Implementation of the graded quasimodular forms ring #31512

DavidAyotte · 2021-03-18T18:01:05Z

The goal of this ticket is to implement the graded ring of quasimodular forms. More precisely, the goal is to first implement a class named QuasiModularFormsRing with similar methods and features as the class ModularFormsRing (though see #31559).

This ticket is part of #31560

Depends on #31559
Depends on #32135

CC: @slel @videlec

Component: modular forms

Keywords: quasimodular-forms gsoc2021

Author: David Ayotte

Branch/Commit: 20e633e

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/31512

The text was updated successfully, but these errors were encountered:

DavidAyotte · 2021-03-18T18:04:51Z

Branch: u/gh-DavidAyotte/implementation_of_the_graded_quasimodular_forms_ring

DavidAyotte · 2021-03-18T18:06:33Z

Commit: 7b029ad

DavidAyotte · 2021-03-18T18:06:33Z

New commits:

`7b029ad`	`Initial implementation of quasimodular forms`

sagetrac-git · 2021-03-18T19:45:48Z

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

`d9940aa`	`Fixed some typos and syntax in the documentation`

sagetrac-git · 2021-03-18T19:45:48Z

Changed commit from 7b029ad to d9940aa

videlec · 2021-03-19T10:29:29Z

comment:5

Hi David,

Great start.

Let us stick to SL(2,Z) in this ticket. Further improvements (other congruence subgroups, Bloch-Okounkov brackets should be reserved for other tickets).

Some concrete remarks

QuasiModularFormsRing could simply be QuasiModularForms
The main class should inherit from Parent and the category should be properly initialized, see https://doc.sagemath.org/html/en/thematic_tutorials/coercion_and_categories.html
The objective is to manipulate exact formal objects. Not approximate q-series. The following operations should be available on the elements
- equality tests between two qm-forms
- decomposition of a qm-form with respect to the grading (ie by level)
- testing modularity
- computing the q-series expansion of a qm-form (arbitrary precision)
- multiplication by a modular form (maybe the simplest to achieve this is to define qm-forms as an algebra over modular forms?)
- (further ticket) computing algebraic or differential equations (for that purpose it is necessary to have formal derivatives, not the derivative of the q-expansion)
- (further ticket) asymptotics of coefficients
The following methods should be available on the parent (the algebra itself)
- vector space basis of a given graded component
- basis and generators up to modular forms

sagetrac-git · 2021-03-24T14:39:37Z

Changed commit from d9940aa to 9fa1397

sagetrac-git · 2021-03-24T14:39:37Z

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

`9fa1397`	`Changed the name of the main class to QuasiModularForms. Added inheritance from Parent and UniqueRepresentation. Implemented category framework to the main class`

DavidAyotte · 2021-03-24T20:44:28Z

comment:7

Replying to @sagetrac-git:

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

`9fa1397`	`Changed the name of the main class to QuasiModularForms. Added inheritance from Parent and UniqueRepresentation. Implemented category framework to the main class`

I just realized that there are some inconsistencies in the code of that commit. They will be fixed this week.

sagetrac-git · 2021-03-25T15:32:04Z

Changed commit from 9fa1397 to 13a2441

sagetrac-git · 2021-03-25T15:32:04Z

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

`13a2441`	`Implementation of QuasiModularFormsElement class. Fixed some inconsistencies in the code. The default precision is now 6 (to be consistent with classical ModularForms)`

videlec · 2021-03-25T18:13:16Z

Changed keywords from graded quasimodular forms gsoc2021 to quasimodular-forms gsoc2021

sagetrac-git · 2021-06-09T18:47:04Z

Changed commit from 13a2441 to 8433a5a

sagetrac-git · 2021-06-09T18:47:04Z

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

`0ef06e3`	`Initial implementation of quasimodular forms`
`39642c2`	`Fixed some typos and syntax in the documentation`
`33d0897`	`Changed the name of the main class to QuasiModularForms. Added inheritance from Parent and UniqueRepresentation. Implemented category framework to the main class`
`f6d57bf`	`Implementation of QuasiModularFormsElement class. Fixed some inconsistencies in the code. The default precision is now 6 (to be consistent with classical ModularForms)`
`8433a5a`	`Merge branch 'u/gh-DavidAyotte/implementation_of_the_graded_quasimodular_forms_ring' of trac.sagemath.org:sage into t/31512/implementation_of_the_graded_quasimodular_forms_ring`

