#20930: Generalize multiplicity() and intersection_multiplicity() for subschemes
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Reporter: gjorgenson | Owner:
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-7.3
Component: algebraic | Resolution:
geometry |
Keywords: gsoc2016 | Merged in:
Authors: Grayson Jorgenson | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/gjorgenson/ticket/20930 | a655e09cec3ca127364d471d3c71ffab04122eea
Dependencies: | Stopgaps:
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Changes (by gjorgenson):
* status: new => needs_review
Old description:
> Currently there is a `multiplicity()` function for algebraic curves which
> computes the multiplicity of a point on a curve as the multiplicity of
> the maximal ideal in the local ring of the curve corresponding to that
> point. This definition still works for arbitrary projective/affine
> subschemes and it would be good to implement it in the more general case.
>
> Also, by using affine patches, it is possible to compute intersection
> multiplicities for subschemes of products of projective spaces, so it
> would be good to implement that here as well.
>
> These implementations should be made available to both the subscheme
> classes and corresponding point classes.
New description:
Currently there is a `multiplicity()` function for algebraic curves which
computes the multiplicity of a point on a curve as the multiplicity of the
maximal ideal in the local ring of the curve corresponding to that point.
This definition still works for arbitrary projective/affine subschemes and
it would be good to implement it in the more general case.
Also, by using affine patches, it is possible to compute multiplicities
and intersection multiplicities of points of subschemes of products of
projective spaces, so it would be good to implement that here as well.
These implementations should be made available to both the subscheme
classes and corresponding point classes.
--
Comment:
I had forgotten that intersection_multiplicity functions were already
implemented for points in #20811. I merged with 7.3 beta7 and added checks
to give nicer errors if multiplicity or intersection_multiplicity are
called for an ambient space point.
--
Ticket URL: <https://trac.sagemath.org/ticket/20930#comment:4>
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