[AG98]     Beatrice Amrhein and Oliver Gloor. The fractal walk. In Bruno Buchberger and Franz Winkler, editors, Gröbner Bases and Applications, volume 251 of London Mathematical Society Lecture Note Series, pages 305–322. Cambridge University Press, Feb 1998.

[AGK96a]     Beatrice Amrhein, Oliver Gloor, and Wolfgang Kuechlin. How fast does the walk run? In 5th Rhine Workshop on Computer Algebra, volume PR 801/96, pages 8.1–8.9. Institut Franco–Allemand de Recherches de Saint–Louis, Jan 1996.

[AGK96b]     Beatrice Amrhein, Oliver Gloor, and Wolfgang Kuechlin. Walking faster. In J. Calmet and C. Limongelli, editors, DISCO 1996: Design and Implementation of Symbolic Computation Systems, volume 1128 of Lecture Notes in Computer Science, pages 150–161. Springer, 1996.

[All78]     J. R. Allen. The Anatomy of LISP. McGraw-Hill, New York, 1978.

[ALSU06]     Alfred V. Aho, Monica S. Lam, Ravi Sethi, and Jeffrey D. Ullman. Compilers: Principles, Techniques, and Tools (2nd Edition). Addison Wesley, August 2006.

[AM90]     V. S. Adamchik and O. I. Marichev. The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system. In S. Watanabe and Morio Nagata, editors, Proceedings of the 1990 International Symposium on Symbolic and Algebraic Computation, pages 212–224. ACM, Addison-Wesley, 1990.

[Ape92]     Joachim Apel. A relationship between Gröbner bases of ideals and vector modules of G-algebras, volume 131.2 of Contemporary Mathematics, pages 195–204. AMS, 1992.

[AS72]     Milton Abramowitz and Irene A. Stegun, editors. Handbook of Mathematical Functions. Dover Publications, 1972.

[ASW89]     Werner Antweiler, Andreas Strotmann, and Volker Winkelmann. A TeX-REDUCE-interface. SIGSAM Bulletin, 23(2):26–33, February 1989.

[ASY74]     E A Arais, V P Shapeev, and N N Yanenko. Computer realization of cartan’s exterior calculus,. Soviet Math Dokl, 15:203–205, 1974.

[Bar67a]     D. Barton. A scheme for manipulative algebra on a computer. Computer Journal, 9(4):340–344, Feb 1967.

[Bar67b]     D. Barton. A scheme for manipulative algebra on a computer. Astronomical Journal, 72:1281–1287, 1967.

[BB89]     A. V. Bocharov and M. L. Bronstein. Efficiently Implementing Two Methods of the Geometrical Theory of Differential Equations: An Experience in Algorithm and Software Design, pages 143–166. Number 16 in Acta Applicandae Mathematicae. Kluwer, 1989.

[BC82]     Gregory Butler and John J. Cannon. Computing in permutation and matrix groups. I. Normal closure, commutator subgroups, series. Math. Comp., 39:663–670, 1982.

[BC94]     A. Burnel and H. Caprasse. Computing the BRST operator used in quantization of gauge theories. International Journal of Modern Physics C, 5(6):1035–1047, December 1994.

[BCD\(^{+}\)99]     A. V. Bocharov, V. N. Chetverikov, S. V. Duzhin, N. G. Khor’kova, A. V. Samokhin, Yu. N. Torkhov, and A. M. Verbovetsky:. Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, volume 182 of Translations of Math. Monographs. AMS, 1999.

[BCG\(^{+}\)91]     Robert L Byrant, S S Chern, Robert B Gardner, Hubert L Goldschmidt, and P A Griffiths. Computer realization of Cartan’s exterior calculus, volume 18 of Mathematical Sciences Research Institute Publications. Springer-Verlag New York, 1991.

[BCRT93]     Anna Maria Bigatti, Pasqualina Conti, Lorenzo Robbiano, and Carlo Traverso. A “Divide and conquer” algorithm for Hilbert-Poincaré series, multiplicity and dimension of monomial ideals. In G. Cohen, T. Mora, and O. Moreno, editors, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1993, volume 673 of Lecture Notes in Computer Science, pages 76–88, Berlin, Heidelberg, 1993. Springer-Verlag.

[BF72]     D. Barton and J. P. Fitch. The application of symbolic algebra system to physics. Reports on Progress in Physics, 35(1):235–314, Jan 1972.

[BGDW95]     P. A. Broadbery, T. Gómez-Díaz, and S. M. Watt. On the Implementation of Dynamic Evaluation. In A. Levelt, editor, Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation, ISSAC ’95, pages 77–84, New York, NY, USA, 1995. ACM Press.

[BGK86]     W. Boege, R. Gebauer, and H. Kredel. Some examples for solving systems of algebraic equations by calculating Groebner bases. Journal of Symbolic Computation, 2(1):83–98, March 1986.

[BGM96]     George A. Baker and Peter Graves-Morris. Padé Approximants, volume 13 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, 2nd edition, 1996.

[BH10]     D. E. Baldwin and W. Hereman. A symbolic algorithm for computing recursion operators of nonlinear partial differential equations. International Journal of Computer Mathematics, 87(5):1094–1119, 2010.

[BHPS86]     R. J. Bradford, A. C. Hearn, J. A. Padget, and E. Schrüfer. Enlarging the reduce domain of computation. In SYMSAC ’86: Proceedings of the fifth ACM symposium on Symbolic and algebraic computation, pages 100–106, New York, NY, USA, 1986. ACM.

[BL85]     Gregory Butler and Clement W. H. Lam. A General Backtrack Algorithm for the Isomorphism Problem of Combinatorial Objects. Journal of Symbolic Computation, 1(4):363–381, 1985.

[BO78]     Carl M. Bender and Steven A. Orszag. Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill, 1978.

[Bou72]     S. R. Bourne. Literal expressions for the co-ordinates of the moon. I. The First Degree Terms. Celestial Mechanics, 6(2):167–186, Sep 1972.

[Bra93]     Russell Bradford. Algebraic simplification of multiple-valued functions. In John Fitch, editor, DISCO 1992: Design and Implementation of Symbolic Computation Systems, volume 721 of Lecture Notes in Computer Science, pages 13–21, Berlin, Heidelberg, 1993. Springer Berlin Heidelberg.

[Bro96]     E. W. Brown. An Introductory Treatise on the Lunar Theory. Cambridge University Press, 1896.

[Bro97]     Manuel Bronstein. Symbolic Integration I: Transcendental Functions. Springer-Verlag, Heidelberg, 1997.

[BS81]     Ilja N. Bronstein and K. A. Semendjajew. Taschenbuch der Mathematik. Verlag Harri Deutsch, Thun und Frankfurt (Main), 1981.

[BS92]     Dave Bayer and Mark Stillman. Computation of Hilbert functions. Journal of Symbolic Computation, 14(1):31–50, 1992.

[Buc85]     Bruno Buchberger. Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory, pages 184–232. Reidel, Dordrecht, 01 1985.

[Buc88]     Bruno Buchberger. Applications of Gröbner bases in non-linear computational geometry. In R. Janssen, editor, Mathematical Aspects of Scientific Software, volume 296 of Lecture Notes in Computer Science, pages 52–88. Springer, New York, 1988.

