%                          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 =        aug # " and " # nov,
}

@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",
}

%"For an accelerator lattice..."  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",
  abstract =     "{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",
  abstract =     "{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",
}

%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.

@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",
}

%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",
}

%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 =        feb,
  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",
}

%"Numerical modeling of the solar and lunar semidiurnal atmospheric
%tides has been performed by invoking a comprehensive approach that
%includes both algebraic manipluation 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",
}

% 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",
}

%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 =        feb,
}

@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 =        dec,
}

@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 =        "Cyclindrically 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{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",
}

%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",
}

%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",
}

%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",
}

%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",
}

%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",
}

%Plasma.  "REDUCE was used to analyse the general set of equations
%for large numbers of Fourier harmonics ...."

@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",
}

%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",
}

@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",
}

%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",
}

%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 =        feb,
}

@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 =        dec,
}

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 =        mar,
}

@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 =        feb,
}

@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 =        jan,
}

%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 =        sep,
}

@InProceedings{Bradford:86,
  author =       "R. J. Bradford and A. C. Hearn and J. A. Padget and E.
                 {Schr\"{u}fer}",
  title =        "Enlarging the {REDUCE} Domain of Computation",
  booktitle =    "Proc. of {SYMSAC} '86",
  year =         "1986",
  pages =        "100--106",
}

@InProceedings{Bradford:88,
  author =       "R. J. Bradford and J. H. Davenport",
  title =        "Effective Tests for Cyclotomic Polynomials",
  booktitle =    "Proc. of {ISSAC} '88",
  publisher =    "Springer-Verlag",
  year =         "1988",
  volume =       "358",
  pages =        "244--251",
}

@Article{Broadhurst: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",
}

%Uses REDUCE to calculate explicitely 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 =        aug,
}

%Stanford Linear Accelerator Center Report.

@InProceedings{Brodsky:71,
  author =       "S. J. Brodsky",
  title =        "Algebraic Computation Techniques in Quantum
                 Electrodynamics",
  year =         "1971",
  volume =       "II",
  pages =        "IV-1--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 =        aug,
}

%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",
}

%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....plasma..."

@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",
}

%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 =        dec,
  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",
}

%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",
}

%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 =        aug,
}

%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 =       "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 =        oct,
}

@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 =        aug,
}

@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 =        dec,
}

@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 =        feb # " and " # may,
}

%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: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 =        jan,
}

%Based on a renormalization group equation met in Quantum Field Theory,
%Continuous Iterations of a large class of functions are computed using
%REDUCE.

@Article{Caprasse: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{Carlson:80,
  author =       "P. Carlson",
  title =        "Coordinate Free Relativity",
  journal =      "J. Math. Phys.",
  year =         "1980",
  volume =       "21",
  pages =        "1149--1154",
}

%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",
}

%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 =        feb,
}

@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",
}

%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",
}

% 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",
}

%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 =        feb,
}

@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",
}

%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 =        sep,
  booktitle =    "Proc. of the Workshop in Symbolic Computation, Dubna,
                 {U.S.S.R.}",
}

%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",
}

%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 =        feb,
}

@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 =        nov,
}

@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 =        sep,
  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",
  year =         "1988",
}

@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 =        nov,
}

@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 =        jul,
}

@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",
}

%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",
}

%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",
}

%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 =        aug,
}

@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",
}

%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 =        dec,
}

%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",
}

%"...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 =        jul,
}

%Presented at 15th UK Plasma Physics Conference, UMIST.

@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",
}

%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 =        oct,
}

%"For the case of several interacting chiral superfields the propagators
%for the unconstrained superfield potentials in the 'shifted' theory,
%where the supersymmetry is explicity 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",
}

%(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",
}

%(In Portuguese) Lecture notes of a course on 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 =        oct,
}

@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 =        jun,
}

%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 =        oct,
}

@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 =        aug,
}

@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",
}

%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",
}

%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 =        feb,
}

@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 =        dec,
}

@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",
}

%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",
}

%"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",
}

%"...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 =        dec,
}

@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 # "/" # jun,
}

@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 =        dec,
}

@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 =        jul,
}

@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",
}

%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",
}

%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 =        jun,
}

@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",
}

@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 =        jul,
}

@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 =        nov,
}

@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 =        feb,
}

%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",
}

%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",
}

%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 =        apr,
}

%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 =        nov,
}

@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",
}

%"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".

