add Pollack/Stevens overconvergent modular symbols code

[craigcitro]

I'm just starting to work on implementing Pollack & Stevens' methods for using overconvergent modular symbols for p-adic L-functions, Stark-Heegner points, etc.

CC: @loefflerd @roed314 @craigcitro @categorie

Component: modular forms

Keywords: p-adic L-functions

Author: Marc Masdeu, David Roe

Branch/Commit: 44c321f

Reviewer: Chris Wuthrich

Issue created by migration from https://trac.sagemath.org/ticket/812

[sagetrac-mabshoff]

comment:3

Craig,

I know I must be bothering you by now, but what is the status here?

Cheers,

Michael

[williamstein]

comment:4

Could somebody post a link to the Magma code here?

[sagetrac-GeorgSWeber]

comment:5

Sure,
it's part of the "shp package" at:

http://www.math.mcgill.ca/darmon/programs/shp/shp.html

[williamstein]

comment:6

From Jennifer Balakrishnan:

Rob Pollack just ported over some of his p-adic L-series via
overconvergent modular symbols code to Sage, which could be very
useful for our p-adic BSD paper.

The code he sent me originally didn't quite produce results matching
our data, but I've worked on it over the last few days, fixed a few
bugs, noticed a few more, and thought this might be a good coding
sprint project for us this week.

Here's where the code currently stands:
-- it can compute the p-adic L-series in the split p case (with data
matching what we've already computed naively)
-- Rob says inert p is straightforward, just a matter of knowing how
to call the right objects in Sage, which I think I can do
-- I've tested it against the regulators I computed in my thesis, and
we can easily produce 10+ digits of precision in the L-value!!
-- for some primes, it results in memory errors (I've put examples,
working and not, in the docstring in the test file). I'm not sure how
to fix these.

As an enhancement, maybe we could also use some of your very fast code
for modular symbols?

Perhaps most mathematically interesting, the special values computed
by his program also result in the same +/-1 "sign" in the BSD formula
that our previous methods produced!

The code is available here:

http://sage.math.washington.edu/home/jen/OMS

To run it, attach master.sage and Jen/test_run_generic.sage. The
second file (http://sage.math.washington.edu/home/jen/OMS/Jen/test_run_generic.sage)
has some examples in the docstring.

Jen

[mmasdeu]

Commit: 9acf3ac

[mmasdeu]

New commits:

1b85377	Initial commit. Cloned from experimental branch of roed314's github.
1656711	Made all tests to pass.
72923ab	Increased coverage.
caaa672	Fixed precision of p_stabilize. Two more tests pass.
c0331a5	Fixed one test.
9fd7d69	All files pass the doctests except padic_lseries.py
4bbe597	All doctests passed, have 100% coverage.
c5aa41d	Removed ocmodule.py
ce76f3c	Removed references to old OCVn.
9acf3ac	Fixed one doctest.

[mmasdeu]

Branch: u/mmasdeu/moved_from_github-fixed_several_bugs

[mmasdeu]

comment:10

I think the code is usable enough that it should made into Sage. It includes the btquotients code, which is in a quite stable state as well. Several parts of the code are in need for more debugging, though. Especially the dist.pyx and distributions.py, which are not very robust.

[fchapoton]

comment:11

There are some failing doctests, see patchbot's report

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

a875b16

Fixed a doctest which failed when run without magma and long time flag enabled.

[sagetrac-git]

Changed commit from 9acf3ac to a875b16

[mmasdeu]

comment:13

OK, I just learned that:
# long time optional - magma
does not work. One has to do:
# long time, optional - magma

So hopefully now it works!

[williamstein]

comment:14

I just (very) quickly skimmed the patches -- this is some beautiful code!

[pjbruin]

comment:16

Just some general "top-level" remarks, without really looking at the code yet:

• In sage/modular/all.py, the import * commands may not be what you want; this will all end up in the global namespace.
• It would be nice to add the new modules to the relevant src/doc/en/reference/*/index.rst files, probably with * = modfrm, modmisc and/or modsym.

[roed314]

comment:17

Hi Marc,
Jen and I worked on reviewing this last weekend, but I'm getting married on Saturday and haven't had time to upload our progress, etc. I'll try to have some comments and changes next week.

[rwst]

comment:18

patchbot:

sage -t --long src/sage/doctest/sources.py  # 1 doctest failed
sage -t --long src/sage/modular/pollack_stevens/distributions.py  # 1 doctest failed
sage -t --long src/sage/modular/btquotients/pautomorphicform.py  # 2 doctests failed

[chriswuthrich]

comment:94

To me all tests still pass and I can't check 32-bit or optional magma. So I set this to positive review, fearing of course that a bot or vbraun will find yet another issue.

