#11394: Scheme.is_projective() should use mathematical definition
----------------------------------+-----------------------------------------
Reporter: novoselt | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.1
Component: algebraic geometry | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
----------------------------------+-----------------------------------------
The current implementation of `is_projective` in
{{{
sage.schemes.generic.algebraic_scheme.AlgebraicScheme
}}}
is
{{{
return self.ambient_space().is_projective()
}}}
which in turn works as
{{{
def is_projective(self):
"""
Return whether this ambient space is projective n-space.
EXAMPLES::
sage: AffineSpace(3,QQ).is_projective()
False
sage: ProjectiveSpace(3,QQ).is_projective()
True
"""
# overloaded in the projective space derived class
return False
}}}
Both are wrong. It is possible to have a projective scheme sitting in a
non-projective variety, as well as an ambient space which is projective,
yet it is not a projective n-space.
There are methods that rely on this behavior, so they should be fixed and
the above methods changed so that they either answer the question "Is X a
projective scheme?" in the mathematical sense or raise a
`NotImplementedError` if the answer is unknown.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11394>
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 post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
