On Friday 12 January 2024 at 14:30:06 UTC-5 Martin R wrote:

I made a tiny bit of progress, and now face the following problem:

sage: I.<F> = InfinitePolynomialRing(QQ) 
sage: P.<z, q> = I[] 
sage: e = z*q 
sage: Q.<z, q> = QQ[] 
sage: z*e
z*z*q 

Is this correct behaviour?

I don't think it's desperately wrong. To sage, these structures look like:

sage: P.construction()
(MPoly[z,q], Infinite polynomial ring in F over Rational Field)
sage: Q.construction()
(MPoly[z,q], Rational Field)
sage: parent(z*e).construction()
(MPoly[z,q],
 Infinite polynomial ring in F over Multivariate Polynomial Ring in z, q 
over Rational Field)

Note that an "infinite polynomial ring" is a different object than an 
MPoly, and obviously it has different rules/priorities for finding common 
overstructures.
 

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