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



On Wed, Nov 04, 2009 at 08:34:52PM +0000, Willem Jan Palenstijn wrote:
> 
> Hi all,
> 
> 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 -- Lecturer in Mathematics -- The University of Melbourne
-- Australia -- http://www.ms.unimelb.edu.au/~aghitza/

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