Ticket #13093 (new enhancement)
implement numerical computation of periods of modular forms
| Reported by: | was | Owned by: | craigcitro |
|---|---|---|---|
| Priority: | minor | Milestone: | sage-5.10 |
| Component: | modular forms | Keywords: | |
| Cc: | Work issues: | ||
| Report Upstream: | N/A | Reviewers: | |
| Authors: | Merged in: | ||
| Dependencies: | Stopgaps: |
Description
Implement some of chapter 10 of my book: http://wstein.org/books/modform/
Attachments
-
trac_13093.patch
(12.9 KB) -
added by was 12 months ago.
Change History
comment:1 Changed 11 months ago by fstromberg
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.
comment:2 Changed 10 months ago by robertwb
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 (sgn*alpha_pow*denom) 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.
