallum:86, AUTHOR = "M. A. H. MacCallum", TITLE = "Dynamical Spacetimes and Numerical Relativity", PUBLISHER = "Cambridge UP", 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"} @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{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"} @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"} @BOOK{REDUCE:84, AUTHOR = "J. D. McCrea", TITLE = "The Use of {REDUCE} in Finding Exact Solutions of the Quadratic Poincar{\'e} Gauge Field Equations, in 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{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.}} @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"} @INPROCEEDINGS{Moritsugu:85, AUTHOR = "S. Moritsugu and N. Inada and E. Goto", TITLE = "Symbolic {Newton} Iteration and its Application", YEAR = 1985, BOOKTITLE = "Proc. of the Second {RIKEN} International Symposium on Symbolic and Algebraic Computation by Computers", PUBLISHER = "World Scientific", ADDRESS = "Singapore", PAGES = "105-117"} @TECHREPORT{Moritsugu:88, AUTHOR = "S. Moritsugu and E. Goto", TITLE = "A Proposal for Improvement of Facilities of {REDUCE}", INSTITUTION = "Department of Information Science, University of Tokyo, Japan", YEAR = 1988, MONTH = "December"} @ARTICLE{Moritsugu:89, AUTHOR = "Shuichi Moritsugu and Eiichi Goto", TITLE = "A Note on the Preconditioning for Factorization of Homogeneous Polynomials", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1989, VOLUME = 23, NUMBER = 1, PAGES = "9-12", MONTH = "January"} @ARTICLE{Moritsugu:89a, AUTHOR = "Shuichi Moritsugu and Makoto Matsumoto", TITLE = "A Note on the Numerical Evaluation of Arctangent Function", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1989, VOLUME = 23, NUMBER = 3, PAGES = "8-12", MONTH = "July"} @ARTICLE{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{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"} @TECHREPORT{Neun:88, AUTHOR = "Winfried Neun and Herbert Melenk", TITLE = "Implementation of the {LISP}-Arbitrary Precision Arithmetic for a Vector Processor", INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik, Berlin", YEAR = 1988, TYPE = "Preprint", NUMBER = "SC 88-1", MONTH = "January"} @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"} @INPROCEEDINGS{Neun:89a, AUTHOR = "Herbert Melenk and Winfried Neun", TITLE = "Parallel Polynomial Operations in the Large Buchberger Algorithm", BOOKTITLE = "Computer Algebra and Parallelism", EDITOR = "J. Della-Dora and J. Fitch", PAGES = "143-158", YEAR = 1989, PUBLISHER = "Academic Press"} @ARTICLE{Neutsch:85, AUTHOR = "W. Neutsch and E. Schr{\"u}fer and A. Jessner", TITLE = "Note on Efficient Integration on the Hypersphere", JOURNAL = "J. Comp. Phys.", YEAR = 1985, VOLUME = 59, PAGES = "167-175", COMMENT = {{REDUCE} used for integration on 4-D hypersphere. {REDUCE} use rather small.}} @ARTICLE{Neutsch:86, AUTHOR = "W. Neutsch and E. Schr{\"u}fer", TITLE = "Simple Integrals for Solving {Kepler}'s Equation", JOURNAL = "Astrophysics and Space Science", YEAR = 1986, VOLUME = 125, PAGES = "77-83", COMMENT = {Uses {REDUCE} to verify calculations to give integral form which is numerically good, involving only rationals and exponentials.}} @ARTICLE{Ng:89, AUTHOR = "Tze Beng Ng", TITLE = "Computation of the Cohomology of ${B\hat{S}O_{n}<16>}$ for $23 \leq n \leq 26$ using {REDUCE}", JOURNAL = "J. Symbolic Computation", YEAR = 1989, VOLUME = 7, NUMBER = 1, PAGES = "93-99", MONTH = "January"} @ARTICLE{Niki:84, AUTHOR = "Naoto Niki and Sadanori Konishi", TITLE = "Higher Order Asymptotic Expansions for the Distribution of the Sample Correlation Coefficient", JOURNAL = "Comm. Statist.