sagetrac-git · 2021-07-22T14:37:38Z

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

`f921724`	`Merge branch 'develop' into t/31512/implementation_of_the_graded_quasimodular_forms_ring`

sagetrac-git · 2021-07-22T14:37:38Z

Changed commit from 8433a5a to f921724

sagetrac-git · 2021-07-28T02:36:02Z

Changed commit from f921724 to 45f1791

sagetrac-git · 2021-07-28T02:36:02Z

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

`c4595c1`	`Merge branch 'gamma1_modform_conversion' into t/31559/make_modularformrings_manipulate_formal_objects`
`a6c745d`	`small fixes`
`906b8ab`	`fixes: pyflakes, failing doctest in find_generators`
`523c7b0`	`fix some doctring`
`7dbaf4e`	`fix indentation error`
`5887973`	fix docstring, changed some syntax, removed `_rmul_`, add negative weight checker for `__getitem__`, fix weight of zero element bug
`7fdca22`	changed `_repr_` method of ModularFormsRing, added TestSuite in doctests, added some_elements method, fixed conversion bug
`1b9332e`	`moved sage.modular.modform.find_generators.py in sage.rings, attempt at making decrecation work (without success)`
`4305360`	`Merge branch 't/31559/make_modularformrings_manipulate_formal_objects' into t/31512/implementation_of_the_graded_quasimodular_forms_ring`
`45f1791`	Major changes: Implementation of `_add_`, `_mul_`, `_lmul_`, __neg__. Added Docstring. Implemented conversion. Added generators methods.

DavidAyotte · 2021-07-28T02:38:16Z

Dependencies: #31559

videlec · 2021-08-16T15:03:35Z

comment:28

Why is it only implemented for SL(2,Z)? The isomorphism QM = M[E2] is valid in general.

videlec · 2021-08-16T15:04:16Z

comment:29

typo: def weigt_2_eisenstein_series(self): (missing a h)

DavidAyotte · 2021-08-16T15:17:32Z

comment:30

Replying to @videlec:

Why is it only implemented for SL(2,Z)? The isomorphism QM = M[E2] is valid in general.

I will check if this doesn't break anything, but I mostly stick to the case of SL2Z because of comment:5. But thanks for reminding me this isomorphism, it should not be a problem.

videlec · 2021-08-16T15:31:12Z

comment:31

Better to switch DAVID AYOTTE -> David Ayotte

videlec · 2021-08-16T15:36:03Z

comment:32

Maybe we made a mistake, but the initialization from polynomial is confusing. The reason is that both E2 * E4 - 3 * E2^2 and -1/24 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 are polynomials.

DavidAyotte · 2021-08-16T15:50:20Z

comment:33

Replying to @videlec:

Maybe we made a mistake, but the initialization from polynomial is confusing. The reason is that both E2 * E4 - 3 * E2^2 and -1/24 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 are polynomials.

This is in fact really important. To fix this confusion, my idea would be to give more examples and explanations in the doc. Do you have an other idea to fix this?

videlec · 2021-08-16T15:57:04Z

comment:34

In the case of ModularFormsRing._element_constructor_, when the input is a polynomial the code calls from_polynomial. This is very different from what is happening with the quasimodular forms.

DavidAyotte · 2021-08-16T17:09:18Z

comment:35

Replying to @videlec:

In the case of ModularFormsRing._element_constructor_, when the input is a polynomial the code calls from_polynomial. This is very different from what is happening with the quasimodular forms.

Ok, so maybe the element constructor of ModularFormsRing should not call from_polynomial. What do you think?

videlec · 2021-08-16T17:43:50Z

comment:36

Replying to @DavidAyotte:

Replying to @videlec:

In the case of ModularFormsRing._element_constructor_, when the input is a polynomial the code calls from_polynomial. This is very different from what is happening with the quasimodular forms.

