Hi David! On Nov 26, 9:07 am, David Kohel <drko...@gmail.com> wrote: > Rather I would say that "sparse" should be the default: > > P.<x> = InfinitePolynomialRing(QQ, implementation="sparse")
No. The main purpose of InfinitePolynomialRing is the computation of symmetric Groebner bases, and simply it turned out in examples that "sparse" is much slower in Groebner basis computations. > Moreover, this syntax (and for gens, etc.) is inconsistent > with PolynomialRing. Why? One possible way of creating a polynomial ring is sage: R.<x,y>=PolynomialRing(QQ) So, my syntax is perfectly consistent. > The syntax: > > PolynomialRing(ring, integer, sparse=True) > > would be a more coherent, where integer=Set(ZZ) would give > an infinite polynomial ring. Mathematically, let G be the symmetric group of the natural numbers. Then, PolynomialRing(QQ,x) is the free QQ(G) module with generator x. And, by work of Aschenbrenner and Hillar, it is actually noetherian as a QQ(G) module. And this implies at least three reasons why I don't like your suggestion. 1) An InfinitePolynomialRing is not just a polynomial ring with infinitely many variables. This is a point against using the PolynomialRing constructor for its creation. 2) The variables x[0],x[1],x[2],x[3],... are *not* considered the generators of an infinite polynomial ring. You would have just *one* generator x, and this one generator gives rise to an infinity of variables. So, it simply makes not much sense to define an infinite polynomial ring by an (infinite) list of variables. Again, my syntax is consistent, since InfinitePolynomialRing(QQ,'x') lists the *generators* of the object. 3) Sometimes one wants to have *several* generators of an infinite polynomial ring, and one wants to chose a *name* for the generator. Your suggestion does not address any of these points. Cheers, Simon -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