-Simula. Comp.", YEAR = 1984, VOLUME = 13, NUMBER = 2, PAGES = "169-182"} @TECHREPORT{Nikityuk:87, AUTHOR = "N. M. Nikityuk", TITLE = "Some Questions of Using Coding Theory and Analytical Calculation Methods on Computers", INSTITUTION = "J.I.N.R., Dubna", YEAR = 1987, NUMBER = "E11-87-10"} @ARTICLE{Noor:79, AUTHOR = "A. K. Noor and C. M. Andersen", TITLE = "Computerized Symbolic Manipulation in Structural Mechanics - Progress and Potential", JOURNAL = "Computers and Structures", YEAR = 1979, VOLUME = 10, PAGES = "95-118", COMMENT = {Concentrates on {MACSYMA} but mentions {FORMAC} and {REDUCE} as also having been used in structures. Mainly finite elements. Includes program and output.}} @INPROCEEDINGS{Norman:77, AUTHOR = "A. C. Norman and P. M. A. Moore", TITLE = "Implementing the New {Risch} Integration Algorithm", YEAR = 1977, MONTH = "March", BOOKTITLE = "Proc. of the Fourth Colloquium on Advanced Comp. Methods in Theor. Phys., St. Maximin, France"} @ARTICLE{Norman:78, AUTHOR = "Arthur Norman", TITLE = "Towards a {REDUCE} solution to {SIGSAM} Problem 7", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1978, VOLUME = 12, NUMBER = 4, PAGES = "14-18", MONTH = "November"} @INPROCEEDINGS{Norman:79, AUTHOR = "A. C. Norman and J. H. Davenport", TITLE = "Symbolic Integration - The Dust Settles?", BOOKTITLE = "Proc. {EUROSAM} 1979, Lecture Notes in Computer Science", YEAR = 1979, VOLUME = 72, PAGES = "398-407", PUBLISHER = "Springer-Verlag"} @ARTICLE{Norman:83, AUTHOR = "Arthur C. Norman and Paul S. Wang", TITLE = "A Comparison of the {Vaxima} and {REDUCE}", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "28-30", MONTH = "February"} @InProceedings{Norman90, author = "A. C. Norman", title = "A Critical-Pair/Completion based Integration Algorithm", booktitle = "Proceedings of the International Symposium on Symbolic and Algebraic Computation", year = "1990", editor = "S. Watanabe and Morio Nagata", pages = "201-205", organization = "ACM", publisher = "Addison-Wesley" } @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 Arbitary 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.}} @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{Pattnaik:83, AUTHOR = "P. C. Pattnaik and G. Fletcher and J. L. Fry", TITLE = "Improved Numerical Stability for Norm-Conserving ion-{Ure} Pseudopotentials", JOURNAL = "Phys. Rev. B", YEAR = 1983, VOLUME = 28, NUMBER = 6, PAGES = "3364-3365", COMMENT = {{REDUCE} and {FORTRAN}; inverting a matrix algebraically would be more accurate than a numerical inverse, and used {REDUCE} for this part of their work.}} @ARTICLE{Pearce:81, AUTHOR = "P. D. Pearce and R. J. Hicks", TITLE = "The Application of Algebraic Optimisation Techniques to Algebraic Mode Programs for {REDUCE}", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1981, VOLUME = 15, NUMBER = 4, PAGES = "15-22", MONTH = "November"} @ARTICLE{Pearce:83, AUTHOR = "P. D. Pearce and R. J. Hicks", TITLE = "Data Structures and Execution Times of Algebraic Mode Programs for {REDUCE}", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1983, VOLUME = 17, NUMBER = 1, PAGES = "31-37", MONTH = "February"} @ARTICLE{Perjes:84, AUTHOR = "Z. Perj{\'e}s", TITLE = "Stationary Vacuum Fields with a Conformally Flat Three-Space. {III}. {Complete} Solution", JOURNAL = "General Relativity and Gravitation", YEAR = 1984, VOLUME = 18, PAGES = "531-547", COMMENT = {{REDUCE} used to perform the necessary calculations.