#15148: Make count_points() faster
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Reporter: goncalves | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-6.0
Component: algebraic geometry | Resolution:
Keywords: | Merged in:
Authors: Cécile Gonçalves | Reviewers:
Report Upstream: N/A | Work issues:
Branch: u/goncalves/ticket/15148 | Commit:
Dependencies: | Stopgaps:
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Comment (by jantuitman):
When you only want the number of rational points (and not the complete
zeta function) you can use a (g times) lower precision. In this case you
shouldn't use .frobenius_polynomial but ._frobenius_matrix and compute the
trace of this matrix.
It is not necessary to exclude the case n>2g, but in this case (and
already for n>=g) it is probably better to use .frobenius_polynomial and
compute the number of points by expanding a power series (as we discussed
in Rennes).
So:
1) for n<g use ._frobenius_matrix to compute matrix F and compute the
traces of F, ... ,F^n.
2) for n>=g use .frobenius_polynomial and compute the coefficients of the
log of the zeta function.
Would you like to change this, or can I give it a try? (I'm at SAGE days
this week, trying to do something useful)
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Ticket URL: <http://trac.sagemath.org/ticket/15148#comment:3>
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