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Software

Synopsis: 26 software packages (including some updates) mainly for Mathematica (commercial software), some for Macsyma (commercial software, now obsolete). The Macsyma program symmgpr.max for Lie-point symmetries of differential equations has been adapted to Maxima (i.e., DOE-Macsyma, a free computer algebra system in the public domain).

Most of the software has been developed with support of the National Science Foundation of the U.S.A.. Please acknowledge the software if it has been of use to you, either as a central or exploratory tool or for verification purposes. You can do this by refering to the web page where the software is located or to related publications.

NOTE (added December 2011, last updated July 4, 2020): The Mathematica software was developed for Mathematica versions 4 through 7 (depending on the package). Compatibility with newers versions of Mathematica, including v. 8, 9, 10, 11, and 12 is being tested and the packages are (slowly) being upgraded as specified below.
  1. A. Cook, W. Hereman, and Ü. Göktas Homogenize-And-Solve-Oct14-2012-v1-wh.m : A Mathematica program for the symbolic computation of solitary wave and soliton solutions of some scalar nonlinear evolution equations with polynomial terms (2012). [Works for Mathematica 5. May work for v. 6 and 7. Has not been tested for Mathematica v. 8 and higher.]
  2. T. J. Bridgman and W. Hereman, LaxPairPartialDifferenceEquations.m : A Mathematica package for the symbolic computation of Lax pairs of systems of nonlinear partial difference equations defined in quadrilaterals (2012-2018). [Works for Mathematica 7. Does not work for Mathematica 6 or lower. Has not been tested yet for Mathematica v. 8 and higher.]
  3. Ü. Göktas and W. Hereman, DDERecursionOperator.m : A Mathematica package for the symbolic computation of recursion operators for systems of nonlinear differential-difference equations (2010). [Works for Mathematica 5. Has not been tested for Mathematica v. 6 and higher.]
  4. W. Hereman, symmgrp2020.max : A Maxima program for the calculation of Lie point symmetries of large systems of differential equations (2020). The package symmgrp2020.max is an update of symmgrp2009.max and works under Maxima (a.k.a. DOE-Macsyma), a computer algebra system which can be freely downloaded from SourceForge. Our paper The computer calculation of Lie point symmetries of large systems of differential equations and the 2018 report Symmetry Analysis Using Symbolic Computation by E. J. Albright and J. D. McHardy serve as manuals. The notes Lie Symmetry Group Methods for Differential Equations provided by Faruk Güngör serve as theoretical background.
  5. W. Hereman and B. Huard, symmgrp2009.max: A Maxima program for the calculation of Lie point symmetries of large systems of differential equations (2009). The package symmgrp2009.max works under both the commercial computer algebra system Macsyma (now obsolete) and Maxima (the freely available DOE-Macsyma). Data and command files are available for either Macsyma (MacsymaFiles) or Maxima (MaximaFiles).
    The package symmgrp.max (written in 1991) was last updated in 2006. That code, still called symmgrp.max, only works under Macsyma, the commercial computer algebra system (now obsolete but some may still have a working copy).
  6. L.D. Poole and W. Hereman, ConservationLawsMD.m : A Mathematica package for the symbolic computation of conservation laws of systems of nonlinear partial differential equations in multiple space dimensions (2009). [Requires Mathematica 7. Does now work for Mathematica 5. Has not been tested for Mathematica v. 8 and higher.]
  7. W. Hereman, LaxPairLattices.m : A Mathematica program for the symbolic computation of Lax pairs of scalar two-dimensional nonlinear partial difference equations defined on quad-graphs (2007-2009). Joint work with Reinout Quispel and Peter van der Kamp. [Works for Mathematica 5. Has not been tested for Mathematica v. 6 and higher.]
  8. L.D. Poole and W. Hereman, HomotopyIntegrator.m : A Mathematica package for the application of the homotopy method for (i) integration by parts of expressions involving unspecified functions of one variable and (ii) the inversion of a total divergence involving unspecified functions of two or three independent variables (2009). [Works for Mathematica 5. Has not been tested for Mathematica v. 6 and higher.]
  9. D. Baldwin and W. Hereman, PDERecursionOperator.m : A Mathematica package for the symbolic computation of recursion operators for systems of nonlinear partial differential equations (2003, updated: 2009). [Works for Mathematica 5. Has not been tested for Mathematica v. 6 and higher.]
  10. P.J. Adams and W. Hereman, TransPDEDensityFlux.m: A Mathematica program for the symbolic computation of conserved densities and fluxes for systems of partial differential equations with transcendental nonlinearities (2002). [Works for Mathematica 5. Has not been tested for Mathematica v. 6 and higher.]
  11. H. Eklund and W. Hereman, DDEDensityFlux.m: A Mathematica program for the symbolic computation of conserved densities and fluxes for nonlinear systems of differential-difference equations (2002). [Works for Mathematica 5. Has not been tested for Mathematica v. 6 and higher.]
  12. J. Blevins, J. Heath, and W. Hereman, PDESolutionTester.m: A Mathematica program for the symbolic verification of exact solutions of nonlinear partial differential equations (2002). [Works for Mathematica 5. Has not been tested for Mathematica v. 6 and higher.]
