Rankin Cohen brackets for (quasi) modular forms for Hecke triangle groups

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 9 years ago

This ticket adds support for Rankin Cohen brackets for (quasi) modular forms:

The ticket also adds support for listing the homogeneous and quasi parts of an element and fixes some bugs.

CC: @sagetrac-mraum @videlec @JohnCremona

Component: modular forms

Keywords: modular forms hecke triangle groups rankin cohen bracket

Author: Jonas Jermann

Branch/Commit: u/jj/rankin_cohen_bracket @ 2de1a1b

Issue created by migration from https://trac.sagemath.org/ticket/17909

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

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

fd1edff add missing doctests and documentation

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from bf89241 to fd1edff

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 9 years ago

Description changed:

--- 
+++ 
@@ -1,4 +1,4 @@
-This ticket (will) add support for Rankin Cohen brackets for (quasi) modular forms.
+This ticket adds support for Rankin Cohen brackets for (quasi) modular forms.
 The formulas shouldn't changefor Hecke triangle groups.

 See:
@@ -6,10 +6,9 @@
 - http://arxiv.org/abs/math/0509653
 - http://arxiv.org/abs/1306.3634v2

-Todo:
-- Check more general analytic types (quasi weak/meromorphic forms)
-- Add validation of parameters (s,t)
-- Explore the algebraic nature of the bracket:
-  If s or t is None the bracket is no longer bilinear but it satisfy a Leibnitz rule
-- More documentation and tests
+Possible Todos:
+- Review the definition for more general analytic types (quasi weak/meromorphic forms)
+- Restrict/validate the parameters s, t
+- Review the algebraic structure of the bracket:
+  If s or t is None the bracket is no longer bilinear but it satisfy a Leibnitz rule?
 - Explore alternative brackets

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 9 years ago

Description changed:

--- 
+++ 
@@ -1,5 +1,7 @@
 This ticket adds support for Rankin Cohen brackets for (quasi) modular forms.
 The formulas shouldn't changefor Hecke triangle groups.
+
+The ticket also adds support for listing the homogeneous and quasi parts of an element.

 See:

@@ -12,3 +14,4 @@
 - Review the algebraic structure of the bracket:
   If s or t is None the bracket is no longer bilinear but it satisfy a Leibnitz rule?
 - Explore alternative brackets
+- Extend the definition from form spaces to form rings?

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from fd1edff to 38dfd7a

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

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

`83c2396`	`Merge tag '6.6.beta3' into u/jj/theta_coercion`
`38dfd7a`	`Merge branch 'u/jj/theta_coercion' into u/jj/rankin_cohen_bracket`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from 38dfd7a to ca28b8b

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`987392f`	`allow coercions from the forms over n=3 to forms over n=infinity`
`a91d126`	`add the multiplication-by-weight operator`
`2b6826a`	`initial version of Rankin Cohen brackets`
`ca28b8b`	`add missing doctests and documentation`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from ca28b8b to 1396805

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`48d9918`	`allow coercions from the forms over n=3 to forms over n=infinity`
`21b72f7`	`add the multiplication-by-weight operator`
`781a7b2`	`initial version of Rankin Cohen brackets`
`1396805`	`add missing doctests and documentation`

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 9 years ago

comment:7

Rebase on u/jj/theta_coercion

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 9 years ago

Description changed:

--- 
+++ 
@@ -8,6 +8,9 @@
 - http://arxiv.org/abs/math/0509653
 - http://arxiv.org/abs/1306.3634v2

+Also see:
+http://math.univ-bpclermont.fr/~royer/ens/Mali/M2_Mali.html
+
 Possible Todos:
 - Review the definition for more general analytic types (quasi weak/meromorphic forms)
 - Restrict/validate the parameters s, t

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 1396805 to 47d1902

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`7d9146a`	`allow coercions from the forms over n=3 to forms over n=infinity`
`4d36e7a`	`trac #17261 fixing doc formatting in readme`
`dbf5f26`	`trac #17261 again better doc in readme`
`ba88e5e`	`improvements after review from chapoton`
`e2a4ef8`	`add the multiplication-by-weight operator`
`be0e7ad`	`initial version of Rankin Cohen brackets`
`47d1902`	`add missing doctests and documentation`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 47d1902 to 73de053

