Multivariate Polynomials in Sage

Viviane Pons 1
1 Combinatoire algébrique
LIGM - Laboratoire d'Informatique Gaspard-Monge
Abstract : We have developed a patch implementing multivariate polynomials seen as a multi-base algebra. The patch is to be released into the software Sage and can already be found within the Sage-Combinat distribution. One can use our patch to define a polynomial in a set of indexed variables and expand it into a linear basis of the multivariate polynomials. So far, we have the Schubert polynomials, the Key polynomials of types A, B, C, or D, the Grothendieck polynomials and the non-symmetric Macdonald polynomials. One can also use a double set of variables and work with specific double-linear bases like the double Schubert polynomials or double Grothendieck polynomials. Our implementation is based on a definition of the basis using divided difference operators and one can also define new bases using these operators.
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Submitted on : Tuesday, May 21, 2013 - 11:13:44 AM
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  • HAL Id : hal-00824143, version 1


Viviane Pons. Multivariate Polynomials in Sage. Seminaire Lotharingien de Combinatoire, Université Louis Pasteur, 2011, 66 (B66z), pp.1-18. ⟨hal-00824143⟩



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