Add a more efficient implementation of index for Gamma(N).

[simon-king-jena]

Gamma(N).index used the default implementation which was slow. Attached is a new implementation which works for the specific subgroup.

CC: @roed314

Component: modular forms

Author: Simon Morris

Reviewer: John Cremona, David Roed

Merged: Sage 4.1.1.alpha1

Issue created by migration from https://trac.sagemath.org/ticket/6606

[simon-king-jena]

Attachment: gamma.patch.gz

[JohnCremona]

comment:1

The code loooked (though I would have written p**(3e-2)(p*p-1) ) but after applying to 4.1:

sage: Gamma(19).index()
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)

/home/john/.sage/temp/ubuntu/25083/_home_john__sage_init_sage_0.py in <module>()

/home/john/sage-4.1/local/lib/python2.6/site-packages/sage/modular/arithgroup/congroup_gamma.pyc in index(self)
    105             32893086819240
    106         """
--> 107         return prod([p**(3*e) - p**(3*e-2) for (p,e) in self.level().factor()])
    108 

Looks like someone forgot to run sage -t before submitting the patch...

[JohnCremona]

Reviewer: John Cremona

[simon-king-jena]

comment:2

Attachment: gamma.2.patch.gz

[roed314]

comment:3

I ran sage -t after applying the patch, and all tests pass. Looks good to me.

[JohnCremona]

comment:4

That's better!

[sagetrac-mvngu]

comment:5

Simon: The patch gamma.2.patch doesn't contain your username. I've committed it in your name.

[sagetrac-mvngu]

Changed reviewer from John Cremona to John Cremona, David Roed

[sagetrac-mvngu]

Changed author from simon to Simon Morris

[sagetrac-mvngu]

Merged: Sage 4.1.1.alpha1