Hello, > I'm a bit confused about Sage's answer if Ideal(1) is prime. > > R.<x,y>= QQ[] > I = Ideal(R(1)) > I.is_prime() > > Sage (5.11, not only) says yes, > conflicting to the definition, > http://en.wikipedia.org/wiki/Prime_ideal > Has somebody an expanation of this behaviour?
The example Singular session below suggests that the problem lies in Singular (I'm not too familiar with Singular, but I think the answers should all be the same, and only primdecSY(J) seems to be correct). Peter $ sage -singular SINGULAR / Development A Computer Algebra System for Polynomial Computations / version 3-1-5 0< by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann \ Jul 2012 FB Mathematik der Universitaet, D-67653 Kaiserslautern \ > LIB "primdec.lib" (...) > ring R = 0, (x, y), dp; > ideal I = 1; > primdecSY(I); [1]: [1]: _[1]=1 [2]: _[1]=1 > primdecGTZ(I); [1]: [1]: _[1]=1 [2]: _[1]=1 > ideal J = x, x + 1; > primdecSY(J); empty list > primdecGTZ(J); [1]: [1]: _[1]=1 [2]: _[1]=1 -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.