}} @ARTICLE{Perjes:84a, AUTHOR = "Z. Perj{\'e}s and B. Luk{\'a}cs and A. Sebesty{\'e}n and A. Valentini", TITLE = "Solution of the Stationary Vacuum Equations of Relativity for Conformally Flat 3-Spaces", JOURNAL = "Phys. Lett.", YEAR = 1984, VOLUME = {100A}, NUMBER = 8, PAGES = "405-406", MONTH = "February"} @TECHREPORT{Perjes:84b, AUTHOR = "Z. Perj{\'e}s", TITLE = "Improved Characterization of the {Kerr} Metric", INSTITUTION = "Hungarian Academy of Sciences, Central Research Institute for Physics", YEAR = 1984, NUMBER = "KFKI-1984-115"} @TECHREPORT{Perjes:84c, AUTHOR = "Z. Perj{\'e}s", TITLE= "Stationary Vacuum Fields with a Conformally Flat Three-Space. {IV}. {Complete} Solution", INSTITUTE = "Institute for Nuclear Study, University of Tokyo", YEAR = 1984, NUMBER = "INS-REP.-487", MONTH = "January"} @TECHREPORT{Perjes:86, AUTHOR = "Z. Perj{\'e}s", TITLE = "Ernst Coordinates", INSTITUTION = "Hungarian Academy of Sciences, Central Research Institute for Physics", YEAR = 1986, TYPE = "Preprint", NUMBER = "KFKI-1986-33/B"} , @ARTICLE{Perjes:86a, AUTHOR = "Z. Perj{\'e}s", TITLE = "Stationary Vacuum Fields with a Conformally Flat Three-Space. {II}. {Proof} of Axial Symmetry", JOURNAL = "General Relativity and Gravitation", YEAR = 1986, VOLUME = 18, NUMBER = 5, PAGES = "511-530", MONTH = "May"} @ARTICLE{Perjes:88, AUTHOR = "Z. Perj{\'e}s", TITLE = "Approaches to Axisymmetry by Man and Machine", BOOK = "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} @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.}} @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"} @BOOK{Rogers:89, AUTHOR = "C. Rogers and W. F. Ames", TITLE = "Nonlinear Boundary Value Problems in Science and Engineering", PUBLISHER = "Academic Press, Inc.", YEAR = 1989} @ARTICLE{Roque:88, AUTHOR = "Waldir L. Roque and Renato P. dos Santos", TITLE = "Computa\c{c}\~{a}o alg\'{e}brica: ``um assistente matem\~{a}tico''", JOURNAL = "Ci\^{e}ncia e Cultura", YEAR = 1988, VOLUME = 40, NUMBER = 9, PAGES = "843-852", MONTH = "September", ABSTRACT = {In this paper we discuss in a simple and informative way the theme ``algebraic computing'' in an attempt to encourage the Brasilian scientific community to make use of this new tool{\ldots}. Many algebraic computing systems have been developed in a variety of research fields. Some of these systems, their main characteristics and applications will be discussed.}, COMMENT = {In Portuguese}} @ARTICLE{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{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"} @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{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"} @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}.}} @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"} @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"} @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"} @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 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{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.