Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multivariate Polynomials in Sage   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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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
3
The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat