On Tue, Apr 7, 2020 at 2:29 AM Fernando Gouvea <fqgou...@colby.edu> wrote: > > 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?
I think that it's a Groebner basis (w.r.t. the default monomial ordering) of the ideal in question. > > 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" > > -- > 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 view this discussion on the web visit > https://groups.google.com/d/msgid/sage-support/1f24f76e-7925-adbe-8e05-5648babaef4c%40colby.edu. -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CAAWYfq0Uu7tuV2irUYk8j6Zhv77C%2BhS64aYSe7babXOxpD%2B2Tg%40mail.gmail.com.