}} @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"} @ARTICLE{vandenHeuvel:86, AUTHOR = "Pim van den Heuvel", TITLE = "Adding Statements to {REDUCE}", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1986, VOLUME = 20, NUMBER = "1 and 2", PAGES = "8-14", MONTH = "February and May"} @TECHREPORT{vandenHeuvel:86a, AUTHOR = "Pim van den Heuvel", TITLE = "Some Experiments in {REDUCE} Related to the Calculation of {Groebner} Bases", INSTITUTION = "Department of Computer Science, Twente University of Technology, The Netherlands", YEAR = 1986, MONTH = "June"} @INPROCEEDINGS{vandenHeuvel:87, AUTHOR = "P. van den Heuvel and J. A. van Hulzen and V. V. Goldman", TITLE = "Automatic Generation of {FORTRAN}-Coded {Jacobians} and {Hessians}", BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "120-131", PUBLISHER = "Springer-Verlag"} @ARTICLE{vandenHeuvel:87a, AUTHOR = "P. van den Heuvel and B. J. A. Hulshof and J. A. van Hulzen", TITLE = "Some Simple {Pretty-Print} Facilities for {REDUCE}", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1987, VOLUME = 21, NUMBER = 1, PAGES = "14-17", MONTH = "February"} @TECHREPORT{vanHeerwaarden, AUTHOR = "M. C. van Heerwaarden and J. A. van Hulzen", TITLE = "Pretty Print Facilities for {REDUCE}", INSTITUTION = "Department of Computer Science, University of Twente, The Netherlands", YEAR = 1988, TYPE = "Memorandum", NUMBER = "INF-88-36", MONTH = "August"} @ARTICLE{vanHulzen:80, AUTHOR = "J. A. van Hulzen", TITLE = "Computational Problems in Producing {Taylor} Coefficients for the Rotating Disk Problem", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1980, VOLUME = 14, NUMBER = 2, PAGES = "36-49", MONTH = "May"} @TECHREPORT{vanHulzen:81, AUTHOR = "J. A. van Hulzen", TITLE = "Breuer's Grow Factor Algorithm in Computer Algebra", INSTITUTION = "Department of Applied Mathematics, Twente University of Technology, The Netherlands", YEAR = 1981, TYPE = "Memorandum", NUMBER = 332, MONTH = "April", COMMENT = {A shorter version appears in: Proceedings SYMSAC 81 (Paul S. Wang, ed.) ACM, August 1981.}} @ARTICLE{vanHulzen:82, AUTHOR = "J. A. van Hulzen and B. J. A. Hulshof", TITLE = "An Expression Analysis Package for {REDUCE}", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1982, VOLUME = 16, NUMBER = 4, PAGES = "32-44", MONTH = "November"} @INPROCEEDINGS{vanHulzen:82a, AUTHOR = "J. A. van Hulzen", TITLE = "Computer Algebra Systems Viewed by a Notorious User", BOOKTITLE = "Proc. {EUROCAM} 1982, Lecture Notes in Computer Science", YEAR = 1982, VOLUME = 144, PAGES = "166-180"} @INCOLLECTION{vanHulzen:83, AUTHOR = "J. A. van Hulzen and J. Calmet", TITLE = "Computer Algebra Systems", EDITOR = "B. Buchberger and G. E. Collins and R. Loos and R. Albrecht", BOOKTITLE = "Computer Algebra and Symbolic and Algebraic Computation", EDITION = "2nd", PUBLISHER = "Springer-Verlag", YEAR = 1983} @INPROCEEDINGS{vanHulzen:83a, AUTHOR = "J. A. van Hulzen", TITLE = "Code Optimization of Multivariate Polynomial Schemes: A Pragmatic Approach", BOOKTITLE = "Proc. {EUROCAL} 1983, Lecture Notes in Computer Science", YEAR = 1983, VOLUME = 162, PAGES = "286-300", PUBLISHER = "Springer-Verlag"} @INPROCEEDINGS{vanHulzen:87, AUTHOR = "J. A. van Hulzen", TITLE = "Program Generation Aspects of the Symbolic-Numeric Interface", BOOKTITLE = "Proc. Third Intern. Conf. on Computer Algebra and its applications in Theor. Phys, 1985", YEAR = 1987, PAGES = "104-113", PUBLISHER = "{J.I.N.R., Dubna, USSR}"} @TECHREPORT{vanHulzen:88, AUTHOR = "J. A. van Hulzen", TITLE = "Formule Manipulatie m.b.v. {REDUCE} (in {Dutch})", INSTITUTION = "Department of Computer Science, Twente University of Technology, The Netherlands", YEAR = 1988, MONTH = "October"} @INPROCEEDINGS{vanHulzen:89, AUTHOR = "J. A. van Hulzen and B. J. A. Hulshof and B. L. Gates and M. C. Van Heerwaarden", TITLE = "A Code Optimization Package for {REDUCE}", BOOKTITLE = "Proc. of {ISSAC} '89", PUBLISHER = "{ACM} Press, New York", YEAR = 1989, PAGES = "163-170", COMMENT = {Lecture Notes.