[But82]     Gregory Butler. Computing in permutation and matrix groups ii: Backtrack algorithm. Mathematics of Computation, 39(160):671–680, 1982.

[BW92]     A. Brand and T. Wolf. The computer algebra package CRACK for investigating PDEs. In Proc. of ERCIM, Partial Differential Equations and Group Theory, Bonn, page 24, 1992.

[BW95]     A. Brand and T. Wolf. Investigating DEs with CRACK and related programs. SIGSAM Bulletin, Special Issue:1–8, June 1995.

[BWK93]     Thomas Becker, Volker Weispfenning, and Heinz Kredel. Gröbner bases, a computational approach to commutative algebra. Springer - Verlag (Graduate Texts in Mathematics 141), 1993.

[Cap97]     H. Caprasse. Brst charge and poisson algebras. Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only], 1(2):115–127, 1997.

[Car88]     B.C. Carlson. A table of elliptic integrals of the third kind. 51 (183), pp. 267–280, s1–s5. Mathematics of Computation, 51 (183):267–280, 1988.

[Car99]     B.C. Carlson. Toward symbolic integration of elliptic integrals. J. Symbolic Computation, 28(6):739–753, 1999.

[CAT]     CATHODE (Computer Algebra Tools for Handling Ordinary Differential Equations). OBSOLETE: http://www-lmc.imag.fr/CATHODE/, http://www-lmc.imag.fr/CATHODE2/.

[CF00]     B.C. Carlson and J. FitzSimmons. Reduction theorems for elliptic integrands with the square root of two quadratic factors. J. Computational Applied Mathematics, 118(1-2):71–85, 2000.

[CGG\(^{+}\)91]     Bruce W. Char, Keith O. Geddes, Gaston H. Gonnet, Benton Leong, Michael B. Monagan, and Stephen M. Watt. Maple V Language Reference Manual. Springer, 1991.

[Chi63]     J. S. R. Chisholm. Relativistic scalar products of \(\gamma \) matrices. Il Nuovo Cimento (1955-1965), 30(1):426–428, Oct 1963.

[CHW91]     B. Champagne, W. Hereman, and P. Winternitz. The computer calculation of Lie point symmetries of large systems of differential equations. Computer Physics Communications, 66(2–3):319–340, 1991.

[CJ92]     Robert M. Corless and David J. Jeffrey. Well … It Isn’t Quite That Simple. SIGSAM Bull., 26(3):2–6, Aug 1992.

[CKM97]     S. Collart, M. Kalkbrenner, and D. Mall. Converting Bases with the Gröbner Walk. Journal of Symbolic Computation, 24(3-4):465–469, Sep 1997.

[CLO92]     D. Cox, J. Little, and D. O’Shea. Ideals, Varieties and Algorithms: An Introduction of Computational Algebraic Geometry and Commutative Algebra. Springer-Verlag, 1992.

[CLV20]     M. Casati, P. Lorenzoni, and R. Vitolo. Three computational approaches to weakly nonlocal poisson brackets. Studies in Applied Mathematics, 2020.

[CN81]     B.C. Carlson and E.M. Notis. Algorithm 577: Algorithm for incomplete elliptic intergrals [s21]. ACM Transactions Mathematical Software, 7(3):398–403, 1981.

[Col75]     George E. Collins. Quantifier elimination for real closed fields by cylindrical algebraic decompostion. In H. Brakhage, editor, Automata Theory and Formal Languages 2nd GI Conference Kaiserslautern, May 20–23, 1975, volume 33 of Lecture Notes in Computer Science, pages 134–183, Berlin, Heidelberg, 1975. Springer Berlin Heidelberg.

[Cvi76]     Predrag Cvitanović. Group theory for Feynman diagrams in non-Abelian gauge theories. Phys. Rev. D, 14:1536, Sep 1976.

[Dan]     George Bernard Dantzig. Linear programming and extensions. Technical report, RAND Corporation.

[Dav81]     James Harold Davenport. On the Integration of Algebraic Functions, volume 102 of Lecture Notes in Computer Science. Springer-Verlag, 1981.

[Del86]     C. Delaunay. Théorie du Mouvement de la Lune. Extraits des Mém. Acad. Sci. Mallet-Bachelier, Paris, 186.

[DF94]     James Davenport and Christèle Faure. The “unknown” in computer algebra. Programming and Computer Software, 20:1–5, 01 1994.

[DGV96]     D. Duval and Laureano González-Vega. Dynamic evaluation and real closure. Mathematics and Computers in Simulation, 42:551–560, 11 1996.

[DLS90]     Ladislav Drska, Richard Liska, and Milan Sinor. Two practical packages for computational physics-GCPM, RLFI. Computer Physics Communications, 61(1-2):225–230, November 1990.

[DN83]     B. A. Dubrovin and S. P. Novikov. Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the bogolyubov-whitham averaging method. Dokl. Akad. Nauk SSSR, 27(3):665–669, 1983. Translated by J. R. Schulenberger.

[DN84]     B. A. Dubrovin and S. P. Novikov. Poisson brackets of hydrodynamic type. Dokl. Akad. Nauk SSSR, 30(3):651–654, Jan 1984.

[DP85]     James Davenport and Julian Padget. HEUGCD: how elementary upperbounds generate cheaper data. In Proc. EUROCAL 1985, Lecture Notes in Computer Science, volume 204, pages 18–28. Springer-Verlag, 1985.

[DR94a]     Dominique Duval and Jean-Claude Reynaud. Sketches and computation I: basic definitions and static evaluation. Mathematical Structures in Computer Science, 4(2):185–238, 1994.

[DR94b]     Dominique Duval and Jean-Claude Reynaud. Sketches and computation II: dynamic evaluation and applications. Mathematical Structures in Computer Science, 4(2):239–271, 1994.

[DS96]     Andreas Dolzmann and Thomas Sturm. Redlog user manual. Technical Report MIP-9616, FMI, Universität Passau, D-94030 Passau, Germany, October 1996. Edition 1.0 for Version 1.0.

[DS97a]     Andreas Dolzmann and Thomas Sturm. REDLOG: Computer algebra meets computer logic. ACM SIGSAM Bulletin, 31(2):2–9, June 1997.

[DS97b]     Andreas Dolzmann and Thomas Sturm. Simplification of quantifier-free formulae over ordered fields. Journal of Symbolic Computation, 24(2):209–231, August 1997.

[DS99]     Andreas Dolzmann and Thomas Sturm. Redlog User Manual. FMI, Universität Passau, D-94030 Passau, Germany, April 1999. Edition 2.0 for Version 2.0.

[DST93]     J. H. Davenport, Y. Siret, and E. Tournier. Computer Algebra, Systems and Algorithms for Algebraic Computation. Academic Press, 2nd edition, 1993.

[Dub96]     Boris Dubrovin. Geometry of 2D topological field theories. In Mauro Francaviglia and Silvio Greco, editors, Integrable Systems and Quantum Groups: Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, June 14–22, 1993, volume 1620 of Lecture Notes in Mathematics, pages 120–348. Springer, Berlin Heidelberg, 1996.

[Eas87]     James W. Eastwood. Orthovec: A REDUCE program for 3-D vector analysis in orthogonal curvilinear coordinates. Computer Physics Communications, 47(1):139–147, October 1987.

