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Expand a polynomial into Schubert basis

asked 2013-11-24 10:30:13 -0500

anh gravatar image

updated 2017-01-08 05:12:39 -0500

FrédéricC gravatar image

Hi,

I have a few polynomials, such as

(x1^3*x2 + x1^2*x2^2 + x1*x2^3 + x1^3*x3 + 2*x1^2*x2*x3 + 2*x1*x2^2*x3+ x2^3*x3)*x1^7*x2^5*x3^3*x4

and I would like to expand it into Schubert polynomials. The only way I've found is to use

A = AbstractPolynomialRing(ZZ)
Schub =  A.schubert_basis_on_vectors()

And use Schub(from_expr(expr)) where I can plug in the polynomial that I have for expr. The documentation for AbstractPolynomialRing is here: Multivariate Polynomials with Several Bases

However, it seems that AbstractPolynomialRing is not available in SAGE. I would really appreciate it if you know another way to do it, or point me to how to make this method work. Thank you.

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answered 2013-11-24 11:48:41 -0500

Luca gravatar image

It looks like this is experimental code by the combinat group. See instructions on how to install the combinat patches here: http://wiki.sagemath.org/combinat/.

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Hi Luca, thank you for the answer. I'm using the cloud notebook, so I'm not sure if that is possible. I'll try install SAGE on my machine then.

anh gravatar imageanh ( 2013-11-26 13:05:29 -0500 )edit

Not natively, indeed. But you can install your own version of sage (binary or from source) in a cloud project, see <https://github.com/sagemath/cloud/wiki/FAQ#wiki-own-sage-bin>. Then you can install combinat patches on top of it.

Luca gravatar imageLuca ( 2013-11-27 01:10:50 -0500 )edit

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Asked: 2013-11-24 10:30:13 -0500

Seen: 115 times

Last updated: Nov 24 '13