}} @TECHREPORT{vanHulzen:89a, AUTHOR = "J. A. van Hulzen", TITLE = "Computer Algebra and Numerical Mathematics: The Odd Couple?", INSTITUTION = "Department of Computer Science, Twente University of Technology, The Netherlands", NUMBER = "Informatica 89-40", YEAR = 1989, MONTH = "June"} @TECHREPORT{VanProeyan:76, AUTHOR = "A. Van Proeyen", TITLE = "Quantum Gravity Corrections on the Anomalous Magnetic and Quadrupole Moments of a Spin-1 Particle", INSTITUTION = "Instituut voor Theor. Fys., Leuven", YEAR = 1976, MONTH = "October"} @TECHREPORT{VanProeyan:79, AUTHOR = "A. Van Proeyan", TITLE = "Gravitational Divergences of the Electromagnetic Interactions of Massive Vectorparticles", INSTITUTION = "Universiteit Leuven", YEAR = 1979, TYPE = "Preprint", NUMBER = "KUL-TF-79/032", MONTH = "October", ABSTRACT = {In a search for the explanation of the finite quantum gravity corrections to anomalous moments we examined a spontaneous broken 0(3) model with Yang-Mills particles and Higgs scalars coupled to gravitons.}} @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{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{Wassam:87, AUTHOR = "W. A. {Wassam, Jr.} and Go. Torres-Vega", TITLE = "Dual {Lanczos} Transformation Theory: Closed Set of Algebraic Equations Connecting {Lanczos} Parameters with Moments in Moment Expansions of Time-Dependent Quantities", JOURNAL = "Chemical Phys. Lett.", YEAR = 1987, VOLUME = 134, NUMBER = 4, PAGES = "355-360", COMMENT = {"The utility of this set of equations is illustrated by using them with the aid of symbolic manipulation on a computer to construct a previously unknown exact continued fraction for the spectral density of the incoherent scattering function{\ldots}" The system used is {REDUCE} on a Burroughs. Appear enthusiastic about the possibilities for computer algebra in related fields.}} @ARTICLE{Wassam:87a, AUTHOR = "W. A. {Wassam, Jr.} and Go. Torres-Vega and J. Neito-Frausto", TITLE = "Dual {Lanczos} Transformation Theory: Exact Continued Fraction Expression for Resonant $\gamma$-ray Absorption Spectrum of a Harmonically Bound Atom Executing Classical Motion Described by {Smoluchowski} Dynamics", JOURNAL = "Chemical Phys. Lett.", YEAR = 1987, VOLUME = 136, NUMBER = 1, PAGES = "26-30", COMMENT = {"{\ldots}with the aid of symbolic manipulation techniques, we construct a previously unknown exact continued fraction for the resonance $\gamma$-ray absorption spectrum{\dots}" The system used is {REDUCE} on a Burroughs.}} @TECHREPORT{Watanabe:85, AUTHOR = "Yoichi Watanabe", TITLE = "Symbolic Manipulation of Structure Functions in Availability Analysis", INSTITUTION = "Fusion Technology Institute, University of Wisconsin, Madison, Wisconsin", YEAR = 1985, NUMBER = "UWFDM-658", MONTH = "November"} @ARTICLE{Watanabe:76, AUTHOR = "Shunro Watanabe", TITLE = "Formula Manipulations Solving Linear Ordinary Differential Equations {II}", JOURNAL = "Publications of the Research Institute for Mathematical Sciences, Kyoto University", YEAR = 1976, VOLUME = 11, NUMBER = 2, PAGES = "297-337"} @ARTICLE{Watanabe:79, AUTHOR = "Shunro Watanabe", TITLE = "A Verification for Non-existence of Movable Branch Points of Six