[Eas91]     James W. Eastwood. ORTHOVEC: version 2 of the REDUCE program for 3-D vector analysis in orthogonal curvilinear coordinates. Computer Physics Communications, 64(1):121–122, April 1991.

[Edm57]     A. R. Edmonds. Angular Momentum in Quantum Mechanics. Princeton University Press, 1957.

[Eis95]     David Eisenbud. Commutative Algebra with a View Toward Algebraic Geometry, volume 150 of Graduate Texts in Math. Springer-Verlag, Berlin and New York, 1995.

[Eul48]     L. Euler. Introductio in analysin infinitorum, Vol. 1, chapter 18. 1748.

[Fat74]     Richard J. Fateman. On the multiplication of poisson series. Celestial Mechanics, 10(2):243–247, Oct 1974.

[Fat87]     Richard J. Fateman. TeX output from macsyma-like systems. ACM SIGSAM Bulletin, 21(4):1–5, 1987.

[FGLM93]     J. C. Faugère, P. Gianni, D. Lazard, and T .Mora. Efficient Computation of Zero-dimensional Gröbner Bases by Change of Ordering. Journal of Symbolic Computation, 16(4):329–344, Oct 1993.

[FGMN97]     E. V. Ferapontov, C .A. P. Galvao, O. Mokhov, and Y. Nutku. Bi-hamiltonian structure in 2-d field theory. Communications in Mathematical Physics, 186(3):649–669, Jan 1997.

[FH74]     John A. Fox and Anthony C. Hearn. Analytic computation of some integrals in fourth order quantum electrodynamics. Journal of Computational Physics, 14(3):301–317, March 1974.

[Fil92]     Sandra Fillebrown. Faster computation of bernoulli numbers. Journal of Algorithms, 13(3):431–445, September 1992.

[Fit75]     J. P. Fitch. Syllabus for algebraic manipulation lectures in cambridge. SIGSAM Bulletin, 32:15, 1975.

[Fit83]     J. P. Fitch. CAMAL User’s Manual. Technical report, University of Cambridge Computer Laboratory, 1983. 2nd edition.

[FJ03]     J. C. Faugère and A. Joux. Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases. In Advances in Cryptology - CRYPTO 2003, volume 2729 of Lecture Notes in Computer Science, pages 44–60. Springer, Berlin, Heidelberg, 2003.

[FK89]     W. I. Fushchich and V. V. Kornyak. Computer algebra application for determining lie and lie–bäcklund symmetries of differential equations. Journal of Symbolic Computation, 7:611–619, 1989.

[FPV14]     E. V. Ferapontov, M .V. Pavlov, and R.F. Vitolo. Projective-geometric aspects of homogeneous third-order hamiltonian operators. Journal of Geometry and Physics, 85:16–28, 2014.

[FPV16]     E. V. Ferapontov, M. V. Pavlov, and R. F. Vitolo. Towards the classification of homogeneous third-order hamiltonian operators. International Mathematics Research Notices, 2016(22):6829–6855, Jan 2016.

[Gas95]     G. Gasper. Lecture notes for an introductory minicourse on q-series. 1995.

[GB98]     V. P. Gerdt and Yu. A. Blinkov. Involutive bases of polynomial ideals. Math. Comp. Simul., 45(5-6):519–541, March 1998.

[GCL92]     K.O. Geddes, S.R. Czapor, and G. Labahn. Algorithms for Computer Algebra. Kluwer Academic Publishers, 1992.

[GD96]     Teresa Gómez-Díaz. Examples of using dynamic constructible closure. Mathematics and Computers in Simulation, 42(4–6):375–383, 1996.

[gde]     Geometry of differential equations web site.

[Ger05]     Vladimir P. Gerdt. Involutive algorithms for computing groebner bases. In Svetlana Cojocaru, Gerhard Pfister, and Victor Ufnarovski, editors, Computational Commutative and Non-Commutative Algebraic Geometry, volume 196 of NATO Science Series, III: Computer and Systems Sciences, pages 199–225, 2005. Proceedings of the NATO Advanced Research Workshop "Computational commutative and non-commutative algebraic geometry" (Chishinau, June 6-11, 2004).

[Get02]     Ezra Getzler. A darboux theorem for hamiltonian operators in the formal calculus of variations. Duke Mathematical Journal, 111, Mar 2002.

[GH79]     Martin L. Griss and Anthony C. Hearn. Portable LISP compiler. Software - Practice and Experience, 11(6):541–605, June 1979.

[GK82]     Daniel H. Greene and Donald E. Knuth. Mathematics for the Analysis of Algorithms, volume 1 of Progress in Computer Science and Applied Logic (PCS). Birkhäuser Boston, 2nd edition, 1982.

[GM88]     Rüdiger Gebauer and H. Michael Möller. On an installation of Buchberger’s algorithm. Journal of Symbolic Computation, 6(2 and 3):275–286, 1988.

[GMM\(^{+}\)81]     V G Ganzha, S V Meleshko, F A Murzin, V P Shapeev, and N N Yanenko. Computer realization of an algorithm for investigating the compatibility of systems of partial differential equations,. Soviet Math Dokl, 24:638–640, 1981.

[GMN\(^{+}\)91]     Alessandro Giovini, Teo Mora, Gianfranco Niesi, Lorenzo Robbiano, and Carlo Traverso. “;one sugar cube, please” or selection strategies in the buchberger algorithm. In Watt [Wat91], pages 49–54.

[Gos78]     R. W. Gosper, Jr. Decision procedure for indefinite hypergeometric summation. Proc. Natl. Acad. Sci. USA, 75(1):40–42, January 1978.

[GR90]     G. Gasper and M. Rahman. Basic Hypergeometric Series. Number 35 in Encyclopedia of Mathematics and its Applications. Cambridge University Press, London and New York, 1990.

[Grä93]     Hans-Gert Gräbe. Two remarks on independent sets. Journal of Algebraic Combinatorics, 2:137–145, 1993.

[Grä94a]     Hans-Gert Gräbe. On factorized gröbner bases. In J. Fleischer, J. Grabmeier, F. W. Hehl, and W. Küchlin, editors, Computer Algebra in Science and Engineering. World Scientific, 1994. Proceedings of the Conference, Bielefeld, Germany, 28–31 August 1994.

[Grä94b]     Hans-Gert Gräbe. The tangent cone algorithm and homogenization. Journal of Pure and Applied Algebra, 97(3):303–312, Dec 1994.

[Grä95a]     Hans-Gert Gräbe. Algorithms in local algebra. Journal of Symbolic Computation, 19(6):545–577, Jun 1995.

[Grä95b]     Hans-Gert Gräbe. Triangular systems and factorized gröbner bases. In Gérard Cohen, Marc Giusti, and Teo Mora, editors, Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, Lecture Notes in Computer Science, pages 248–261, Berlin, Heidelberg, 1995. Springer.

[Grä97]     Hans-Gert Gräbe. Minimal primary decomposition and factorized gröbner bases. Applicable Algebra in Engineering, Communication and Computing, 8(4):265–278, 1997.

[Gru96]     Dominik Gruntz. On Computing Limits in a Symbolic Manipulation System. PhD thesis, ETH Zürich, 1996.

[GTZ88]     Patrizia Gianni, Barry Trager, and Gail Zacharias. Gröbner bases and primary decomposition of polynomial ideals. Journal of Symbolic Computation, 6(2-3):149–167, Oct 1988.

