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.Comment: 18 page
