implement scalar-valued Siegel modular forms on Sp(4,Z)

[aghitza]

At Sage Days 20.25 in Montreal, we have decided to submit an initial version of the Siegel modular forms code by Friday 16 April 2010.

It's now a few minutes before midnight, and lest I turn into a pumpkin, I am uploading a patch with what we have so far.

I'm marking it as "needs work" since there are still a number of issues to be resolved. I'll list these in the comments soon.

To clarify: I submitted this just before midnight Seattle time, so one could argue that it was before the deadline :)

The patch applies cleanly to sage-4.4.3 and sage-4.4.4.alpha0, and passes all tests. The doctest coverage is 98.8% (81 out of 82 functions). The patch will not work with earlier versions of Sage since it depends on patches at #8602 and #8681 which have now been merged.

I believe that the objective of this first submission is to have something that works perfectly in the case of scalar-valued forms on Sp(4,Z). Here are the issues that I am aware of and are still blocking this:

1. We need top-level documentation in siegel_modular_form.py that explains in detail how the code is meant to be used, what the interesting features are, etc. We also need to explain how precisions work (either in the main file or in siegel_modular_form_prec.py
2. The computation of the generators for weights='all' breaks at the fifth generator
3. The argument degree in _siegel_modular_forms_generators should be properly documented, and there should be a doctest for it (I don't like the name "degree" BTW, because it already has a meaning for Siegel modular forms)
4. The argument default_prec in SiegelModularFormsAlgebra should be documented
5. We should put copyright headers in all the source files in the directory.

If you want to add to or modify these, please feel free to do this by editing the description on this ticket.

CC: @sagetrac-NilsSkoruppa @sagetrac-mraum @tornaria @williamstein @novoselt @ncalexan @mstreng

Component: modular forms

Keywords: siegel modular forms

Author: Nils-Peter Skoruppa, Nathan Ryan, Martin Raum, Gonzalo Tornaría, Craig Citro, Alex Ghitza

Branch/Commit: u/chapoton/8701 @ 4e4f04d

Issue created by migration from https://trac.sagemath.org/ticket/8701

[williamstein]

comment:2

:-)

[aghitza]

comment:3

To clarify: I submitted this just before midnight Seattle time, so one could argue that it was before the deadline :)

The patch applies cleanly to sage-4.3.5, and passes all but one test. The doctest coverage is 99%. The patch should also apply cleanly to earlier versions of Sage, but depending of how far back you go the tests might not pass any more. I checked with sage-4.3.3 and it was fine.

Since this patch includes the patches at trac #8602 and #8681, it will fail to apply when those tickets get reviewed positively and merged. In fact, #8602 just got merged into sage-4.4.alpha0, so I will eventually rebase the Siegel patch on top of that.

I believe that the objective of this first submission is to have something that works perfectly in the case of scalar-valued forms on Sp(4,Z). Here are the issues that I am aware of and are still blocking this:

1. SiegelModularFormsFunctor does not completely fit in with the other similar functors in Sage. For one thing, it seems that the right place to put it is in sage.categories.pushout. We should have a careful look at this class.
2. We need top-level documentation in siegel_modular_form.py that explains in detail how the code is meant to be used, what the interesting features are, etc. We also need to explain how precisions work (either in the main file or in siegel_modular_form_prec.py
3. The computation of the generators for weights='all' breaks at the fifth generator
4. The argument degree in _siegel_modular_forms_generators should be properly documented, and there should be a doctest for it (I don't like the name "degree" BTW, because it already has a meaning for Siegel modular forms)
5. The argument default_prec in SiegelModularFormsAlgebra should be documented
6. There are a few docstrings left that are not valid ReST, and there is one error while building the documentation
7. We should have some tests of the form TestSuite(s).run()

[aghitza]

comment:5

I am replacing the patch with one that has fixes for a couple of issues on the list (and I'm updating the list to reflect this).

[aghitza]

Attachment: siegel_combined.patch.gz

applies to sage-4.4.3 and sage-4.4.4.alpha0

[aghitza]

comment:6

Since a few more prerequisites went into Sage, I had to rebase the patch so it applies to 4.4.3 and 4.4.4.alpha0.