[GZ08a]     V. P. Gerdt and M. V. Zinin. Involutive method for computing Gröbner bases over \(\mathbb {F}_{2}\). Programming and Computer Software, 34(4):191–203, Jul 2008.

[GZ08b]     Vladimir P. Gerdt and Mikhail V. Zinin. A pommaret division algorithm for computing grobner bases in boolean rings. In Proceedings of the Twenty-first International Symposium on Symbolic and Algebraic Computation, ISSAC ’08, pages 95–102, New York, NY, USA, 2008. ACM.

[GZB10]     V. P. Gerdt, M. V. Zinin, and Yu. A. Blinkov. Programming and computing software. Program. Comput. Softw., 36(2):117–123, mar 2010.

[Han75]     E. R. Hansen. A table of series and products. Prentice-Hall, Englewood Cliffs, NJ, 1975.

[Har12]     G. H. Hardy. Properties of logarithmico-exponential functions. Proceedings of the London Mathematical Society, s2-10(1):54–90, 1912.

[Har79]     Steven J. Harrington. A new symbolic integration system in REDUCE. The Computer Journal, 22(2):127–131, 1979.

[Har89]     David Harper. Vector33: a REDUCE program for vector algebra and calculus in orthogonal curvilinear coordinates. Computer Physics Communications, 54(2 and 3):295–305, June and July 1989.

[HCGJ92]     D. E. G. Hare, R. M. Corless, G. H. Gonnet, and D. J. Jeffrey. On Lambert’s W Function. Preprint, University of Waterloo, 1992.

[HCJE93]     H. Hong, G. E. Collins, J. R. Johnson, and M. J. Encarnacion. QEPCAD interactive version 12, Sep 1993. Kindly communicated to us by Hoon Hong.

[Hea68]     Anthony C. Hearn. REDUCE: A user-oriented interactive system for algebraic simplification. In M. Klerer and J. Reinfelds, editors, Interactive Systems for Experimental Applied Mathematics, pages 79–90, New York, 1968. Academic Press.

[Hea69]     Anthony C. Hearn. The problem of substitution. In R.G. Tobey, editor, Proc. of the 1968 Summer Institute on Symbolic Mathematical Computation, pages 3–19, Cambridge, Mass, 1969. IBM Boston Prog. Center.

[Hea71]     Anthony C. Hearn. REDUCE 2: A system and language for algebraic manipulation. In S.R. Petrick, editor, SYMSAC ’71: Proceedings of the second ACM symposium on Symbolic and algebraic manipulation, pages 128–133. ACM, New York, 1971.

[Hea79]     Anthony C. Hearn. Non-modular computation of polynomial GCDs using trial division. In Symbolic and Algebraic Computation (EUROSAM ’79, An International Symposium on Symbolic and Algebraic Manipulation, Marseille, France, June 1979), volume 72 of Lecture Notes in Computer Science, pages 227–239. Springer Berlin / Heidelberg, 1979.

[Hea95]     Anthony C. Hearn. REDUCE User’s Manual, Version 3.6. Report CP 78, RAND, July 1995.

[Her95]     W. Hereman. Symbolic Software for Lie Symmetry Analysis, volume 3, chapter 13. CRC Press, Boca Raton, Florida, 1995. Systems described in this paper are among others:
DELiA (Alexei Bocharov et.al.) Pascal
DIFFGROB2 (Liz Mansfield) Maple
DIMSYM (James Sherring and Geoff Prince) REDUCE
HSYM (Vladimir Gerdt) Reduce
LIE (V. Eliseev, R.N. Fedorova and V.V. Kornyak) Reduce
LIE (Alan Head) muMath
Lie (Gerd Baumann) Mathematica
LIEDF/INFSYM (Peter Gragert and Paul Kersten) Reduce
Liesymm (John Carminati, John Devitt and Greg Fee) Maple
MathSym (Scott Herod) Mathematica
NUSY (Clara Nucci) Reduce
PDELIE (Peter Vafeades) Macsyma
SPDE (Fritz Schwarz) Reduce and Axiom
SYM_DE (Stanly Steinberg) Macsyma
Symmgroup.c (Dominique Berube and Marc de Montigny) Mathematica
STANDARD FORM (Gregory Reid and Alan Wittkopf) Maple
SYMCAL (Gregory Reid) Macsyma and Maple
SYMMGRP.MAX (Benoit Champagne, Willy Hereman and Pavel Winternitz) Macsyma
LIE package (Khai Vu) Maple
Toolbox for symmetries (Mark Hickman) Maple
Lie symmetries (Jeffrey Ondich and Nick Coult) Mathematica.

[Hil99]     Dietmar Hillebrand. Triangulierung nulldimensionaler Ideale - Implementierung und Vergleich zweier Algorithmen - in German . Diplomarbeit im Studiengang Mathematik der Universität Dortmund. Betreuer: Prof. Dr. H. M. Möller. Technical report, Universität Dortmund, 1999.

[HT91]     David Hartley and Robin W. Tucker. A constructive implementation of the Cartan-Kähler theory of exterior differential systems. Journal of Symbolic Computation, 12(6):655–667, December 1991.

[HT93]     David Hartley and Philip Tuckey. A direct characterisation of gröbner bases in clifford and grassmann algebras. Preprint MPI-Ph/93–96, Max-Planck-Institut für Physik, 1993.

[IK96]     V. A. Ilyin and A. P. Kryukov. ATENSOR - REDUCE program for tensor simplification. Computer Physics Communications, 96(1):36–52, July 1996.

[IKRT89]     V. A. Ilyin, A. P. Kryukov, A. Ya. Rodioniov, and A. Yu. Taranov. Fast algorithm for calculation of Dirac’s gamma-matrices traces. SIGSAM Bulletin, 23(4):15–24, Oct 1989.

[IVV04]     Sergei Igonin, A. Verboretsky, and Raffaele Vitolo. Variational multivectors and brackets in the geometry of jet spaces. In R.O. Popovych A.G. Nikitin, V.M. Boyko and I.A. Yehorchenko, editors, V Int. Conf. on on Symmetry in Nonlinear Mathematical Physics, Kyiv 2003, volume 50, pages 1335–1342, Oct 2004.

[Jan29]     M. Janet. Leçons sur les systèmes d’équations aux dérivées. Gauthier-Villars, Paris, 1929.

[JDB65]     Sidney D. Drell James D. Bjorken. Relativistic Quantum Mechanics. International Series In Pure and Applied Physics. McGraw-Hill, New York, 1965.

[Jef70]     W. H. Jefferys. A fortran-based list processor for poisson series. Celestial Mechanics, 2(4):474–480, Dec 1970.

[JR94]     D. J. Jeffrey and A. D. Rich. The evaluation of trigonometric integrals avoiding spurious discontinuities. ACM Trans. Math. Softw., 20(1):124–135, March 1994.

[JT80]     W.B. Jones and W.J. Thron. Continued Fractions: Analytic Theory and Applications, volume 11 of Encyclopedia of mathematics and its applications. Addison-Wesley Publishing Company, 1980.

[Kah68]     Joseph Kahane. Algorithm for reducing contracted products of \(\gamma \) matrices. Journal of Mathematical Physics, 9(10):1732–1738, 1968.

