implement numerical computation of periods of modular forms

[williamstein]

Implement some of chapter 10 of the book: http://wstein.org/books/modform/

Component: modular forms

Keywords: modular form, period

Work Issues: doctest failures

Author: William Stein

Branch/Commit: u/chapoton/13093 @ c3e79ce

Issue created by migration from https://trac.sagemath.org/ticket/13093

[williamstein]

Attachment: trac_13093.patch.gz

[fredstro]

comment:1

After applying the patch I get an import error for sage.modular.periods.periods in the file sage/modular/modsym/space.py
I think this is simply a problem with a missing __init__.py file in the periods/ directory

Also, I think that the formula for the exponential integral in the cited book (Lemma 10.4) has the wrong sign (easy to check in the case alpha=i, n=1 and m=0). This is simple to fix by initializing sgn=-1 instead of 1.

[robertwb]

comment:2

I'm surprised the exponential integral is not efficiently implemented elsewhere already. Note, however, that you could compute this more efficiently by keeping track of the single value (sgnalpha_powdenom) which changes by a constant factor of -1/(alpha * t) each iteration (if this is a bottleneck). Doctests on these functions might be useful as well.

[fchapoton]

Description changed:

--- 
+++ 
@@ -1 +1,3 @@
 Implement some of chapter 10 of my book: http://wstein.org/books/modform/
+
+Apply [attachment: trac_13093_period_v2.patch](https://github.com/sagemath/sage-prod/files/10655738/trac_13093_period_v2.patch.gz)

[fchapoton]

comment:3

Attachment: trac_13093_period_v2.patch.gz

I have made a new patch, just cleaning up things a little bit.

for the bot: apply only trac_13093_period_v2.patch​

[fchapoton]

comment:5

for the patchbots:

apply trac_13093_period_v2.patch