#10506: efficient counting of cusps for the principal congruence subgroup
Gamma(n)
-----------------------------+----------------------------------------------
Reporter: rje | Owner: John Cremona
Type: enhancement | Status: new
Priority: minor | Milestone: sage-4.6.1
Component: modular forms | Keywords: cusps, ncusps(), Gamma(n),
principal congruence subgroup
Author: Ron Evans | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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In the sage-support group, John Cremona suggested writing a ticket aimed
at replacing the current code for G.ncusps, where G is the principal
congruence subgroup Gamma(n), with more efficient code. Please make a
patch using the following replacement code. This new code will compute
say Gamma(15).ncusps() in less than a second, instead of the hours it
takes with the current code.
n=self.level()
if n<=2:
return[None,1,3][n]
return ZZ((1/2)*sum([moebius(d)*(n/d)*(n/d) for d in n.divisors()]))
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10506>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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