I'm working with ideals in the polynomial ring in three variables.
sage> R.<u,v,w>=QQ[]
sage> f=u*v-w
sage> g=u^2-v
sage> I=Ideal(f,g)
sage> I.is_prime()
True
sage> I.associated_primes()
[Ideal (v^2 - u*w, u*v - w, u^2 - v) of Multivariate Polynomial
Ring in u, v, w over Rational Field]
That last ideal is the same as I, since u(uv - w) - v(u^2-v) = v^2-uw.
So why do I get an extra generator?
Thanks,
Fernando
--
=============================================================
Fernando Q. Gouvea http://www.colby.edu/~fqgouvea
Carter Professor of Mathematics
Dept. of Mathematics and Statistics
Colby College
5836 Mayflower Hill
Waterville, ME 04901
So if a man's wit be wandering,let him study the mathematics; for in
demonstrations, if his wit be called away never so little, he must
begin again.
-- Francis Bacon, "Of Studies"
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