#20790: Computing plane curve models for algebraic curves
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Reporter: gjorgenson | Owner:
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-7.3
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: gsoc2016 | Reviewers:
Authors: Grayson Jorgenson | Work issues:
Report Upstream: N/A | Commit:
Branch: | 0de1323a77147059de0f82c7a8642c44c31552ed
u/gjorgenson/ticket/20790 | Stopgaps:
Dependencies: |
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Changes (by gjorgenson):
* status: new => needs_review
Comment:
I implemented a function to project affine curves that allows the user to
specify coordinates to use in the projection. If the given coordinates
yield a projection that doesn't have a curve as its image, an error will
be raised. I also implemented a plane_projection function that doesn't
take any user input but just tries to find two coordinates that will yield
a projection that has a plane curve as its image. I think such a
projection should always exist, but right now my approach to finding one
is just trying all possible projections to two coordinates.
For projective curves, I added some functionality for working with curves
defined over finite fields. Now the projection function will test all of
the points of the ambient space of a curve over a finite field until it
finds a point not on the curve. An error is returned if the curve contains
all of the ambient space points.
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Ticket URL: <http://trac.sagemath.org/ticket/20790#comment:4>
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