#8530: affine patches of projective curves should be affine curves
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Reporter: AlexGhitza | Owner: AlexGhitza
Type: defect | Status: new
Priority: minor | Milestone: sage-4.3.4
Component: algebraic geometry | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Let C be a projective curve. At the moment, the method {{{affine_patch}}}
is just the generic one for projective schemes. In particular, this
returns a subscheme of the affine plane:
{{{
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| Sage Version 4.3.3, Release Date: 2010-02-21 |
| Type notebook() for the GUI, and license() for information. |
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sage: R.<x, y, z> = QQ[]
sage: C = Curve(x^3 + y^3 - z^3)
sage: C
Projective Curve over Rational Field defined by x^3 + y^3 - z^3
sage: C.affine_patch(2)
Closed subscheme of Affine Space of dimension 2 over Rational Field
defined by:
x0^3 + x1^3 - 1
}}}
Of course, this is actually an affine curve, and it would make more sense
for {{{C.affine_patch()}}} to return an affine curve, in our example:
{{{
sage: Curve(C.affine_patch(2).defining_polynomials()[0])
Affine Curve over Rational Field defined by x0^3 + x1^3 - 1
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8530>
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