Dear Sage Support group, I've been trying some simple operations with ideals in polynomial rings with ZZ coefficients in Sage 4.1, and I have been puzzled by some of the results:
1. If I define a polynomial ring and ideal using, say sage: R.<x> = PolynomialRing(ZZ) sage: J = R.ideal(x^2 - 3, 25 + 6*x, 20 + 7*x) , then J does not have access to the methods available for ideals in multivariable polynomial rings such as groebner_basis. Is this to be expected? Is there a clean way to get access to the other methods? The methods that are available for ideals such as J seem either not to be implemented (e.g. is_prime) or not to work properly. Consider, for example, sage: R.ideal(x^2 - 5, 2) == R.ideal(x^2 - 3, 2) False 2. If I do add an extra variable to get access to the multivariable- polynomial-ring methods, then I can get a Groebner basis, but it does not look completely standardized. Consider, for example, sage: S.<x,y> = PolynomialRing(ZZ) sage: L = S.ideal(x^2 - 3, 10 + 2*x, 11) sage: L.groebner_basis() [x - 50, 11] . I might have expected to get [x+5, 11], which looks more reduced to me (and matches the behavior of groebner_basis() for ideals in polynomial rings over QQ). This behavior is presumably something inherited from Singular, but I couldn't find the explanation its conventions for standard bases over ZZ in the Singular documentation. 3. Perhaps as a consequence of the not-completely-standardized Groebner bases, I get some strange answers as in (1.), even when I work in S: sage: M == S.ideal(x - 50, 11) True sage: M == S.ideal(x + 5, 11) False . On the other hand, we do have sage: x+5 in M True . (The analogous method in R is not implemented.) Regards, James Parson --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
