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
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