[Kah87]     W. Kahan. Branch cuts for complex elementary functions or much ado about nothing’s sign bit. In A. Iserles and M.J.D. Powell, editors, The State of the Art in Numerical Analysis : Proceedings of the Joint IMA/SIAM Conference on the State of the Art in Numerical Analysis held at the University of Birmingham, 14-18 April 1986, Oxford, 1987. Clarendon Press.

[Kam59]     E. Kamke. Differentialgleichungen, Lösungsmethoden und Lösungen, Band 1, Gewöhnliche Differentialgleichungen, volume 1. Chelsea Publishing Company, New York, 1959.

[Kaz87]     C. Kazasov. Laplace transformations in REDUCE 3. In Proc. EUROCAL ’87, Lecture Notes in Computer Science, volume 378, pages 132–133. Springer-Verlag, 1987.

[Ken82]     A. D. Kennedy. Diagrammatic methods for spinors in feynman diagrams. Phys. Rev. D, 26:1936–1955, Oct 1982.

[Khi64]     Aleksandr J. Khinchin. Continued Fractions. University of Chicago Press, 1964.

[KKV04]     P. H. M. Kersten, I. S. Krasil’shchik, and A. M. Verbovetsky. Hamiltonian operators and \(\ell ^*\)-covering. Journal of Geometry and Physics, 50(1–4):273–302, 2004.

[KKV06]     P. H. M. Kersten, I. S. Krasil’shchik, and A. M. Verbovetsky. A geometric study of the dispersionless boussinesq type equation. Acta Applicandae Mathematica, 90:143–178, 2006. 1–2.

[KKVV09]     P. Kersten, I. S. Krasil’shchik, A. Verboretsky, and Vito. Hamiltonian Structures for General PDEs, pages 187–198. Abel Symposia. Springer Berlin Heidelberg, Berlin, Heidelberg, 2009.

[Knu81]     Donald E. Knuth. The Art of Computer Programming, Volume 2: Seminumerical Algorithms. Addison-Wesley Publishing Company, 2nd edition, 1981.

[Knu84]     Donald E. Knuth. The TeXbook. Computers & typesetting. Addison-Wesley, Reading, 1984.

[Koe92]     Wolfram Koepf. Power series in computer algebra. Journal of Symbolic Computation, 13(6):581–603, June 1992.

[Koe93a]     Wolfram Koepf. Algorithmic development of power series. In J. Calmet and J. A. Campbell, editors, Artificial intelligence and symbolic mathematical computing, volume 737 of Lecture Notes in Computer Science, pages 195–213, Berlin, Heidelberg, 1993. Springer-Verlag. International Conference AISMC-1, Karlsruhe, Germany, August 1992, Proceedings.

[Koe93b]     Wolfram Koepf. Examples for the algorithmic calculation of formal puiseux, laurent and power series. ACM SIGSAM Bulletin, 27(1):20–32, Jan 1993.

[Koe94a]     Wolfram Koepf. Algorithmic work with orthogonal polynomials and special functions. Preprint sc 94-5, Konrad-Zuse-Zentrum Berlin (ZIB), 1994.

[Koe94b]     Wolfram Koepf. Algorithms for the indefinite and definite summation. Preprint SC 94-33, Konrad-Zuse-Zentrum für Informationstechnik Berlin, December 1994.

[Koe95a]     Wolfram Koepf. Algorithms for \(m\)-fold hypergeometric summation. Journal of Symbolic Computation, 20(4):399–417, Oct 1995.

[Koe95b]     Wolfram Koepf. REDUCE package for the indefinite and definite summation. SIGSAM Bulletin, 29(1):14–30, January 1995.

[Koo93]     T. H. Koornwinder. On Zeilberger’s algorithm and its \(q\)-analogue: a rigorous description. J. of Comput. and Appl. Math., 48(1-2):91–111, October 1993.

[KR88]     A. P. Kryukov and A. Ya. Rodionov. Program “COLOR” for computing the group-theoretic weight of Feynman diagrams in Non-Abelian gauge theories. Computer Physics Communications, 48(2):327–334, February 1988.

[Kre87]     Heinz Kredel. Primary ideal decomposition. In James Davenport, editor, EUROCAL ’87, European Conference on Computer Algebra, Leipzig, GDR, June 2-5, 1987, Proceedings, 1987.

[Kre88]     Heinz Kredel. Admissible term orderings used in computer algebra systems. SIGSAM Bulletin, 22(1):28–31, January 1988.

[KS94]     R. Koekoek and R. F. Swarttouw. The askey-scheme of hypergeometric orthogonal polynomials and its \(q\)-analogue. Report 94-05, Faculty of Technical Mathematics and Informatics, Technische Universiteit Delft, Delft, 1994.

[Kub]     M. Kubitza. Private communication.

[Kup94]     B. A. Kuperschmidt. Geometric Hamiltonian forms for the Kadomtsev-Petviashvili and Zabolotskaya-Khokhlov equations, pages 155–172. World Scientific, 1994.

[KV11]     Joseph Krasil’shchik and Alexander Verbovetsky. Geometry of jet spaces and integrable systems. Journal of Geometry and Physics, 61:1633–1674, 2011.

[KVV12]     Joseph Krasil’shchik, Alexander Verbovetsky, and Raffaele Vitolo. A unified approach to computation of integrable structures. Acta Applicandae Mathematicae, 120(1):199–218, Aug 2012.

[KVV18]     Joseph Krasil’shchik, Alexander Verbovetsky, and Raffaele Vitolo. The Symbolic Computation of Integrability Structures for Partial Differential Equations. Texts & Monographs in Symbolic Computation. Springer International Publishing, 1 edition, 2018.

[KW88]     Heinz Kredel and Volker Weispfenning. Computing dimension and independent sets for polynomial ideals. Journal of Symbolic Computation, 6(2-3):231–247, Oct 1988.

[Lam86]     Leslie Lamport. LaTeX - A Document Preparation System. Addison-Wesley, Reading, 1986.

[Law89]     Derek F. Lawden. Elliptic Functions and Applications. Springer-Verlag, 1989.

[Laz83]     D. Lazard. Gröbner bases, gaussian elimination and resolution of systems of algebraic equations. volume 162 of Lecture Notes in Computer Science, pages 146–157. Springer, Proceedings of EUROCAL ’83.

[LB68]     Landolt-Boernstein. Zahlenwerte und Funktionen aus Naturwissenschaften und Technik. Springer, 1968.

[LD90]     R. Liska and L. Drska. FIDE: A REDUCE package for automation of FInite difference method for solving pDE. In S. Watanabe and Morio Nagata, editors, Proceedings of the 1990 International Symposium on Symbolic and Algebraic Computation, pages 169–176. ACM, Addison-Wesley, 1990.

[Leo80]     Jeffrey S. Leon. On an algorithm for finding a base and a strong generating set for a group given by generating permutations. Mathematics of Computation, 35(151):941–974, 1980.

[Leo84]     Jeffrey S. Leon. Computing Automorphism Groups of Combinatorial Objects. In Michael D. Atkinson, editor, Computational Group Theory: Proceedings of the London Mathematical Society Symposium on Computational Group Theory. London Mathematical Society, Academic Press, 1984.

