#11709: FareySymbol
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Reporter: hmonien | Owner: craigcitro
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.0
Component: modular forms | Resolution:
Keywords: Farey symbol | Work_issues:
Upstream: N/A | Reviewer: Martin Raum, Leif Leonhardy
Author: Hartmut Monien | Merged:
Dependencies: |
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Changes (by hmonien):
* milestone: => sage-5.0
Comment:
Since many things have changed in 4.7.2 I have decided to lump everything
in one new patch.
'''FareySymbol''' has been checked for special cases (not implemented in
the KFarey package) including the unique index two subgroup. It now
handles gracefully subgroups which contain SL2Z([-1, 1, -1, 0]).
The drawing of the fundamental domain has been changed slightly. The
coloring of the pairing has been changed to include the first and last
side.
The current algorithm for calculating the FareySymbol is O(n!^2) where n
is the index of the subgroup which is the general case. This could be
improved to O(n) for Gamma0, Gamma1 and Gamma as Georg Weber pointed out.
The current algorithm runs for about a second to calculate all properties
of the FareySymbol for Gamma(16) with index 1536. This is probably
satisfactory at the moment (and still much faster than Magma).
The documentation has been corrected.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11709#comment:23>
Sage <http://www.sagemath.org>
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