We present two algorithms to compute a regular differential system for some ranking, given an equivalent regular differential system for another ranking. Both make use of Kähler differentials. One of them is a lifting for differential algebra of the FGLM algorithm and relies on normal forms computations of differential polynomials and of Kähler differentials modulo differential relations. Both are implemented in MAPLE V. A straightforward adaptation of FGLM for systems of linear PDE is presented too. Examples are treated.
Publié le : 2000-07-05
Classification:
Euler equations for perfect fluids,
differential algebra,
Kähler differentials,
FGLM,
Euler equations for perfect fluids.,
[MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC],
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],
[INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC]
@article{hal-00139738,
author = {Boulier, Fran\c cois},
title = {Efficient computation of regular differential systems by change of rankings using K\"ahler differentials},
journal = {HAL},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00139738}
}
Boulier, François. Efficient computation of regular differential systems by change of rankings using Kähler differentials. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00139738/