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`e3e9b31`	`add the multiplication-by-weight operator`
`13ee3d6`	`initial version of Rankin Cohen brackets`
`73de053`	`add missing doctests and documentation`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 73de053 to 2fd8e13

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`7815555`	`add the multiplication-by-weight operator`
`5887183`	`initial version of Rankin Cohen brackets`
`2fd8e13`	`add missing doctests and documentation`

fchapoton commented 8 years ago

Changed branch from u/jj/rankin_cohen_bracket to u/chapoton/17909

fchapoton commented 8 years ago

Changed commit from 2fd8e13 to fb03d29

fchapoton commented 8 years ago

comment:15

I just changed a broken import

New commits:

`6aec29e`	`Merge branch 'u/jj/rankin_cohen_bracket' in 7.4.b2`
`fb03d29`	`modern import`

fchapoton commented 7 years ago

comment:16

ping ?

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 7 years ago

Changed dependencies from #17261 to none

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 7 years ago

Changed commit from fb03d29 to bef5a6b

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 7 years ago

comment:17

rebased on develop, applied chapoton's commit

New commits:

`5277bba`	`add the multiplication-by-weight operator`
`c836ea8`	`initial version of Rankin Cohen brackets`
`f883d1b`	`add missing doctests and documentation`
`bef5a6b`	`apply modern import commit from chapoton`

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 7 years ago

Changed branch from u/chapoton/17909 to u/jj/rankin_cohen_bracket

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Changed commit from bef5a6b to 9b46edd

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

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

9b46edd use submodule_with_basis instead of submodule, so that coordinate vectors really correspond to the specified basis, bugfix regarding exception

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

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

85bdbfd make series interpretation work more generally with basic validation, allow trivial series in rationalize_series, don't forget denom_factor

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Changed commit from 9b46edd to 85bdbfd

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 7 years ago

Description changed:

--- 
+++ 
@@ -1,7 +1,7 @@
 This ticket adds support for Rankin Cohen brackets for (quasi) modular forms.
-The formulas shouldn't changefor Hecke triangle groups.
+The formulas shouldn't change for Hecke triangle groups.

-The ticket also adds support for listing the homogeneous and quasi parts of an element.
+The ticket also adds support for listing the homogeneous and quasi parts of an element and fixes some bugs.

 See:

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Changed commit from 85bdbfd to 16c5d1d

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`439e598`	`add the multiplication-by-weight operator`
`b180c56`	`initial version of Rankin Cohen brackets`
`c50b4ce`	`add missing doctests and documentation`
`7a47fa1`	`apply modern import commit from chapoton`
`f15ab00`	`use submodule_with_basis instead of submodule, so that coordinate vectors really correspond to the specified basis, bugfix regarding exception`
`16c5d1d`	`make series interpretation work more generally with basic validation, allow trivial series in rationalize_series, don't forget denom_factor`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`b5b8ef5`	`add the multiplication-by-weight operator`
`56a3642`	`initial version of Rankin Cohen brackets`
`c7ac17e`	`add missing doctests and documentation`
`fb4b2f5`	`apply modern import commit from chapoton`
`3856464`	`use submodule_with_basis instead of submodule, so that coordinate vectors really correspond to the specified basis, bugfix regarding exception`
`687e9a0`	`make series interpretation work more generally with basic validation, allow trivial series in rationalize_series, don't forget denom_factor`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Changed commit from 16c5d1d to 687e9a0

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Changed commit from 687e9a0 to f616890

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`08957bf`	`add the multiplication-by-weight operator`
`bd26578`	`initial version of Rankin Cohen brackets`
`38d092b`	`add missing doctests and documentation`
`7d46d36`	`apply modern import commit from chapoton`
`4adea7d`	`use submodule_with_basis instead of submodule, so that coordinate vectors really correspond to the specified basis, bugfix regarding exception`
`f616890`	`make series interpretation work more generally with basic validation, allow trivial series in rationalize_series, don't forget denom_factor`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`b410a00`	`add the multiplication-by-weight operator`
`cccd1c4`	`initial version of Rankin Cohen brackets`
`fb7ad68`	`add missing doctests and documentation`
`4eb7759`	`apply modern import commit from chapoton`
`6eb4bd4`	`use submodule_with_basis instead of submodule, so that coordinate vectors really correspond to the specified basis, bugfix regarding exception`
`ffe93d8`	`make series interpretation work more generally with basic validation, allow trivial series in rationalize_series, don't forget denom_factor`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Changed commit from f616890 to ffe93d8

