On Wednesday 17 January 2024 at 23:51:05 UTC-8 Martin R wrote: Over at https://github.com/sagemath/sage/pull/37033 I am hitting the following question:
Is it possible to have a ring UndeterminedCoefficientRing(R) which, for every functorial construction F(R) has pushout F(UndeterminedCoefficientRing(R)). I suspect that for QQ['x']['x'] you'll run into trouble. Also, I'd expect quotient constructions will have trouble commuting with your new functor: sage: R.<a,b>=QQ[] sage: I=R.ideal(a^2+b^2-1) sage: S=R.quo(I) sage: S.construction() (QuotientFunctor, Multivariate Polynomial Ring in a, b over Rational Field) although I don't think that's a fundamental obstruction. Another obstacle may be noncommutative group rings etc. Or (hinting at what you're describing later on already) when completions have been taken -- i.e., certain variables may occur as power series variables somewhere in the tower. A best effort attempt probably gives you a ring extension functor such that it has a pushout for many functorial constructions F. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/da483529-1a6e-4ef0-b228-10cf9e6c0b1en%40googlegroups.com.
