#7956: constructing a scheme morphism to an affine curve
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Reporter: wjp | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-4.3.1
Component: algebraic geometry | Keywords:
Work_issues: | Author:
Upstream: N/A | Reviewer:
Merged: |
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From http://groups.google.com/group/sage-
devel/browse_thread/thread/1f3d4eca8bbff6c2/d3108ab8f2060050
Ronald van Luijk encountered the following problem:
sage: S.<p,q> = QQ[]
sage: A1.<r> = AffineSpace(QQ,1)
sage: A1_emb = Curve(p-2)
sage: type(A1_emb)
<class 'sage.schemes.plane_curves.affine_curve.AffineCurve_generic'>
sage: g = A1.hom([2,r],A1_emb)
TypeError: _point_morphism_class() takes exactly 1 non-keyword argument (3
given)
We browsed through the schemes module a bit, and the functionality for a
morphism to an affine curve does seem to exist through functions such as
AlgebraicScheme_subscheme_affine._point_morphism_class(), but
is not accessible since AlgebraicScheme_subscheme_affine is not a
superclass of AffineCurve_generic. Comparing it to the projective case,
AlgebraicScheme_subscheme_projective _is_ a superclass of
ProjectiveCurve_generic.
Is this a simple oversight in the class hierarchy for AffineCurve_generic,
or is there a more fundamental reason why this does not yet work?
I made a patch (for sage 4.2) that makes the class hierarchy for affine
curves similar to that of projective curves, but would appreciate if
someone familiar with the schemes module could take a look since it is a
rather invasive change:
http://www.math.leidenuniv.nl/~wpalenst/sage/affine_morphism.patch
The patch also changes the constructor of
SchemeMorphism_on_points_affine_space to expect a number of polynomials
equal to the dimension of the ambient space instead of the dimension of
the curve/subscheme, analogous to a change to
SchemeMorphism_on_points_projective_space by David Kohel from 2007.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7956>
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