[Leo91]     Jeffrey S. Leon. Permutation group algorithms based on partitions, i: Theory and algorithms. Journal of S, 12:533–583, 1991.

[Lie67]     S. Lie. Differentialgleichungen. Chelsea Publishing Company, New York, 1967.

[Lie75]     S. Lie. Sophus lie’s 1880 transformation group paper. Translated by M. Ackerman, comments by R. Hermann, Mathematical Sciences Press, Brookline, 1975.

[Lin91]     Stephen A. Linton. Double coset enumeration. Journal of Symbolic Computation, 12(4):415–426, 1991.

[Lis91]     R. Liska. Numerical code generation for finite difference schemes solving. In R. Vichnevetsky and J.J.H. Miller, editors, IMACS’91 13th World Congress on Computation and Applied Mathematics, July 22-26, 1991, pages 92–93, Dublin, 1991. IMACS.

[LM94]     Eugenio Roanes Lozano and Eugenio Roanes Macias. An implementatio of “turtle graphics” in maple v. In Tony Scott, editor, Maple in Mathematics and the Sciences - Maple Technical Newsletter Special Issue, pages 82–85. Birkhäuser, 12 1994.

[Loo82]     R. Loos. Computing in Algebraic Extensions, pages 173–187. Springer Vienna, Vienna, 1982.

[Loo83]     Rüdiger Loos. Computing rational zeros of integral polynomials by \(p\)-adic expansion. SIAM J. Computing, 12(2):286–293, 1983.

[Mac88]     M. A. H. MacCallum. An ordinary differential equation solver for REDUCE. In Proc. of ISSAC ’88, volume 358, pages 196–205. Springer-Verlag, 1988.

[Mac89]     M. A. H. MacCallum. An ordinary differential equation solver for reduce. In P. Gianni, editor, Symbolic and Algebraic Computation, pages 196–205, Berlin, Heidelberg, 1989. Springer Berlin Heidelberg.

[Mac99]     M. A. H. MacCallum. On the Classification of the Real Four-Dimensional Lie Algebras, pages 299–317. Springer New York, New York, NY, 1999.

[MAE\(^{+}\)62]     John McCarthy, Paul W. Abrahams, Daniel J. Edwards, Timothy P. Hart, and Michael I. Levin. LISP 1.5 Programmer’s Manual. M.I.T. Press, Aug 1962.

[Man94]     Y.-K. Man. Algorithmic Solution of ODEs and Symbolic Summation Using Computer Algebra. PhD thesis, School of Mathematical Sciences, Queen Mary and Westfield College, University of London, July 1994.

[Man96]     Elizabeth L. Mansfield. The differential algebra package diffgrob2. Mapletech, 3(2):33–37, 1996.

[Mar93]     Jed Marti. RLISP ’88 An Evolutionary Approach to Program Design and Reuse, volume 42 of World Scientific Series in Computer Science. World Scientific, Singapore, 1993.

[Mar09]     M. Marvan. Sufficient set of integrability conditions of an orthonomic system. Foundations of Computational Mathematics, 9:652–674, Jan 2009.

[McI85]     Kevin McIsaac. Pattern matching algebraic identities. SIGSAM Bulletin, 19(2):4–13, May 1985.

[McK78]     Brendan D. McKay. Computing automorphisms and canonical labellings of graphs. In D. A. Holton and Jennifer Seberry, editors, Combinatorial Mathematics, pages 223–232, Berlin, Heidelberg, 1978. Springer Berlin Heidelberg.

[Mel95]     Herbert Melenk. Reduce symbolic mode primer. Technical report, Konrad-Zuse-Institut, 1995.

[MF93]     E Mansfield and E D Fackerell. Differential gröbner bases and involutivity of systems of non-linear partial differential equations. Preprint 92/108, School of Mathematics, Physics, Computer Science, and Electronics, Macquarie University, Sydney, Australia, 1993.

[MHGG80]    J. Marti, A. C. Hearn, M. L. Griss, and C. Griss. Standard Lisp report. SIGSAM Bulletin, 14(1):23–41, February 1980.

[Mis93]     Bhubaneswar Mishra. Algorithmic Algebra. Monographs in Computer Science. Springer, New York, 1993.

[MM86]     H. Michael Möller and Ferdinando Mora. New constructive methods in classical ideal theory. Journal of Algebra, 100(1):138–178, 1986.

[MM97]     Yiu-Kwong Man and Malcolm A. H. MacCallum. A rational approach to the prelle-singer algorithm. Journal of Symbolic Computation, 24(1):31–43, Jul 1997.

[MMM91]     M. G. Marinari, H. M. Möller, and T. Mora. Gröbner bases of ideals given by dual bases. In Watt [Wat91].

[MMN88]     H. Melenk, H. M. Möller, and W. Neun. On Gröbner bases computation on a supercomputer using REDUCE. Preprint SC 88-2, Konrad-Zuse-Zentrum für Informationstechnik Berlin, January 1988.

[MN02]     H. Melenk and W. Neun. Rr: Parallel symbolic algorithm support for psl based reduce. Technical report, ZIB, 2002.

[Möl93]     H. Michael Möller. On decomposing systems of polynomial equations with finitely many solutions. Applicable Algebra in Engineering, Communication and Computing, 4(4):217–230, 1993.

[MPT92]     Teo Mora, Gerhard Pfister, and Carlo Traverso. An Introduction to the Tangent Cone Algorithm. JAI Press, 1992.

[MR88]     Teo Mora and Lorenzo Robbiano. The gröbner fan of an ideal. Journal of Symbolic Computation, 6(2-3):183–208, Oct 1988.

[MY73]     Joel Moses and David Y. Y. Yun. The ez gcd algorithm. In ACM Annual Conference, pages 159–166. Association for Computing Machinery, 08 1973.

[ND79]     A. C. Norman and J. H. Davenport. Symbolic integration - the dust settles? In Proc. EUROSAM 1979, volume 72 of Lecture Notes in Computer Science, pages 398–407. Springer-Verlag, 1979.

[NM77]     A. C. Norman and P. M. A. Moore. Implementing the new Risch integration algorithm. In Proc. of the Fourth Colloquium on Advanced Comp. Methods in Theor. Phys., St. Maximin, France, March 1977.

[NM81]     Arthur C. Norman and Mary Ann Moore. Implementing a polynomial factorization and gcd package. In SYMSAC ’81: Proceedings of the fourth ACM symposium on Symbolic and algebraic computation, pages 109–116. Association for Computing Machinery, 08 1981.

[NNS05]     F. Neyzi, Y. Nutku, and M. B. Sheftel. Multi-hamiltonian structure of plebanski’s second heavenly equation. Journal of Physics A, 38(39):8473, 2005.

[Nuc92]     C. M. Nucci. Interactive REDUCE programs for calculating classical, non-classical, and approximate symmetries of differential equations, pages 345–350. Elsevier, Amsterdam, 1992.

[Nuc96]     Maria Clara Nucci. Interactive REDUCE programs for calculating Lie point, non-classical, Lie-Bäcklund, and approximate symmetries of differential equations: Manual and floppy disk, volume 3 of CRC Handbook of Lie Group Analysis of Differential Equations, pages 415–481. CRC Press, Boca Raton, Jan 1996.

