#20676: Projective closure and affine patches for algebraic curves
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Reporter: gjorgenson | Owner:
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-7.3
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: | Reviewers: Ben Hutz
Authors: Grayson Jorgenson | Work issues:
Report Upstream: N/A | Commit:
Branch: | 0039d7b13dad64025ef70542f407bf3af7423e1a
u/gjorgenson/ticket/20676 | Stopgaps:
Dependencies: #20697, #20698 |
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Changes (by bhutz):
* status: needs_review => needs_work
* reviewer: => Ben Hutz
Comment:
- line 1916:
{{{R.ideal([R(f) for f in self.defining_polynomials()])}}}
could be replaced with
{{{self.defining_ideal()}}}
- projective closure should take projective space parameter
{{{
A.<x,y> = AffineSpace(QQ, 2)
P.<u,v,w>=ProjectiveSpace(QQ,2)
C = Curve([y-x^2], A)
D=C.projective_closure(1,P)
}}}
- Affine patch should take affine space parameter
{{{
A.<x,y> = AffineSpace(QQ, 2)
P.<u,v,w>=ProjectiveSpace(QQ,2)
C = Curve([u^2-v^2], P)
C.affine_patch(1,A)
}}}
- Affine patch should have a default patch and that default should match
up with the projective closure default
{{{
A.<x,y,z> = AffineSpace(GF(3), 3)
C = Curve([y-x^2,z-x^3], A)
D=C.projective_closure()
D.affine_patch()==C
}}}
- you should mention in the doc for projective embedding that the image is
the projective closure
--
Ticket URL: <http://trac.sagemath.org/ticket/20676#comment:15>
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