ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 28 Jul 2015 14:27:52 -0500Implement mapping symmetric polynomial to Laurent polynomialhttps://ask.sagemath.org/question/28717/implement-mapping-symmetric-polynomial-to-laurent-polynomial/ How can you implement transforming a symmetric polynomial into a Laurent polynomial by mapping some variables to the inverses of others? In other words, given, say, a polynomial in $x_0,y_0,x_1,y_1$, how can we output this polynomial under the map sending $y_i$ to $x_i^{-1}$? I'm specifically looking to apply this to Hall-Littlewood polynomials if that helps.Mon, 27 Jul 2015 17:01:08 -0500https://ask.sagemath.org/question/28717/implement-mapping-symmetric-polynomial-to-laurent-polynomial/Answer by nbruin for <p>How can you implement transforming a symmetric polynomial into a Laurent polynomial by mapping some variables to the inverses of others? In other words, given, say, a polynomial in $x_0,y_0,x_1,y_1$, how can we output this polynomial under the map sending $y_i$ to $x_i^{-1}$? I'm specifically looking to apply this to Hall-Littlewood polynomials if that helps.</p>
https://ask.sagemath.org/question/28717/implement-mapping-symmetric-polynomial-to-laurent-polynomial/?answer=28718#post-id-28718Is the fact that you're interested in symmetric polynomials relevant? For polynomial rings in general defining the homomorphism is quite straightforward, so I would expect that by restricting the map you'll also get it for symmetric polynomials:
sage: R.<x0,x1,y0,y1>=QQ[]
sage: S.<X0,X1>=LaurentPolynomialRing(QQ)
sage: H=Hom(R,S)
sage: m=H([X0,X1,X0^(-1),X1^(-1)])
sage: m(x0+2*x1+3*y0+4*y1)
X0 + 2*X1 + 4*X1^-1 + 3*X0^-1
Tue, 28 Jul 2015 01:29:19 -0500https://ask.sagemath.org/question/28717/implement-mapping-symmetric-polynomial-to-laurent-polynomial/?answer=28718#post-id-28718Comment by rogervanpeski for <p>Is the fact that you're interested in symmetric polynomials relevant? For polynomial rings in general defining the homomorphism is quite straightforward, so I would expect that by restricting the map you'll also get it for symmetric polynomials:</p>
<pre><code>sage: R.<x0,x1,y0,y1>=QQ[]
sage: S.<X0,X1>=LaurentPolynomialRing(QQ)
sage: H=Hom(R,S)
sage: m=H([X0,X1,X0^(-1),X1^(-1)])
sage: m(x0+2*x1+3*y0+4*y1)
X0 + 2*X1 + 4*X1^-1 + 3*X0^-1
</code></pre>
https://ask.sagemath.org/question/28717/implement-mapping-symmetric-polynomial-to-laurent-polynomial/?comment=28719#post-id-28719That's exactly what I needed, thanks!Tue, 28 Jul 2015 14:27:52 -0500https://ask.sagemath.org/question/28717/implement-mapping-symmetric-polynomial-to-laurent-polynomial/?comment=28719#post-id-28719