How do you factor Schubert Polynomials in Sage?

combinatorics

asked 2013-03-15 17:18:37 +0100

mjoyce
3 ●2

I am interested in factoring (sums of) Schubert polynomials using Sage (which uses Singular). Here's my input attempt:

> X = SchubertPolynomialRing(QQ)

> f = X([5,4,2,6,1,3]).expand(); f

> f.factor()

However, while the second line gives a correct output, x0^4*x1^3*x2^2*x3 + x0^4*x1^3*x2*x3^2, when I try to factor this output, I get the following error message: "NotImplementedError: Factorization of multivariate polynomials over non-fields is not implemented."

I don't know how to get Sage to recognize a SchubertPolynomialRing as being over a field. Any suggestions?

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answered 2013-03-22 11:51:06 +0100

This post is a wiki. Anyone with karma >750 is welcome to improve it.

This is because the defaut base ring is ZZ and not QQ.

sage: X = SchubertPolynomialRing(QQ)
sage: f = X([5,4,2,6,1,3]).expand(); f
x0^4*x1^3*x2^2*x3 + x0^4*x1^3*x2*x3^2
sage: f.parent()
Multivariate Polynomial Ring in x0, x1, x2, x3, x4, x5 over Integer Ring
sage: f.change_ring(QQ)
x0^4*x1^3*x2^2*x3 + x0^4*x1^3*x2*x3^2
sage: f.change_ring(QQ).factor()
x3 * x2 * (x2 + x3) * x1^3 * x0^4
sage:

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Thank you -- this helped a lot!

mjoyce ( 2013-05-24 14:28:59 +0100 )edit

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Asked: 2013-03-15 17:18:37 +0100

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Last updated: Mar 22 '13

How do you factor Schubert Polynomials in Sage? edit

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