PROGRAM SUMMARY
Title of program:
DiffElim
Catalogue identifier:
ADOI
Ref. in CPC:
139(2001)192
Distribution format: tar gzip file
Operating system: Linux/ix86
High speed store required:
16M K words
Number of lines in distributed program, including test data, etc:
131674
Keywords:
Differential elimination, Differential Grobner basis,
Symbolic computation, Computer algebra.
Programming language used: C
Computer:
PII 333MHz computer .
Nature of problem:
Differential Elimination of linear and polynomially nonlinear systems of
ODE/PDE with coefficients in Z[x1, ..., xn], where x1, .., xn are the
independent variables.
Method of solution:
Application of an elimination process bearing some similarity to both
Grobner Basis methods, and Gauss Elimination, but generalized to systems
of PDE.
Restrictions:
The algorithm is restricted to systems of PDE that are fully polynomial
in their dependent and independent variables. No special functions
(such as sin, cos, exp, ln), fractional exponents, or rational
numbers/expressions are allowed.
The implementation is currently under development. All results used as
benchmarks in the paper can be obtained from the current program, but
many of the features discussed (such as the program running in Rif-mode)
are incomplete.
The current implementation only uses full reduction, for which some
problems fail to terminate (depending on the degree of nonlinearity).
A later release of the program will have these restrictions removed, but
it will still be possible to run the program in full reduction mode, as
partial results of the computations running with full reduction often
yield information that is useful in simplification of the input system.
Typical running time:
The presented implementation has a counterpart with some similarity
implemented in the symbolic programming language Maple (RifSimp). For
the presented benchmark systems, the new implementation/algorithm has a
running time of (on average)1/400 of that of RifSimp. Note that the
more difficult results of the paper require at most 5 minutes on a PII
333MHz machine.
Unusual features:
The program is only capable of running on a Linux/x86 platform at this
time.