  13. W. Hereman and R. Kragler, PDESpecialSolutionsV4-Jul4-2020.m: A Mathematica package for the symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for systems of nonlinear partial differential equations (last updated: July 4, 2020). [Works for Mathematica v.11 and v.12. Has not been tested for Mathematica v.10 or lower.]
  14. D. Baldwin, Ü. Göktas, W. Hereman, L. Hong, R. Martino, and J.C. Miller, PDESpecialSolutions.m: A Mathematica package for the symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for systems of nonlinear partial differential equations (2002, last updated: March 2010). [Works for Mathematica 5. Has not been tested for Mathematica v. 6 and higher.]
  15. D. Baldwin, Ü. Göktas, W. Hereman, DDESpecialSolutions.m: A Mathematica package for the symbolic computation of tanh solutions for systems of nonlinear differential-difference equations (2001, last updated: March 2010). 2001 version of program (with manual) was added to Computer Physics Communications Program Library, Queen's University of Belfast, North Ireland (2001). [Works for Mathematica 5. Has not been tested for Mathematica v. 6 and higher.]
  16. D. Baldwin and W. Hereman, PainleveTestV4-2018.m : A Mathematica package for the Painleve test of systems of nonlinear ordinary and partial differential equations (2001-2018). Last updated by Willy Hereman: July 6, 2018. [Works for the newest versions of Mathematica . Code PainleveTestV4-2018.m is compatible with Mathematica v. 7, 8, 9, 10 and 11.]
  17. Ü. Göktas and W. Hereman, InvariantsSymmetries.m: A Mathematica integrability package for the computation of invariants and symmetries of nonlinear systems of partial differential equations and differential-difference equations (1997, updated: 2009). Package also available at Wolfram Research Library Archive. [Works for Mathematica 5. Has not been tested for Mathematica v. 6 and higher.]
  18. Ü. Göktas and W. Hereman, diffdens2009.m: A Mathematica program for the symbolic computation of conserved densities for systems of nonlinear differential-difference equations (1997, updated: 2009). The original diffdens.m package was further developed into DDEDensityFlux.m (2002-2007). [Works for Mathematica 5. Has not been tested for Mathematica v. 6 and higher.]
  19. Ü. Göktas and W. Hereman, condens2009.m: A Mathematica program for the symbolic computation of conserved densities for systems of nonlinear evolution equations (1996). Software package has been improved and updated to run under Mathematica versions 3, 4, and 5 (updated: 2009). [Works for Mathematica 5. Has not been tested for Mathematica v. 6 and higher.]
  20. Ü. Göktas and W. Hereman, PAINSYS.MAX: A Macsyma program for the Painleve test of systems of nonlinear ordinary and partial differential equations (1995). [Note: Code was designed for Macsyma, the commercial computer algebra system. No guarantee that the code will work under Maxima, the public domain version of the computer algebra system.]
  21. W. Hereman and A. Miller, PAINMATH.M: A Mathematica program for the Painleve test of single nonlinear ordinary and partial differential equations (1995). Obsolete package; replaced by PainleveTest.m (Baldwin and Hereman). [Note: Code was designed for Macsyma, the commercial computer algebra system. No guarantee that the code will work under Maxima, the public domain version of the computer algebra system.]
  22. W. Hereman and W. Zhuang, HIROTA.MAX: A Macsyma program for the calculation of soliton solutions of certain nonlinear partial differential equations via Hirota's method (1991-1995).
    [Note: Code was designed for Macsyma, the commercial version of the computer algebra system. No guarantee that the code will work under Maxima, the public domain computer algebra system.]
  23. W. Hereman and W. Zhuang, hirota.m: A Mathematica program for the calculation of soliton solutions of certain nonlinear partial differential equations via Hirota's method (1991-1995). [Works for Mathematica 5. Has not been tested for Mathematica v. 6 and higher.]
  24. B. Champagne, W. Hereman, and P. Winternitz, symmgrp.max: A Macsyma program for the calculation of Lie point symmetries of large systems of differential equations (2006). [The package symmgrp.max, which is an updated version of the code written in 1991, works only under Macsyma, the commercial computer algebra system.] The 1991 version of symmgrp.max (with manual) is still available at the Computer Physics Communications Program Library, Queen's University of Belfast, North Ireland (1991).
  25. W. Hereman and W. Murphy, Trilater.c: The trilateration program.
    Proprietary software program in C++ and manual were used in the "Bulldozer Project in 1991. The software is now obsolete!" Developed for Thunder Basin Coal Company, Wright, Wyoming (1991).
  26. W. Hereman, PAINSING.MAX: A Macsyma program for the Painleve test of single nonlinear ordinary and partial differential equations (1989). The program appeared in Finite Dimensional Integrable Nonlinear Dynamical Systems, Eds.: P.G.L. Leach and W.-H. Steeb, World Scientific, Singapore, 1988. The program was featured in the Macsyma Newsletter, vol. 6, January 1989, Macsyma, Inc., Arlington, Massachusetts (1989). [Note: Code was designed for Macsyma, the commercial computer algebra system. No guarantee that the code will work under Maxima, the public domain version of the computer algebra system.]

Willy Hereman

Last updated: Friday, November 27, 2020