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Software

Synopsis: 24 software packages mainly for Mathematica (commercial software), some for Macsyma (commercial software). The Macsyma program symmgpr.max for Lie-point symmetries of differential equations has been adapted to Maxima (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 and/or to related publications.

NOTE (added December 2011): The Mathematica software was developed for Mathematica versions 4 through 7. Compatibility with Mathematica v. 8 and 9 is being tested. As specified below per individual code, the packages are being updated to run under Mathematica v. 8 and 9.
  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).
  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).
  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).
  4. W. Hereman and B. Huard, symmgrp2009.max : A Macsyma/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 and Maxima, a computer algebra system which can be freely downloaded from SourceForge.
    Notes: Maxima v. 5.16.3 is prefered because wmMaxima (0.7.6) is easier to work with. The code symmgrp2009.max has been tested (and works fine) for Maxima versions 5.16.3 through 5.20.1. WARNING: the code does NOT WORK under Maxima v. 5.21.0 through 5.23.2 (due to a problem with the depends function which hopefully will be fixed in v. 5.24.0). Data and command files are available for either Macsyma (MacsymaFiles) or Maxima (MaximaFiles). The package symmgrp.max (written in 1991) was updated in 2006. The updated code, symmgrp.max , only works under Macsyma, the commercial computer algebra system.
  5. 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).
  6. 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.
  7. 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).
  8. 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).
  9. 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).
  10. 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).
  11. 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).
  12. 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).
  13. 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).
  14. D. Baldwin and W. Hereman, PainleveTestV3-2013.m: : A Mathematica package for the Painleve test of systems of nonlinear ordinary and partial differential equations (2001-2009). Last updated by Unal Goktas: June 23, 2013. Code: PainleveTestV3-2013.m is compatible with Mathematica v. 8 and 9.
  15. 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.
  16. 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).
  17. 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).
  18. 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.]
  19. 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.
  20. 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.
  21. 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).
  22. 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).
  23. W. Hereman and W. Murphy, Trilater.c: The trilateration program.
    Proprietary program in C++ and manual were used in the "Bulldozer Project." Developed for Thunder Basin Coal Company, Wright, Wyoming (1991).
  24. 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: Sunday, August 25, 2013