On Friday 1 March 2024 at 04:26:43 UTC-8 Dima Pasechnik wrote: It seems that exactly the same algorithm will work (I didn't check this!) for Laurent polynomials (they still form a Euclidean domain), and there you better set degree(0)=-oo, otherwise it's going to be a problem.
I think it's been established that LaurentPolynomialRing(QQ,'x').zero().degree() == -1 is problematic. With the definition that (1/x).degree() == -1 it clearly is. I think the question is more: do we have enough evidence that setting degree(0) == -oo for *all* polynomial rings is significantly better (if better at all) that it's worth the pain and incompatibilities that would ensue from changing the rest of sage as well? That's not so clear to me. >From the perspective of multivariate polynomials, the whole valuation interpretation of "degree" goes out of the window, so there "-1" is largely available and quite possibly used extensively by the underlying libraries. I guess one could see what happens if the change is made to Laurent polynomials (and Laurent series as well, perhaps?). Based on how that goes one could re-evaluate degrees of 0 polynomials in other polynomial rings. Alternatively, we could deprecate degree on them in favour of using valuation-inspired terms instead, where the extension val(0)=oo is more universal. As Oscar's example in Matlab shows, the concept of degree gets (mis)used for other, more implementation-oriented definitions as well, so perhaps the term should just be avoided for Laurent polynomials. -- 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/60c42d22-28dc-4221-96a0-b174585c9c23n%40googlegroups.com.