[NUS91]     Arnold F. Nikiforov, Vasilii B. Uvarov, and Sergei K. Suslov. Classical Orthogonal Polynomials of a Discrete Variable. Springer Verlag, Berlin–Heidelberg–New York, 1991.

[NV]     A. C. Norman and R. Vitolo. Inside reduce. Part of the official REDUCE documentation included in the source code.

[OK94]     A. W. Overhauser and Y. J. Kim. An infinite sum from a diffusion problem. SIAM Review, 36(1):107, 1994.

[Oli]     P. Oliveri. ReLie, Reduce software and user guide. online.

[Olv86]     Peter J. Olver. Applications of Lie Groups to Differential Equations, volume 107 of Graduate Texts in Mathematics. Springer Verlag, New York, 1986.

[Olv93]     Peter J. Olver. Applications of Lie Groups to Differential Equations, volume 107 of Graduate Texts in Mathematics. Springer-Verlag New York, 2nd edition, 1993.

[PB90]     Julian Padget and Alan Barnes. Univariate power series expansions in REDUCE. In S. Watanabe and Morio Nagata, editors, Proceedings of the International Symposium on Symbolic and Algebraic Computation, pages 82–87. ACM, Addison-Wesley, 1990.

[PBM89]     A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev. Integrals and Series, Volume 3: More Special Functions. Gordon and Breach Science Publishers, Oct 1989. Transl. from the Russian by G. G. Gould.

[Pos96]     G. F. Post. A manual for the package TOOLS 2.1. Memorandum 1331, Dept. Appl. Math., University of Twente, 1996.

[PR95]     P. Paule and A. Riese. A mathematica \(q\)-analogue of zeilberger’s algorithm based on an algebraically motivated approach to \(q\)-hypergeometric telescoping. In Fields Proceedings of the Workshop ’Special Functions, \(q\)-Series and Related Topics, pages 179–210, Toronto, Ontario, 12-23 June 1995. Fields Institute for Research in Mathematical Sciences at University College.

[PS83]     M. J. Prelle and M. F. Singer. Elementary first integrals of differential equations. Transactions of the American Mathematical Society, 279:215–229, 1983.

[PS95]     Peter Paule and Markus Schorn. A MATHEMATICA version of zeilberger’s algorithm for proving binomial coefficient identities. Journal of Symbolic Computation, 20(5–6):673–698, Nov 1995.

[PV15]     Maxim V. Pavlov and Raffaele. Vitolo. On the bi-hamiltonian geometry of wdvv equations. Letters in Mathematical Physics, 105(8):1135–163, Aug 2015.

[PZ96]     F. Postel and P. Zimmermann. A Review of the ODE Solvers of AXIOM, DERIVE, MAPLE MATHEMATICA, MACSYMA, MUPAD and REDUCE. In Proceedings of the 5th Rhine Workshop on Computer Algebra, April 1-3, 1996, Saint-Louis, France, 1996. Specific references are to the version dated April 11, 1996.

[PZ97]     Zoran Putnik and Budimac Zoran. Implementation of turtle graphics for teaching purposes. In EDUGRAPHICS ’97. Third International Conference on Graphics Education. COMPUGRAPHICS ’97. Sixth International Conference on Computational Graphics and Visualization Techniques. Combined Proceedings, 01 1997.

[Red]     Obtaining REDUCE.

[Rei90]     G. J. Reid. A triangularization algorithm which determines the lie symmetry algebra of any system of pdes. Journal of Physics A, 23(17):L853–L859, 1990.

[Rei91]     Gregory J. Reid. Algorithms for reducing a system of pdes to standard form, determining the dimension of its solution space and calculating its taylor series solution. European Journal of Applied Mathematics, 2(4):293–318, 1991.

[Riq10]     C. Riquier. Les systèmes d’équations aux dérivées partielles. Gauthier–Villars, Paris, 1910.

[RLW93]     R. R. Loos and V. Weispfenning. Applying linear quantifier elimination. The Computer Journal, 36:450–462, Jan 1993.

[RLW01]     Gregory J. Reid, Ping Lin, and Allan D. Wittkopf. Differential elimination–completion algorithms for dae and pdae. Studies in Applied Mathematics, 106(1):1–45, 2001.

[Roa]     Kelly Roach. Difficulties with trigonometrics. Notes of a talk.

[Rob89]     Lorenzo Robbiano. Computer and commutative algebra. In Teo Mora, editor, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, pages 31–44, Berlin, Heidelberg, 1989. Springer Berlin Heidelberg.

[Roe92a]     G. H. M. Roelofs. The INTEGRATOR package for REDUCE, Version 1.0. Memorandum 1100, Dept. Appl. Math., University of Twente, 1992.

[Roe92b]     G. H. M. Roelofs. The SUPER VECTOR FIELD package for REDUCE, Version 1.0. Memorandum 1099, Dept. Appl. Math., University of Twente, 1992.

[RT89]     A.Ya. Rodionov and A.Yu. Taranov. Combinatorial aspects of simplification of algebraic expressions. In James H. Davenport, editor, Eurocal ’87, pages 192–201, Berlin, Heidelberg, 1989. Springer Berlin Heidelberg.

[Rut92]     Elizabeth W. Rutman. Gröbner bases and primary decomposition of modules. Journal of Symbolic Computation, 14(5):483–503, Nov 1992.

[RWB96]     Gregory J. Reid, Allan D. Wittkopf, and Alan Boulton. Reduction of systems of nonlinear partial differential equations to simplified involutive forms. European Journal of Applied Mathematics, 7(6):635–666, 1996.

[Sch85a]     Eberhard Schrüfer. Excalc: A system for doing calculations in modern differential geometry, user’s manual. Technical report, Rand Publication, The Rand Corporation, Santa Monica, 1985.

[Sch85b]     F. Schwarz. Automatically determining symmetries of partial differential equations. Computing, 34(2):91–106, Jun 1985.

[Sch85c]     F. Schwarz. Automatically determining symmetries of partial differential equations. Computing, 34(2):91–106, November 1985.

[Sch87]     Fritz Schwarz. Computer algebra and differential equations of mathematical physics. Technical report, GMD internal report, 1987.

[Sch88]     F. Schwarz. Symmetries of differential equations: From Sophus Lie to computer algebra. SIAM Review, 30(3):450–481, 1988.

[Sch92]     Franziska Schoebel. The symbolic classification of real four-dimensional lie algebras. Technical Report Preprint 27/92, Naturwissenschaftlich-Theoretisches Zentrum, Universitaet Leipzig, Germany, 1992.

[Sch93]     Carsten Schöbel. A classification of real finite-dimensional lie algebras with a low-dimensional derived algebra. Reports on Mathematical Physics, 33(1–2):175..186, Aug–Oct 1993.

[Sei95]     W M Seiler. Applying axiom to partial differential equations. Internal Report 95-17, Universität Karlsruhe, Fakultät für Informatik, 1995.

[Sei10]     Werner M. Seiler. Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra, volume 24 of Algorithms and Computation in Mathematics. Springer Verlag Berlin Heidelberg, 2010.

[Ser77]     Jean-Pierre Serre. Linear Representations of Finite Groups, volume 42 of Graduate Texts in Mathematics. Springer, New York, NY, 1977.

[SF79]     Eduard Stiefel and Albert Fässler. Gruppentheoretische Methoden und ihre Anwendung. Teubner, Stuttgart, 1979.