Ok, so maybe the element constructor of ModularFormsRing should not call from_polynomial. What do you think?

I think it would be fine to allow both. It just needs more parsing of the input

univariate polynomial ring with generator q -> q-expansion (raise a NotImplementedError for now)
multivariate polynomial ring with rational or finite field coefficients -> call from_polynomial as it is now.

sagetrac-git · 2021-08-16T19:17:20Z

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

`600fdff`	`fix typos`
`77e8a3d`	`add congruence subgroups support`
`6884d6d`	`add input parsing for q-expansions in _element_constructor_`

sagetrac-git · 2021-08-16T19:17:20Z

Changed commit from 5a373a3 to 6884d6d

sagetrac-git · 2021-08-30T14:25:14Z

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

`31432ae`	`fixed input parsing for q-expansion, added documentation to reference manual, added a bibliographical reference`

sagetrac-git · 2021-08-30T14:25:14Z

Changed commit from 6884d6d to 31432ae

sagetrac-git · 2021-09-08T13:49:21Z

Changed commit from 31432ae to 377d88b

sagetrac-git · 2021-09-08T13:49:21Z

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

`5ef7767`	`Merge branch 't/31559/make_modularformrings_manipulate_formal_objects' into t/31512/implementation_of_the_graded_quasimodular_forms_ring`
`377d88b`	`resolved merge conflicts`

sagetrac-git · 2021-09-08T13:55:02Z

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

`100f079`	`added missing newline, fix capitalization of title`

sagetrac-git · 2021-09-08T13:55:02Z

Changed commit from 377d88b to 100f079

videlec · 2021-09-08T15:49:41Z

comment:41

Two small remarks:

In the element, why are you storing both the polynomial and its coefficients? The latter is only used in q_expansion for which you could have use equally the polynomial.

The methods is_modular_form and is_graded_modular_form are not quite right for the zero element as

sage: QQ['x'].zero().degree()
-1

DavidAyotte · 2021-09-08T16:13:20Z

comment:42

Two small remarks:

In the element, why are you storing both the polynomial and its coefficients? The latter is only used in q_expansion for which you could have use equally the polynomial.

Since the coefficient attribute is used only once, I will drop it.

The methods is_modular_form and is_graded_modular_form are not quite right for the zero element as
sage: QQ['x'].zero().degree()
-1

Oops, thanks for finding this! I had forgotten that there was a special rule for the degree of the zero polynomial. I'll fix this.

sagetrac-git · 2021-09-08T16:18:12Z

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

`20e633e`	`removed _coefficients attribute, fix bug in is_graded_modular_form and is_modular_form, fix pyflakes`

sagetrac-git · 2021-09-08T16:18:12Z

Changed commit from 100f079 to 20e633e

vbraun · 2021-09-25T23:17:39Z

Changed branch from u/gh-DavidAyotte/implementation_of_the_graded_quasimodular_forms_ring to 20e633e

DavidAyotte added c: modular forms labels Mar 18, 2021

DavidAyotte self-assigned this Mar 18, 2021

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videlec added this to the sage-9.4 milestone Mar 25, 2021

videlec removed the wishlist item label Mar 25, 2021

mkoeppe modified the milestones: sage-9.4, sage-9.5 Jul 19, 2021

videlec added s: positive review and removed s: needs review labels Sep 9, 2021

vbraun removed the s: positive review label Sep 25, 2021

vbraun closed this as completed in 0a4f2a3 Sep 25, 2021

videlec mentioned this issue Jan 29, 2023

quasi-modular forms (GSoC project) #31560

Open

This was referenced Oct 10, 2021

Implement to_polynomial and from_polynomial for quasimodular forms #32336

Closed

Conversion from q-expansion to GradedModularFormElement and QuasiModularFormElement #32337

Open

Typos in documentation of sage/modular/quasimodform #32644

Closed

Implementation of the graded quasimodular forms ring #31512

Implementation of the graded quasimodular forms ring #31512

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