Processing math: 100%

First time here? Check out the FAQ!

Ask Your Question
1

Implement mapping symmetric polynomial to Laurent polynomial

asked 9 years ago

rogervanpeski gravatar image

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 x0,y0,x1,y1, how can we output this polynomial under the map sending yi to x1i? I'm specifically looking to apply this to Hall-Littlewood polynomials if that helps.

Preview: (hide)

1 Answer

Sort by » oldest newest most voted
0

answered 9 years ago

nbruin gravatar image

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:

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
Preview: (hide)
link

Comments

That's exactly what I needed, thanks!

rogervanpeski gravatar imagerogervanpeski ( 9 years ago )

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

Stats

Asked: 9 years ago

Seen: 319 times

Last updated: Jul 28 '15