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?   For comparison:
sage: I.<F> = QQ[] 
sage: P.<z, q> = I[] 
sage: e = z*q 
sage: Q.<z, q> = QQ[] 
sage: z*e
z^2*q 

Martin
On Friday 12 January 2024 at 16:08:55 UTC+1 Martin R wrote:

> I am fighting with various bugs involving substitution / composing into 
> polynomials, mostly involving the InfinitePolynomialRIng, for example 
> https://github.com/sagemath/sage/issues/37047
>
> I would appreciate help *a lot*.
>
> The background is, that I have mostly implemented a solver for lazy series 
> given implicitly by a list of equations.  It works now for univariate 
> series, but it would be really cool if I could get to work also for 
> multivariate series and symmetric functions. See 
> https://github.com/sagemath/sage/pull/37033
>
> Although it is not completely obvious that this will eventually work, it 
> is quite obvious that it won't work as long as we don't get sage to compose 
> polynomials correctly.
>
> Best wishes,
>
> Martin
>

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