Using symmetric function package and multiplication in sagemath
I am having a problem working in SageMath with the following series. In Maple, I could define
n(d):=d∑k=1schur((k,1d−k))∏◻∈(k,1d−k)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.