#19660: Fix bug in word problem for GammaH arithmetic groups
-------------------------------------+-------------------------------------
Reporter: mmasdeu | Owner:
Type: defect | Status: needs_review
Priority: minor | Milestone: sage-6.10
Component: modular forms | Resolution:
Keywords: Farey symbol, | Merged in:
word problem, GammaH | Reviewers:
Authors: Marc Masdeu | Work issues:
Report Upstream: N/A | Commit:
Branch: u/mmasdeu/19660 | a03bf5981fa080bceb31cc4783f6e85b93e5aa0d
-farey-check | Stopgaps:
Dependencies: |
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Comment (by mmasdeu):
Here is an example check of correctness:
{{{
N = 147
G = GammaH(N,[8])
gens = G.generators()
ngens = len(gens)
F = G.farey_symbol()
# Test that both generators and their inverses give the right one-letter
word.
for i,g in enumerate(gens):
assert F.word_problem(g,output = 'standard') == tuple([i+1])
assert F.word_problem(g**-1,output = 'standard', check = True) ==
tuple([-i-1])
# Test some random words
for ntests in range(200):
print 'ntests = %s'%ntests
a, b, c = ZZ.random_element(ngens), ZZ.random_element(ngens),
ZZ.random_element(ngens)
g = gens[a]**-5 * gens[b]**2 * gens[c]**-1
wd = F.word_problem(g, output = 'syllables')
assert g == prod(gens[j]**n for j,n in wd)
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/19660#comment:3>
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