#20676: Projective closure and affine patches for algebraic curves
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Reporter: gjorgenson | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-7.3
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: | Reviewers:
Authors: Grayson Jorgenson | Work issues:
Report Upstream: N/A | Commit:
Branch: | 39dd215adb96f07bc67854c5debd1f1b49c08032
u/gjorgenson/ticket/20676 | Stopgaps:
Dependencies: |
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Comment (by gjorgenson):
Okay, I actually just finished up an attempt to better manage the creation
of ambient spaces in the projective closure/affine patches computation. I
tried piggy-backing off of the existing projective_embedding and
affine_patch functionality for projective/affine spaces, and it seems to
be working so far. Things like:
{{{
P.<x,y,z,w> = ProjectiveSpace(QQ,3)
C = Curve([y*z - x^2,w^2 - x*y])
C.ambient_space() ==
C.affine_patch(0).projective_closure().ambient_space()
}}}
and
{{{
A.<x,y,z> = AffineSpace(QQ,3)
C = Curve([y-x^2,z-x^3])
C.ambient_space() ==
C.projective_closure().affine_patch(0).ambient_space()
}}}
should now return true. Is this the right way to keep track of everything?
I also found something that seems strange:
{{{
A.<x,y,z> = AffineSpace(QQ,3)
C = Curve([y-x^2,z-x^3])
A == C.ambient_space()
}}}
returns false. As far as I can tell, this isn't an issue for projective
space curves. Also, there seems to be an issue with the class structure of
space curves vs plane curves. Right now there is a
ProjectiveSpaceCurve_generic class, and a ProjectiveCurve_generic class,
with the latter corresponding to plane curves, but the plane curve class
does not inherit from the space curve class. Similarly for affine curves.
Is there a reason why plane curves shouldn't inherit from the space curve
class?
--
Ticket URL: <http://trac.sagemath.org/ticket/20676#comment:8>
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