[ncalexan]

comment:8

I am worried that the groups on which the forms are defined are specified by strings ('Gamma0(5)') and not on python objects.

[williamstein]

comment:9

FYI, the patch is now in psage: http://code.google.com/p/purplesage/source/detail?r=508752edecf0b1f41373e5761a74b61c79024c50

[sagetrac-ncryan]

Attachment: trac_8701_siegel_modular_form_documentation.patch.gz

Addresses many of the comments from before. I need still need to add copyright information, include more examples at the top of siegel_modular_forms.py, and deal with the functor stuff.

[sagetrac-ncryan]

Addresses ncalexander's concern about the way the groups are defined

[sagetrac-ncryan]

Attachment: siegel_modular_group.patch.gz

Attachment: hecke_operators_bad_primes_exception.patch.gz

Raises an exception when trying to find the image of a form F under the Hecke operator T(p) when p divides the level of F

[tornaria]

Fix an issue with sage 4.6.2

[tornaria]

Attachment: fix-siegel.gz

Attachment: fix-coeffs-in-ring.gz

Have the constructor coerce the coefficients into the ring they're supposed to be

[fchapoton]

Attachment: trac_8701_siegel_rebased.patch.gz

[fchapoton]

comment:14

For the bot:

apply only trac_8701_siegel_folded_v1.patch

The folded patch trac_8701_siegel_folded_v1.patch can now be used as a new starting point.

[fchapoton]

comment:15

apply only trac_8701_siegel_folded_v1.patch

[fchapoton]

comment:16

Attachment: trac_8701_siegel_folded_v1.patch.gz

apply only trac_8701_siegel_folded_v1.patch

[sagetrac-git]

Changed commit from 785cbe8 to a9f7f95

[sagetrac-git]

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

a9f7f95

trac #8701 some minor doc improvements

[sagetrac-git]

Changed commit from a9f7f95 to 36f42d8

[sagetrac-git]

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

36f42d8

trac #8701 some more details

[sagetrac-git]

Changed commit from 36f42d8 to 1fe21e8

[sagetrac-git]

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

5c8614b	Merge branch 'u/chapoton/8701' into 6.9.b3
1fe21e8	trac #8701 correct raise syntax

[sagetrac-git]

Changed commit from 1fe21e8 to 35c9ac9

[sagetrac-git]

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

62f074a	Merge branch 'u/chapoton/8701' into 7.2
35c9ac9	python3 print

[sagetrac-git]

Changed commit from 35c9ac9 to 31b115d

[sagetrac-git]

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

31b115d

Merge branch 'u/chapoton/8701' in 7.3.b7

[sagetrac-git]

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

fe759f5

Merge branch 'u/chapoton/8701' into 7.3.rc0

[sagetrac-git]

Changed commit from 31b115d to fe759f5

[sagetrac-git]

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

e7e267a	Merge branch 'u/chapoton/8701' in 8.0
765e9f4	trac 8701 refresh imports

[sagetrac-git]

Changed commit from fe759f5 to 765e9f4

[sagetrac-git]

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

44877a2

trac 8701 pep8 and pyflakes cleanup

[sagetrac-git]

Changed commit from 765e9f4 to 44877a2

[sagetrac-git]

Changed commit from 44877a2 to d46b74c

[sagetrac-git]

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

d46b74c

trac 8701 do not create files during testing

[sagetrac-git]

Changed commit from d46b74c to 871f6d3

[sagetrac-git]

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

871f6d3

trac 8701 details

[sagetrac-git]

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

df1e9ec

trac 8701 details

[sagetrac-git]

Changed commit from 871f6d3 to df1e9ec

[sagetrac-git]

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

4e4f04d

Merge branch 'u/chapoton/8701' in 8.5.rc0

[sagetrac-git]

Changed commit from df1e9ec to 4e4f04d

[slel]

Changed author from Nils-Peter Skoruppa, Nathan Ryan, Martin Raum, Gonzalo Tornaria, Craig Citro, Alex Ghitza to Nils-Peter Skoruppa, Nathan Ryan, Martin Raum, Gonzalo Tornaría, Craig Citro, Alex Ghitza