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 Liepoint symmetries of
differential equations has been adapted to Maxima
(i.e., DOEMacsyma, 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.
A Mathematica implementation of the discrete homotopy operator for
inverting the forward difference operator (2003).
[Works for Mathematica 5. Has not been tested for Mathematica v. 6 and
higher.]
>

A. Cook, W. Hereman, and Ü. Göktas
HomogenizeAndSolveOct142012v1wh.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.]

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 (20122018).
[Works for Mathematica 7. Does not work for Mathematica 6 or lower.
Has not been tested yet for Mathematica v. 8 and higher.]

Ü. Göktas and W. Hereman,
DDERecursionOperator.m :
A Mathematica package for the symbolic computation of recursion operators
for systems of nonlinear differentialdifference equations (2010).
[Works for Mathematica 5. Has not been tested for Mathematica v. 6 and
higher.]

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. DOEMacsyma), 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.

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 DOEMacsyma).
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).

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.]

W. Hereman,
LaxPairLattices.m :
A Mathematica program for the symbolic computation of Lax pairs of
scalar twodimensional nonlinear partial difference equations defined
on quadgraphs (20072009).
Joint work with Reinout Quispel and Peter van der Kamp.
[Works for Mathematica 5. Has not been tested for Mathematica v. 6 and
higher.]

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.]

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.]

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.]

H. Eklund and W. Hereman,
DDEDensityFlux.m:
A Mathematica program for the symbolic computation of conserved densities
and fluxes for nonlinear systems of differentialdifference equations (2002).
[Works for Mathematica 5. Has not been tested for Mathematica v. 6 and
higher.]

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.]

W. Hereman and R. Kragler,
PDESpecialSolutionsV4Jul42020.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.]

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.]

D. Baldwin, Ü. Göktas, W. Hereman,
DDESpecialSolutions.m:
A Mathematica package for the symbolic computation of tanh solutions
for systems of nonlinear differentialdifference 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.]

D. Baldwin and W. Hereman,
PainleveTestV42018.m:
A Mathematica package for the Painleve test of systems of nonlinear
ordinary and partial differential equations (20012018).
Last updated by Willy Hereman: July 6, 2018.
[Works for the newest versions of Mathematica . Code
PainleveTestV42018.m is compatible with Mathematica
v. 7, 8, 9, 10 and 11.]

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 differentialdifference 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.]

Ü. Göktas and W. Hereman,
diffdens2009.m:
A Mathematica program for the symbolic computation of conserved densities
for systems of nonlinear differentialdifference equations (1997,
updated: 2009).
The original diffdens.m package was further developed into DDEDensityFlux.m
(20022007).
[Works for Mathematica 5. Has not been tested for Mathematica v. 6 and
higher.]

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.]

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.]

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.]

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
(19911995).
[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.]

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
(19911995).
[Works for Mathematica 5. Has not been tested for Mathematica v. 6 and
higher.]

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).

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).

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: Wednesday, June 22, 2022, at 2:00a.m.