论文信息 - Efficient computation of regular differential systems by change of rankings using Kähler differentials

Efficient computation of regular differential systems by change of rankings using Kähler differentials

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 Kahler 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 Kahler 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.

François Boulier | François Boulier

[1] P. Olver. Equivalence, Invariants, and Symmetry: References , 1995 .

[2] Daniel Lazard,et al. Solving Zero-Dimensional Algebraic Systems , 1992, J. Symb. Comput..

[3] François Boulier,et al. Étude et implantation de quelques algorithmes en algèbre différentielle. (Study and implementation of some algorithms in differential algebra) , 1994 .

[4] David H. Bailey,et al. Analysis of PSLQ, an integer relation finding algorithm , 1999, Math. Comput..

[5] François Boulier,et al. Representation for the radical of a finitely generated differential ideal , 1995, ISSAC '95.

[6] Manuel Bronstein,et al. On Solutions of Linear Ordinary Difference Equations in their Coefficient Field , 2000, J. Symb. Comput..

[7] Donal O'Shea,et al. Ideals, varieties, and algorithms - an introduction to computational algebraic geometry and commutative algebra (2. ed.) , 1997, Undergraduate texts in mathematics.

[8] D. Eisenbud. Commutative Algebra: with a View Toward Algebraic Geometry , 1995 .

[9] P. Aubry,et al. Ensembles triangulaires de polynomes et resolution de systemes algebriques. Implantation en axiom , 1999 .

[10] Marc Moreno Maza,et al. Calculs de pgcd au-dessus des tours d'extensions simples et resolution des systemes d'equations algebriques , 1997 .

[11] François Lemaire,et al. Computing canonical representatives of regular differential ideals , 2000, ISSAC.