Hi! On Sep 1, 8:31 am, Nathann Cohen <[email protected]> wrote: > Could you tell me why there does not seem to be any support for inequalities > in InfinitePolynomialRing ?
Because what you call "inequalities" are symbolic expressions. InfinitePolynomialRing has nothing to do with symbolics. It is about some very recent development in commutative algebra, namely 1. polynomials over a countably infinite set of variables x[1],x[2],x [3],... 2. "symmetric ideals", i.e., ideals that are invariant under variable permutations. The amazing fact is that an InfinitePolynomialRing R, though not noetherian as a ring, is noetherian as an RG_\infty-module, where G_ \infty is the infinite permutation group acting on the indices of the variables. In other words, every "symmetric ideal" can be finitely generated up to sums, multiplication by elements of R, and variable permutation. And using Aschenbrenner's and Hillar's version of Groebner theory, one can solve "symmetric ideal membership" and "symmetric ideal equality" problems. Those things are explained in the Sage documentation. > I would like to express general inequalities of the form x[1] + x[2] < x[3], > but each time I evaluate it I get a boolean, which is not quite what I would > like to keep of the expressopn :-/ x[1] + x[2] < x[3] is not an expression. It is simply a test which of the two polynomials is smaller, in the monomial ordering of the ring. > Besides, what is the meaning of this boolean ? x[1] + x[2] < x[3] returns "True", and this simply means that the leading monomial of x[1] + x[2] is smaller in the monomial ordering of the ring than x[3]. By the way, in an InfinitePolynomialRing one will always have x[1]<x[2]<x[3]< ... However, if you want to use InfinitePolynomialRing as a comfortable way to create symbolic expressions, you can easily do so: sage: SR(x[1]+x[2])<SR(x[3]) x1 + x2 < x3 Now, SR(x[1]+x[2])<SR(x[3]) is a symbolic expression in the symbolic variables x1,x2,x3. I have no idea how one can solve inequalities, though. That's not my field of expertise. Best regards, Simon --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
