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multiplicity of a point in a scheme

asked 2019-03-13 17:13:41 +0200

coste gravatar image

updated 2023-01-09 23:59:50 +0200

tmonteil 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.

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answered 2019-03-13 18:39:43 +0200

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()
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Asked: 2019-03-13 17:13:41 +0200

Seen: 280 times

Last updated: Mar 13 '19