ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 27 Nov 2013 01:10:50 -0600Expand a polynomial into Schubert basishttp://ask.sagemath.org/question/10772/expand-a-polynomial-into-schubert-basis/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](http://combinat.sagemath.org/doc/reference/combinat/sage/combinat/multivariate_polynomials/multivariate_polynomials.html)
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. Sun, 24 Nov 2013 10:30:13 -0600http://ask.sagemath.org/question/10772/expand-a-polynomial-into-schubert-basis/Answer by Luca for <p>Hi,</p>
<p>I have a few polynomials, such as </p>
<pre><code>(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
</code></pre>
<p>and I would like to expand it into Schubert polynomials. The only way I've found is to use </p>
<pre><code>A = AbstractPolynomialRing(ZZ)
Schub = A.schubert_basis_on_vectors()
</code></pre>
<p>And use <code>Schub(from_expr(expr))</code> where I can plug in the polynomial that I have for expr. The documentation for AbstractPolynomialRing is here:
<a href="http://combinat.sagemath.org/doc/reference/combinat/sage/combinat/multivariate_polynomials/multivariate_polynomials.html">Multivariate Polynomials with Several Bases</a></p>
<p>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. </p>
http://ask.sagemath.org/question/10772/expand-a-polynomial-into-schubert-basis/?answer=15717#post-id-15717It 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/>.Sun, 24 Nov 2013 11:48:41 -0600http://ask.sagemath.org/question/10772/expand-a-polynomial-into-schubert-basis/?answer=15717#post-id-15717Comment by anh for <p>It looks like this is experimental code by the combinat group. See instructions on how to install the combinat patches here: <a href="http://wiki.sagemath.org/combinat/">http://wiki.sagemath.org/combinat/</a>.</p>
http://ask.sagemath.org/question/10772/expand-a-polynomial-into-schubert-basis/?comment=16609#post-id-16609Hi 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.Tue, 26 Nov 2013 13:05:29 -0600http://ask.sagemath.org/question/10772/expand-a-polynomial-into-schubert-basis/?comment=16609#post-id-16609Comment by Luca for <p>It looks like this is experimental code by the combinat group. See instructions on how to install the combinat patches here: <a href="http://wiki.sagemath.org/combinat/">http://wiki.sagemath.org/combinat/</a>.</p>
http://ask.sagemath.org/question/10772/expand-a-polynomial-into-schubert-basis/?comment=16605#post-id-16605Not 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.Wed, 27 Nov 2013 01:10:50 -0600http://ask.sagemath.org/question/10772/expand-a-polynomial-into-schubert-basis/?comment=16605#post-id-16605