multiplicity of a point in a scheme

asked 2019-03-13 17:13:41 +0100

coste
11 ●1

updated 2023-01-09 23:59:50 +0100

tmonteil
27423 ●31 ●204 ●517 http://wiki.sagemath.o...

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 +0100

rburing

10929 ●4 ●80 ●218 https://www.rburing.nl/

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 +0100

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Last updated: Mar 13 '19

multiplicity of a point in a scheme edit

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