#5520: [with patch; needs review] implement Pizer's algorithm for computing
Brandt
Modules and Brandt Matrices
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Reporter: was | Owner: craigcitro
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.4.1
Component: modular forms | Keywords:
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Comment(by tornaria):
I suggest a change in interface for {{{BrandtModule}}}, namely, allow the
first parameter to be non-prime, and eliminate parameter r. IOW,
{{{BrandtModule(3,7,5)}}} becomes {{{BrandtModule(3^5,7)}}}:
{{{
BrandtModule(N, M=1, weight=2, base_ring=Rational Field, use_cache=True)
}}}
The rules are:
- N and M must be coprime
- the number of prime factors of N must be odd
- for starters, the prime factors of N must show up with odd power (can
accomodate p^2 factors eventually).
- the ramification of the quat. algebra is given by prime factors of N;
the discriminant of the order would be N*M
The current implementation is for prime N. Sould raise
{{{NotImplementedError}}} otherwise. As it is now, the {{{BrandtModule}}}
constructor succeeds, and the dimension formula works, but then
{{{hecke_matrix}}} gives wrong results.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5520#comment:11>
Sage <http://sagemath.org/>
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