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I am having a problem working in sagemath with the following series. In Maple, I could define $$n(d):= \sum_{k=1}^{d} schur((k,1^{d-k}))\prod_{\square \in (k,1^{d-k})}G(c(\square)h) \tag{*}$$ where schur is function is usual schur function I have created using character formula. $G(h)$ is a series in $h$. The $c(\square)$ is the content of the young tableaux. For example in case of $d=3$ 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 the similar thing in sagemath with jack polynomials instead of schur polynomial. 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 field of rational, even when I define a new variable in sage var('h') I cannot multiply $JJ[2,1] $ and $h$ it gives error hence I cannot compute $*$ with jack polynomial in sagemath. I am sure there is a way around. Please let me know

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

$$n(d):= \sum_{k=1}^{d} schur((k,1^{d-k}))\prod_{\square \operatorname{schur}((k,1^{d-k}))\prod_{\square \in (k,1^{d-k})}G(c(\square)h) \tag{*}$$ \tag{*}$$

where schur is function is \operatorname{schur} is the usual schur function I have created created using character formula. $G(h)$ is a series in $h$. $h$. The $c(\square)$ is the content of the young Young tableaux. For example in case of $d=3$ it can be read as follows $$schur([1,1,1])G(h)G(2h)

$$ \operatorname{schur}([1,1,1]) G(h) G(2h) - schur([2,1])G(h)G(-h)+ schur([3])G(2h)G(h)$$\operatorname{schur}([2,1]) G(h) G(-h) + \operatorname{schur}([3]) G(2h) G(h) $$

I wanted to do the a similar thing in sagemath with jack SageMath with Jack polynomials instead of schur polynomial. Schur polynomials.

Hence I defined

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

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

$$n(d):= \sum_{k=1}^{d} \operatorname{schur}((k,1^{d-k}))\prod_{\square \in (k,1^{d-k})}G(c(\square)h) (k,1^{d-k})} \, G(c(\square)h) \tag{*}$$

where \operatorname{schur} where

• $\operatorname{schur}$ is the usual schur function function I have created created using the character formula. formula,
• $G(h)$ is a series in $h$. The $h$,
• the $c(\square)$ is the content of the Young tableaux. tableaux.

For example in case of for $d=3$ it can be read as follows

$$ \operatorname{schur}([1,1,1]) \, G(h) \, G(2h) - \operatorname{schur}([2,1]) \, G(h) \, G(-h) + \operatorname{schur}([3]) \, G(2h) \, G(h) $$

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.

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

$$n(d):= \sum_{k=1}^{d} \operatorname{schur}((k,1^{d-k}))\prod_{\square \in (k,1^{d-k})} \, G(c(\square)h) \tag{*}$$

where

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

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

$$ \operatorname{schur}([1,1,1]) \, G(h) \, G(2h) - \operatorname{schur}([2,1]) \, G(h) \, G(-h) + \operatorname{schur}([3]) \, G(2h) \, G(h) $$

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.