Programs in Physics & Physical Chemistry
|[Licence| Download | New Version Template] adoi_v1_0.tar.gz(645 Kbytes)|
|Manuscript Title: Fast differential elimination in C: the CDiffElim environment.|
|Authors: A.D. Wittkopf, G.J. Reid|
|Program title: DiffElim|
|Catalogue identifier: ADOI_v1_0|
Distribution format: tar.gz
|Journal reference: Comput. Phys. Commun. 139(2001)192|
|Programming language: C.|
|Computer: PII 333MHz computer.|
|Operating system: Linux/ix86.|
|RAM: 16M K words|
|Keywords: Differential elimination, Differential Grobner basis, Symbolic computation, Computer algebra.|
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.
Application of an elimination process bearing some similarity to both Grobner Basis methods, and Gauss Elimination, but generalized to systems of PDE.
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.
The program is only capable of running on a Linux/x86 platform at this 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.
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