Ask Your Question

# Substitution in Expression of Symmetric Functions over Polynomial Ring

Hi everyone! So I'm working in the ring of symmetric functions over a polynomial ring, say $\mathbb{Q}[q]$, and I have an expression of the form

$$q^2s_{2,1} + (q-1)s_{1,1,1}$$

I want to perform the substitution $q = q+1$ in this expression, but all of the usual methods (subs, substitute, etc.) give me an error. Does anyone know how to do this?

Thanks in advance!

edit retag close merge delete

## 1 Answer

Sort by » oldest newest most voted

Like this

sage: q=polygen(QQ,'q')
sage: s=SymmetricFunctions(q.parent()).s()
sage: f=q*s([4])+(q-1)*s([3,2])
sage: f.map_coefficients(lambda q:q+1)
q*s[3, 2] + (q+1)*s[4]

more

## Comments

Thank you so much!

( 2021-04-06 23:19:22 +0100 )edit
2

In f.map_coefficients(lambda q:q+1), the parameter q has nothing to do with the variable q defined above. One should better use f.substitute({q:q+1}) for replacing the defined variable q with q+1.

( 2021-04-07 15:51:57 +0100 )edit

## Your Answer

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

Add Answer

## Stats

Asked: 2021-04-06 08:12:11 +0100

Seen: 268 times

Last updated: Apr 06 '21