constructing a scheme morphism to an affine curve
Willem Jan Palenstijn
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.
-Willem Jan
P.S. A related issue is that the TypeError above looks incorrect. See ticket
#7389 for a small patch to correct that.
Alex Ghitza
Hi Willem Jan, Ronald,
I'm putting this on my todo list. About half a year ago I did some
work adding doctests and fixing/reorganising things with scheme
morphisms, but I didn't get a chance to finish. I'll try to have a
look at your patch soon.
And: thanks for working on this!
Best,
Alex
Alex Ghitza -- Lecturer in Mathematics -- The University of Melbourne
-- Australia -- http://www.ms.unimelb.edu.au/~aghitza/
Willem Jan Palenstijn
>
>
> Hi Willem Jan, Ronald,
>
>
> I'm putting this on my todo list. About half a year ago I did some
> work adding doctests and fixing/reorganising things with scheme
> morphisms, but I didn't get a chance to finish. I'll try to have a
> look at your patch soon.
I've created ticket #7956 for this.
-Willem Jan
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