#17792: Word problem for FareySymbol
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Reporter: mmasdeu | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.7
Component: modular forms | Resolution:
Keywords: farey symbol, | Merged in:
SL2Z, word problem | Reviewers:
Authors: Marc Masdeu | Work issues:
Report Upstream: N/A | Commit:
Branch: | 18e034409e8b62c81821e93132a11dd15d7fd432
public/ticket/17792 | Stopgaps:
Dependencies: |
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Comment (by cremona):
I agreed with Marc to take a look at this ticket, and now I have done so I
am almost regretting it!
We surely all agree that the functionality exposed here is something we
definitely all want to have aceesible to Sage users. The only issues are
(1) whether to use 1-based or 0-based numbering for the generator indices;
and (2) whether the word_problem / factorization function should return
the actual generators as matrices, or their indices.
Is that a fiar summary of where we are so far?
In reply to Marc's worry about having to do a lot of linear searches to
find out which generator a given generator is, it would be possible to
have a dict of { gens[i]:i } pairs instead.
There could be two options to the word_problem function. One could return
a list of (gen, exponent) pairs where gen is an actual matrix. One could
return a list of (index, exponent) pairs. The only option where 0-basing
causes difficulties is where what is returned is a simple list of signed
indices where +i means the i'th gen while -i means its inverse (and i=0 is
not allowed). To me this looks like a technical internal representation
which need not be exposed to the user.
I am only (so far) trying to clarify the remaining issues. Have I managed
that?
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Ticket URL: <http://trac.sagemath.org/ticket/17792#comment:14>
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