Software
Synopsis: 24 software packages mainly for Mathematica (commercial
software), some for Macsyma (commercial software).
The Macsyma program symmgpr.max for Liepoint 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.

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).

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).

Ü. Göktas and W. Hereman,
DDERecursionOperator.m
:
A Mathematica package for the symbolic computation of recursion operators
for systems of nonlinear differentialdifference equations (2010).

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.

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).

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.

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).

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).

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).

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).

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).

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).

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).

D. Baldwin and W. Hereman,
PainleveTestV32013.m:
:
A Mathematica package for the Painleve test of systems of nonlinear
ordinary and partial differential equations (20012009).
Last updated by Unal Goktas: June 23, 2013.
Code: PainleveTestV32013.m is compatible with Mathematica v. 8 and 9.

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.

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).

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).

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).

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 program in C++ and manual were used in the "Bulldozer
Project."
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: Sunday, August 25, 2013