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Using symmetric function package and multiplication in sagemath

asked 3 years ago

Anupamsage gravatar image

updated 1 year ago

FrédéricC gravatar image

I am having a problem working in SageMath with the following series. In Maple, I could define

n(d):=dk=1schur((k,1dk))(k,1dk)G(c()h)

where

  • schur is the usual schur function I have created using the character formula,
  • G(h) is a series in h,
  • the c() is the content of the Young tableaux.

For example for d=3 it can be read as follows

schur([1,1,1])G(h)G(2h)schur([2,1])G(h)G(h)+schur([3])G(2h)G(h)

I wanted to do a similar thing in SageMath with Jack polynomials instead of Schur polynomials.

Hence I defined

Sym = SymmetricFunctions(QQ)
JJ = Sym.jack(t=1).J()
s = Sym.schur()

I can see that I have defined the symmetric function over the field of rationals. Even when I define a new variable in Sage with var('h') I cannot multiply JJ[2,1] and h -- it gives an error -- hence I cannot compute () with Jack polynomials in SageMath.

I am sure there is a way around. Please let me know.

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answered 3 years ago

Max Alekseyev gravatar image

I'd advise against using symbolic variables. Since you want power series in h, you can define a ring of them upfront and then symmetric functions over that ring:

R.<h> = PowerSeriesRing(QQ)
Sym = SymmetricFunctions(R)
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Thanks a lot

Anupamsage gravatar imageAnupamsage ( 3 years ago )
1

answered 3 years ago

rburing gravatar image

Define

Sym = SymmetricFunctions(SR)

instead.

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Thanks a lot

Anupamsage gravatar imageAnupamsage ( 3 years ago )

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Asked: 3 years ago

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Last updated: Feb 13 '22