On Thu, Nov 05, 2009 at 09:47:30AM +1100, Alex Ghitza wrote:
> 
> 
> 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



> 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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