[Sim71a]     Charles C. Sims. Computation with permutation groups. In S. R. Petrick, editor, Proceedings of the Second ACM Symposium on Symbolic and Algebraic Manipulation, SYMSAC ’71, page 23–28, New York, NY, USA, 1971. Association for Computing Machinery.

[Sim71b]     Charles C. Sims. Determining the conjugation classes of a permutation group. In G. Birckhoff and M. Hall Jr., editors, Computer in Algebra and Number Theory, volume 4 of SIAM-AMS Proceedings, pages 191–195. American Mathematical Society, 1971.

[SLT65]     Pascual Sconzo, A. R. Leschack, and Robert G. Tobey. Symbolic computation of f and g series by computer. The Astronomical Journal, 70:269, May 1965.

[Spi59]     Murray R. Spiegel. Vector Analysis. Schaum’s Outline. McGraw-Hill Education (India) Pvt Limited, 1959.

[Spi79]     Michael Spivak. A comprehensive introduction to differential geometry. Publish or Perish, Berkeley, 1979.

[Ste89]     Hans Stephani. Differential equations, Their solution using symmetries. Cambridge University Press, 1989.

[Sto90]     Timothy Stokes. Gröbner bases in exterior algebra. Journal of Automated Reasoning, 6(3):233–250, Sep 1990.

[Str93]     Volker Strehl. Binomial sums and identities. Maple Technical Newsletter, 10:37–49, 1993.

[SV14]     Giuseppe Saccomandi and Raffaele Vitolo. On the mathematical and geometrical structure of the determining equations for shear waves in nonlinear isotropic incompressible elastodynamics. Journal of Mathematical Physics, 55(8):081502, 2014.

[SW06]     Vladimir V Sokolov and Thomas Wolf. Integrable quadratic classical hamiltonians on so(4) and so(3, 1). Journal of Physics A: Mathematical and General, 39(8):1915, feb 2006.

[Tar48]     A. Tarski. A decision method for elementary algebra and geometry. Technical report, University of California, 1948. Second edn., rev. 1951.

[Tho37]     Joseph Miller Thomas. Differential systems, volume 21. American Mathematical Soc., 1937.

[Tou84]     David S. Touretzky. LISP: A Gentle Introduction to Symbolic Computation. Harper & Row, New York, 1984.

[Tra76]     Barry M. Trager. Algebraic factoring and rational function integration. In Richard D. Jenks, editor, SYMSAC ’76: Proceedings of the Third ACM Symposium on Symbolic and Algebraic Computation, SYMSAC ’76, pages 196–208, New York, NY, USA, 1976. ACM.

[Vit]     CDE: a reduce package for computations in geometry of Differential Equations. Available at https://gdeq.org.

[Vit19]     R. Vitolo. Computing with hamiltonian operators. Comput. Phys. Commun., 244:228–245, 2019. ArXiv: https://arxiv.org/abs/1808.03902.

[Wah93]     Hugo D Wahlquist. Monte carlo calculation of cartan characters: using the maximal-slicing, ricci-flat ideal as an example. In Nora Bretón, Riccardo Capovilla, and Tonatiuh Matos, editors, Proceedings, 12th International School-Seminar on The Actual Problems of Microworld Physics. Vol.1: Gomel, Belarus, July 22 - September 28, 2013, pages 168–174, 1993.

[War91]     M. Warns. Software extensions of reduce for operator calculus in quantum theory. In Proceedings of the IV international Conference on Computer Algebra in Physical Research, Dubna 1990. WORLD SCIENTIFIC, 1991.

[Wat91]     Stephen M. Watt, editor. ISSAC ’91. Proceedings of the 1991 international symposium on Symbolic and algebraic computation. Bonn, Germany, July 15–17, 1991, New York, NY, USA, 1991. ACM.

[WB]     Thomas Wolf and Andreas Brand. Demonstration of the reduce package crack for investigating partial differential equations. online.

[Wei88]     Volker Weispfenning. The complexity of linear problems in fields. Journal of Symb, 5(1–2):3–27, Feb 1988.

[Wei92]     Volker Weispfenning. Comprehensive Gröbner bases. Journal of Symbolic Computation, 14(1):1–29, July 1992.

[Wei94]     Volker Weispfenning. Quantifier elimination for real algebra – the cubic case. In Symbolic and Algebraic Computation, ISSAC, pages 258–263. SIGSAM, ACM, 1994.

[Wei97]     V. Weispfenning. Quantifier elimination for real algebra — the quadratic case and beyond. Applicable Algebra in Engineering, Communication and Computing, 8(2):85–101, Jan 1997.

[WH81]     Patrick Winston and Berthold Horn. LISP. Addison-Wesley, 1981.

[Wil90]     Herbert S. Wilf. Generatingfunctionology. Academic Press, Boston, 1990.

[Wil93]     Herbert S. Wilf. Identities and their computer proofs. 1993. A series of lectures delivered at the U.S. National Security Agency.

[Wir80]     M. C. Wirth. On the Automation of Computational Physics. PhD thesis, Lawrence Livermore National Lab., CA., jan 1980.

[Wol93]     T. Wolf. An efficiency improved program liepde for determining lie-symmetries of pdes. In Proc. of Modern Group Analysis: advanced analytical and computational methods in mathematical physics, Catania, Italy, October 1992, pages 377–385. Kluwer Academic Publishers, 1993.

[Wol95]     Thomas Wolf. APPLYSYM - a package for the application of Lie-symmetries, 1995. Software distributed together with the computer algebra system REDUCE.

[Wol00]     Thomas Wolf. The symbolic integration of exact pdes. Journal of Symbolic Computation, 30(5):619–629, 2000.

[Wol02a]     T. Wolf. A comparison of four approaches to the calculation of conservation laws. Euro. Jnl of Applied Mathematics, 13(2):129–152, 2002.

[Wol02b]     Thomas Wolf. Size reduction and partial decoupling of systems of equations. Journal of Symbolic Computation, 33(3):367–383, 2002.

[Wri97]     F. J. Wright. An Enhanced ODE Solver for REDUCE. Programmirovanie, 3:5–22, 1997.

[Wri99]     F. J. Wright. Design and Implementation of ODESolve 1+ : An Enhanced REDUCE ODE Solver. Technical report, Queen Mary, University of London, May 1999.

[Wt87]     Wu Wen-tsun. A zero structure theorem for polynomial-equations-solving and its applications. In Proceedings of the European Conference on Computer Algebra, EUROCAL ’87, page 44, Berlin, Heidelberg, 1987. Springer-Verlag.

[WW69]     E. T. Whittaker and G. N. Watson. A Course in Modern Analysis. Cambridge University Press, 1969.

[ZB96]     A. Yu. Zharkov and Yu. A. Blinkov. Involution approach to investigating polynomial systems. Mathematics and Computers in Simulation, 42:323–332, 11 1996.

[Zei90]     D. Zeilberger. A fast algorithm for proving terminating hypergeometric identities. Discrete Math., 80(2):207–211, March 1990.

[Zei91]     D. Zeilberger. The method of creative telescoping. Journal of Symbolic Computation, 11(3):195–204, 1991.

[Zwi92]     D. Zwillinger. Handbook of Differential Equations. Academic Press, second edition, 1992.