#16953: Faster enumeration of points for toric varieties
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Reporter: vbraun | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: | Reviewers:
Authors: Volker Braun | Work issues:
Report Upstream: N/A | Commit:
Branch: | 266d921d01f02e1301fb9e2981599fd17d71b152
u/vbraun/faster_enumeration | Stopgaps:
Dependencies: |
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Description changed by vbraun:
Old description:
> This ticket implements a specialized enumerator for points of a toric
> variety over a finite field. It uses linear algebra to solve the
> rescaling relations. It also parallelizes the enumeration of points for
> subvarieties of toric varieties.
New description:
This ticket implements a specialized enumerator for points of a toric
variety over a finite field. It uses linear algebra to solve the rescaling
relations. It also parallelizes the enumeration of points for subvarieties
of toric varieties.
For example:
{{{
$ cat quintic.sage
p = 3
for k in range(1, 5):
F = GF(p^k, 'a')
P4.<z0,z1,z2,z3,z4> = toric_varieties.P(4, base_ring=F)
X = P4.subscheme(z0^5+z1^5+z2^5+z3^5+z4^5-5*z0*z1*z2*z3*z4)
print k, X.point_set().cardinality()
$ time sage quintic.sage
1 36
2 816
3 20691
4 688800
real 14m37.378s
user 136m37.989s
sys 0m18.268s
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/16953#comment:4>
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