Painlev{\'e} Transcendents by Formula Manipulations", JOURNAL = "Tokyo Journal of Mathematics", YEAR = 1979, VOLUME = 2, NUMBER = 2, PAGES = "285-291"} @ARTICLE{Weber:79, AUTHOR = "Lawrence A. Weber and Gerhard Rayna", TITLE = "Problem \#11 Solved in {REDUCE:} A Case Study in Program Translation", JOURNAL = "{SIGSAM} Bulletin", YEAR = 1979, VOLUME = 13, NUMBER = 4, PAGES = "21-24", MONTH = "November"} @ARTICLE{Wehner:86, AUTHOR = "M. F. Wehner and W. G. Wolfer", TITLE = "The Pressure of a Hard Sphere Fluid on a Curved Surface", JOURNAL = "J. Statistical Phys.", YEAR = 1986, VOLUME = 42, PAGES = "509-521", COMMENT = {Integral equation approach and perturbation expansions in {REDUCE}. "Therefore, in order to avoid errors, the integrations have been done in closed form with the algebraic manipulation routine {REDUCE}."}} @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.}} @ARTICLE{Wood:89, AUTHOR = "John C. Wood", TITLE = "Harmonic Two Spheres in the Unitary Group", YEAR = 1989, JOURNAL = "Proc. London Math. Soc.", VOLUME = 3, NUMBER = 58, PAGES = "608-624"} @TECHREPORT{Wright:84, AUTHOR = "F. J. Wright and G. Dangelmayr", TITLE = "Explicit Iterative Algorithms to Reduce a Univariate Catastrophe to Normal Form", INSTITUTION = "Universit{\"a}t T{\"u}bingen", YEAR = 1984} @TECHREPORT{Wulkow:90, AUTHOR = "Michael Wulkow and Peter Deuflhard", TITLE = "Towards an efficient computational treatment of heterogeneous polymer reactions", INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin", YEAR = 1990, TYPE = "Preprint", NUMBER = "SC 90-1", MONTH = "January"} @INPROCEEDINGS{Yamamoto:87, AUTHOR = "T. Yamamoto and Y. Aoki", TITLE = "{REDUCE} 3.2 on {iAPX 86/286}-based Personal Computers", BOOKTITLE = "Proc. {EUROCAL} '87, Lecture Notes in Computer Science", YEAR = 1987, VOLUME = 378, PAGES = "134-135", PUBLISHER = "Springer-Verlag"} @ARTICLE{Yannouleas:88, AUTHOR = "C. Yannouleas and J. M. Pacheco", TITLE = "An Algebraic Program for the States Associated with the ${U(5)} \supset {O(5)} \supset {O(3)}$ Chain of Groups", JOURNAL = "Comp. Phys. Comm.", YEAR = 1988, VOLUME = 52, NUMBER = 1, PAGES = "85-92", MONTH = "December"} @ARTICLE{Yannouleas:89, AUTHOR = "C. Yannouleas and J. M. Pacheco", TITLE = "Algebraic Manipulation of the States Associated with the ${U(5)} \supset {O(5)} \supset {O(3)}$ Chain of {groups:} Orthonormalization and Matrix Elements", JOURNAL = "Comp. Phys. Comm.", YEAR = 1989, VOLUME = 54, NUMBER = "2 and 3", PAGES = "315-328", MONTH = "June and July"} @ARTICLE{Zacrep:75, AUTHOR = "Douglas Zacrep and Bing-Lin Young", TITLE = "Trace and {Ward-Takahashi} Identity Anomalies in an {SU}(3) Current Model with Energy-Momentum Tensor", JOURNAL = "Phys. Rev. D", YEAR = 1975, VOLUME = 12, PAGES = "513-522"} @ARTICLE{Zahalak:87, AUTHOR = "G. I. Zahalak and P. R. Rao and S. P. Sutera", TITLE = "Large Deformations of a Cylindrical Liquid-Filled Membrane by a Viscous Shear Flow", JOURNAL = "J. Fluid Mech.", YEAR = 1987, VOLUME = 179, PAGES = "283-305", COMMENT = {Draws attention to the use of classical perturbation techniques combined with computer algebra as an alternative to numerical calculation.}} @ARTICLE{Zeng:84, AUTHOR = "Wan-zhen Zeng and Bail-lin Hao", TITLE = "Scaling Property of Period-n-Tupling Sequences in One-Dimensional Mappings", JOURNAL = "Commun. in Theor. Phys., Beijing, China", YEAR = 1984, VOLUME = 3, NUMBER = 3, PAGES = "283-295"} @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.}}