Geodesic
Multivariate Polynomials in Sage
Séminaire lotharingien de combinatoire, Tome 66 (2011-2012)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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. 

@article{SLC_2011-2012_66_a4,
     author = {Viviane Pons},
     title = {Multivariate {Polynomials} in {Sage}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {66},
     year = {2011-2012},
     url = {http://geodesic.mathdoc.fr/item/SLC_2011-2012_66_a4/}
}
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AU  - Viviane Pons
TI  - Multivariate Polynomials in Sage
JO  - Séminaire lotharingien de combinatoire
PY  - 2011-2012
VL  - 66
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2011-2012_66_a4/
ID  - SLC_2011-2012_66_a4
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%0 Journal Article
%A Viviane Pons
%T Multivariate Polynomials in Sage
%J Séminaire lotharingien de combinatoire
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%U http://geodesic.mathdoc.fr/item/SLC_2011-2012_66_a4/
%F SLC_2011-2012_66_a4
Viviane Pons. Multivariate Polynomials in Sage. Séminaire lotharingien de combinatoire, Tome 66 (2011-2012). http://geodesic.mathdoc.fr/item/SLC_2011-2012_66_a4/