Program LIE for Lie analysis of differential equations on IBM type PCs
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by
A. K. Head
CSIRO Division of Materials Science and Technology
Melbourne Australia

Postal: Locked Bag 33, Clayton, Vic 3168, Australia
Phone: (03) 542 2861
Telex: AA 32945
Fax: (03) 544 1128
E-mail: [email protected]

Equipment
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Any IBM type PC with at least 256k of free memory.
Any version of DOS.
An attached printer is very useful.

Contents of disk
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README.1ST This file.

MULIE.EXE The operating program.

LIE.DOC Read this for instructions.

MORELIE.DOC More information for those interested.

.DAT files Examples of differential equations you can run.
Read these to see how to write YOUR differential
equations and for the comments therein.

LIE.LIE Source code of LIE.

Update
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Version 3.1
(1) LIE is wrtten in MUMATH, the symbolic mathematics language for
IBM type PCs. Previous versions have required you to have the MUMATH
system. By generous permission of Soft Warehouse Inc, authors and
owners of MUMATH, this is no longer necessary. A limited version of
MUMATH is combined with LIE to give MULIE.EXE which is a complete
stand-alone operating program. Portions of the software are
copyrighted by Soft Warehouse Inc, 3616 Harding Av., Suite 505,
Honolulu, Hawaii 96816 USA, and are used by permission on a gratis,
as-is basis with no liability or support.

(2) With the cumulative improvements to the heuristics of program
LIE, including a new Op that adds integrability conditions to the
defining equations, there is now little need for the user to intervene
( by low level MUMATH operations ) in the solution process. A lot of
the previous documentation was to aid in this intervention and this
has now been much reduced. The MUMATH manual is really what you would
need.

Version 3.2
A multinomial GCD package has been added. This aids in reducing the
size of expressions by detecting and dividing out inessential factors.
Larger problems can now be run without exhausting memory.
If your DE contains symbolic functions or constants then there may
be special values of these that lead to different Lie symmetries. This
may occur in two ways, that a factor which is divided out may be zero
in special cases, or, when splitting a "polynomial", that functions
taken as linearly independent may not be so in special cases.
Selective information on these possibilities can be shown by ( say )
SHOW#:LIST(A,B,K) where the list contains the names of functions and
constants of interest. ( This is turned off by SHOW#:FALSE, the
default value). See SPECIALC.DAT and the non-linear heat equation
HEATNL.DAT.
IMPORTANT: All derivatives of a symbolic function in the DE must
be written as explicit derivatives with respect to the argument of the
function else LIE will misfunction. See HEATNL.DAT.

Version 3.3
Extensions to factorization and to information shown by SHOW#.