The patchbot complains about something, but I don't understand it.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

d11150c

Moved an auxiliary function where it was used.

[sagetrac-git]

Changed commit from d94b19e to d11150c

[mmasdeu]

comment:96

I realized that there was one doctest missing in btquotient.py. This is fixed now. I'm keeping it as "needs review" and hope that the patchbot is happier now.

[chriswuthrich]

comment:97

Well, you deleted lots of commented code and moved an undocumented function to a place where coverage won't complain about it. I guess this is not the optimal solutions, but one can deal with this in #20863.

Coverage also complains about another missing docstring:

SCORE src/sage/schemes/elliptic_curves/padics.py: 92.3% (12 of 13)

Missing doctests:
     * line 72: def _normalize_padic_lseries(self, p, normalize, use_eclib, implementation, precision)

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

31a3e87

Added missing doctest.

[sagetrac-git]

Changed commit from d11150c to 31a3e87

[mmasdeu]

comment:99

I fixed the missing doctest in padics.py as well.

---

New commits:

31a3e87

Added missing doctest.

[chriswuthrich]

comment:100

tests pass.

[vbraun]

comment:101

Building the pdf docs fails

[docpdf] LaTeX Warning: Hyper reference `sage/modular/pollack_stevens/modsym:sage.modula
[docpdf] r.pollack_stevens.modsym.PSModularSymbolElement' on page 162 undefined on input
[docpdf]  line 13297.
[docpdf] 
[docpdf] [162] [163] [164] [165] [166]
[docpdf] Underfull \hbox (badness 10000) in paragraph at lines 13628--13628
[docpdf] \T1/ptm/m/it/10 char-ac-ter=None\T1/ptm/m/n/10 ,
[docpdf] 
[docpdf] Underfull \hbox (badness 10000) in paragraph at lines 13628--13628
[docpdf] \T1/ptm/m/it/10 use_magma=False\T1/ptm/m/n/10 ,
[docpdf] 
[docpdf] Overfull \hbox (152.67451pt too wide) in paragraph at lines 13629--13630
[docpdf] \T1/ptm/m/n/10 Bases: \T1/pcr/m/n/10 sage.structure.sage_object.SageObject\T1/p
[docpdf] tm/m/n/10 , \T1/pcr/m/n/10 sage.structure.unique_representation.UniqueRepresent
[docpdf] ation 
[docpdf] [167] [168] [169] [170] [171] [172] [173] [174] [175] [176] [177] [178]
[docpdf] Overfull \hbox (152.67451pt too wide) in paragraph at lines 14890--14891
[docpdf] \T1/ptm/m/n/10 Bases: \T1/pcr/m/n/10 sage.structure.sage_object.SageObject\T1/p
[docpdf] tm/m/n/10 , \T1/pcr/m/n/10 sage.structure.unique_representation.UniqueRepresent
[docpdf] ation 
[docpdf] [179] [180] [181]
[docpdf] ! Undefined control sequence.
[docpdf] l.15130 modulo \(p\) is not in \(\FF
[docpdf]                                     _p\):
[docpdf] ? 
[docpdf] ! Emergency stop.
[docpdf] l.15130 modulo \(p\) is not in \(\FF
[docpdf]                                     _p\):
[docpdf] !  ==> Fatal error occurred, no output PDF file produced!
[docpdf] Transcript written on modsym.log.
[docpdf] Makefile:68: recipe for target 'modsym.pdf' failed

[chriswuthrich]

Changed branch from u/mmasdeu/812-pollackstevens to u/wuthrich/ticket/812

[chriswuthrich]

comment:102

pdf documentation now build for me.

---

Last 10 new commits:

afeb1a1	Trac #812: Removed unneeded imports.
3a54bd9	Trac #812: Changed "print" to "string" in some of the docstrings to avoid bug in patchbot.
32fa647	Trac 812: changed signature of ModuleElement.
cef9a4a	Merge branch 'develop' into 812-chris2
4374c5b	Trac #812: finished adapting the signatures.
d5fed29	Marked some doctests with random output. Fixed problem with magma maximal order.
d94b19e	Changed doctest to allow 32/64 bit output.
d11150c	Moved an auxiliary function where it was used.
31a3e87	Added missing doctest.
44c321f	trac 812: docstring changes for pdf

[chriswuthrich]

Changed commit from 31a3e87 to 44c321f

[vbraun]

Changed branch from u/wuthrich/ticket/812 to 44c321f