Ask Your Question
1

multiplicity of a point in a scheme

asked 2019-03-13 11:13:41 -0600

coste gravatar image

updated 2019-03-13 12:40:06 -0600

rburing gravatar image

The commands A1.<x>=AffineSpace(1, QQ) X=A1.subscheme([x^1789+x]) Q=X([0]) Q.multiplicity() result in 1789. There seems to be a bug in the multiplicity command for subschemes of the line.

edit retag flag offensive close merge delete

1 answer

Sort by ยป oldest newest most voted
0

answered 2019-03-13 12:39:43 -0600

rburing gravatar image

Yes, this is a bug. Typing Q.multiplicity?? we see that it calls X.multiplicity(Q) and X.multiplicity?? shows that it changes the monomial ordering to negdegrevlex and then tries to use the interface to Singular. However the interface to Singular is broken for univariate polynomial rings with "local" monomial ordering (it always uses the global ordering instead); I reported this as trac ticket #27479.

As a temporary workaround I guess you can add a variable and set it to zero:

sage: A2.<x,y> = AffineSpace(QQ,2)
sage: X = A2.subscheme([x^1789+x,y])
sage: Q = X([0,0])
sage: Q.multiplicity()
1
edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

Stats

Asked: 2019-03-13 11:13:41 -0600

Seen: 68 times

Last updated: Mar 13