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Séminaire Lotharingien de Combinatoire, B66z (2011), 18 pp.

# Viviane Pons

# Multivariate Polynomials in Sage

**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.

Received: July 4, 2011.
Accepted: July 14, 2011.

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