Fix Eisenstein L-series precision

[jdemeyer]

The LCalc interface uses PARI/GP through strings. This is problematic for the Eisenstein series L-function where Sage passes the value of

str(float(pi)**0.5)

to PARI/GP. There are two problems with this:

1. Using float has at most 53 bits precision, regardless of what precision is used in PARI/GP.
2. Using strings causes an additional loss of precision.
   Letting PARI/GP compute the value of sqrt(Pi) solves both these problems.

Component: modular forms

Author: Jeroen Demeyer

Reviewer: Frithjof Schulze, David Loeffler

Merged: sage-4.8.alpha6

Issue created by migration from https://trac.sagemath.org/ticket/12124

[jdemeyer]

comment:1

Attachment: 12124_eisenstein.patch.gz

[kiwifb]

comment:2

Just for clarification, does this work with either python-2.6 or 2.7 or does it require python-2.7?

[jdemeyer]

comment:3

Replying to @kiwifb:

Just for clarification, does this work with either python-2.6 or 2.7 or does it require python-2.7?

It should have nothing to do with Python, it is simply a problem that I discovered because of the Python upgrade.

[strogdon]

comment:4

I backed out that portion of https://github.com/sagemath/sage/files/ticket9958/trac_9958-fixing_numericalnoise-part1_p2.patch.gz from #9958 that touched sage/modular/modform/eis_series.py in my build of sage-4.8.alpha3 with python-2.7 and applied the eisenstein patch of this ticket. Testing the touched file passes on x86 and amd64

./sage -t -long  -force_lib devel/sage-main/sage/modular/modform/eis_series.py
sage -t -long -force_lib "devel/sage-main/sage/modular/modform/eis_series.py"
         [2.6 s]
 
----------------------------------------------------------------------
All tests passed!

[loefflerd]

comment:5

I've assembled a team of people at SD35 to do some modular forms patch reviewing, and we saw this one. Could you perhaps give us a tiny bit of background on what's going on here and why the change is needed?

[loefflerd]

Reviewer: Frithjof Schulze, David Loeffler

[loefflerd]

comment:7

Frithjof and I both looked at this during SD35, and it looks fine. There is some oddness in the eisenstein_series_lseries code -- it is weird that the prec argument is used as both a power series precision and a real-number precision -- but we both feel that is orthogonal to this patch.

[jdemeyer]

Merged: sage-4.8.alpha6