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 5 years ago

Changed commit from ffe93d8 to c23aac2

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 5 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`5b1a331`	`add the multiplication-by-weight operator`
`21b7149`	`initial version of Rankin Cohen brackets`
`748f0b5`	`add missing doctests and documentation`
`6b3155f`	`apply modern import commit from chapoton`
`21743d0`	`use submodule_with_basis instead of submodule, so that coordinate vectors really correspond to the specified basis, bugfix regarding exception`
`c23aac2`	`make series interpretation work more generally with basic validation, allow trivial series in rationalize_series, don't forget denom_factor`

fchapoton commented 5 years ago

comment:29

fix the pyflakes warning (see patchbot plugin)
use the :arxiv:`math/0509653v2` syntax for the links
There should be a double colon here:

+                EXAMPLES:
+

this

+        if len(laurent_series.exponents()) == 0:

could be just

+        if not laurent_series.exponents():

I do not like the change from "Basis matrix:" to "User basis matrix:"
Here you should insert a blank line between the 2 lines

+        Return [self,g]_m, the ``m``th Rankin Cohen bracket of ``self`` with ``g``.
+        See ``self.parent().rankin_cohen_bracket`` for more information.

same here:

+        Return the summands of ``self`` divided by their depths.
+        This assumes that ``self`` has a depth (see :meth:`has_depth`).

Avoid using m=ZZ(1) inside the function arguments. Use m=None there, and set m to 1 inside the function, if m is None.

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 5 years ago

Changed commit from c23aac2 to 7482a7e

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 5 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`eca2bb4`	`add the multiplication-by-weight operator`
`5e1290b`	`initial version of Rankin Cohen brackets`
`52d8357`	`add missing doctests and documentation`
`ac9dd9b`	`apply modern import commit from chapoton`
`908ba60`	`use submodule_with_basis instead of submodule, so that coordinate vectors really correspond to the specified basis, bugfix regarding exception`
`6eab142`	`make series interpretation work more generally with basic validation, allow trivial series in rationalize_series, don't forget denom_factor`
`7482a7e`	`adjustments after review`

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 5 years ago

comment:31

hi chapoton

Thanks for the review. I tried to fix as much as possible.

Regarding the "User basis matrix": That's due to the change "ambient_space._module.submodule" -> "ambient_space._module.submodule_with_basis". This is from like 4 years ago but I remember having had a very good reason for the change (it's a bugfix which I included in this change). If I recall correctly it just makes more sense to have coordinates with respect to the given basis. Why don't you like the change?

I executed pyflakes modform_hecketriangle/*.py and tried to fix most, what should I put in all.py and init.py?

Regards Jonas

fchapoton commented 5 years ago

comment:32

ok, thanks for the explanation about User basis matrix. I am no longer opposed to this change.

Concerning pyflakes, there is nothing to fix in all.py and init.py. I was only refering to the pyflakes plugin (that you can see in some but not all of the patchbot reports): it was complaining about

+src/sage/modular/modform_hecketriangle/abstract_space.py:87:
local variable 'numerator_parent' is assigned to but never used

Did you fix that ?

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 5 years ago

comment:33

Yes, I removed all other warnings.

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 5 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`ca0f922`	`add the multiplication-by-weight operator`
`29dba33`	`initial version of Rankin Cohen brackets`
`59d94e7`	`add missing doctests and documentation`
`c2fb419`	`apply modern import commit from chapoton`
`8aaac49`	`use submodule_with_basis instead of submodule, so that coordinate vectors really correspond to the specified basis, bugfix regarding exception`
`71f5240`	`make series interpretation work more generally with basic validation, allow trivial series in rationalize_series, don't forget denom_factor`
`d5c2813`	`adjustments after review`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 5 years ago

Changed commit from 7482a7e to d5c2813

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 5 years ago

Changed commit from d5c2813 to 85c03e3

sagemath / sage

Rankin Cohen brackets for (quasi) modular forms for Hecke triangle groups #17909