Substituting variables in instances of elements of SymmetricFunctions of polynomial rings

SymmetricFunctions

asked 2024-03-06 18:30:53 +0200

yeetcode

25 ●8

updated 2024-03-07 06:12:13 +0200

I am working with

R.<q,t> = PolynomialRing(QQ)

Q = R.fraction_field()

Sym = SymmetricFunctions(Q)

following which I declare Ht = Sym.macdonald().Ht(). I would now like to evaluate Ht for different relations between q, t. As an example, I would like to be able to compute Ht[2,1,1] with the substitution q -> q and t -> 1.

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I mean being able to evaluate something like Ht[2,1,1] but with the substitution q=t or t=1.

yeetcode ( 2024-03-07 06:10:30 +0200 )edit

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answered 2024-03-07 18:05:41 +0200

Max Alekseyev

5733 ●5 ●37 ●123

updated 2024-03-07 18:06:30 +0200

Is this what you want?

Ht = Sym.macdonald().Ht()
Ht_2 = Sym.macdonald(q=t, t=1).Ht()

f = q*Ht[3,2,1] + t*Ht[2,1,1]
print( Ht_2(f) )

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Seems to be doing the job quite alright. I find it unintuitive and restrictive that the substitution has to be made into Sym.macdonald(), but given that the list of substitutions I'm interested in is very small, I can indeed create a fixed few instances and be happy with it. Thanks! How (if at all) can I make a feature request for element-wise substitution?

yeetcode ( 2024-03-07 21:44:36 +0200 )edit

You can submit a feature request at https://github.com/sagemath/sage/issues

Max Alekseyev ( 2024-03-07 23:51:50 +0200 )edit

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Asked: 2024-03-06 18:30:53 +0200

Seen: 165 times

Last updated: Mar 07

Substituting variables in instances of elements of SymmetricFunctions of polynomial rings edit

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