#20676: Projective closure and affine patches for algebraic curves
-------------------------------------+-------------------------------------
Reporter: gjorgenson | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-7.3
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: | Reviewers:
Authors: Grayson Jorgenson | Work issues:
Report Upstream: N/A | Commit:
Branch: | 39dd215adb96f07bc67854c5debd1f1b49c08032
u/gjorgenson/ticket/20676 | Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Comment (by bhutz):
re: variable names.
The way this is handled for general affine and projective subschemes is to
allow the user to specify the space that it will be embedded into (or
dehomogenized into). This is better functionality than just specifying the
variable names, since you can then embedded different curves into the same
space.
re: ambient space
{{{
A.<x,y,z> = AffineSpace(QQ,3)
C = Curve([y-x^2,z-x^3])
A == C.ambient_space()
}}}
I haven't looked at the code, but it looks like Curve assumes you are
passing in elements from a polynomial ring and doesn't see if they are
actually from a particular affine space and hence creates a new affine
space. This is a bug. If you pass in elements of the coordinate ring of an
affine space, then the curve should be in that space. It may be that you
need to include an optional parameter for the space and/or perhaps have an
A.curve() function.
one last thought: Should these curve classes inherit from affine and
projective subscheme as well? This could save you a fair amount of code
duplication (such as for affine_patch and projective_embedding.
--
Ticket URL: <http://trac.sagemath.org/ticket/20676#comment:10>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
