Substitution in Expression of Symmetric Functions over Polynomial Ring

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

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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!

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answered 2021-04-06 09:21:38 +0100

FrédéricC

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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]

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Thank you so much!

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

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.

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

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

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Last updated: Apr 06 '21

Substitution in Expression of Symmetric Functions over Polynomial Ring edit