Implementation of the q-bracket

DavidAyotte commented 3 years ago

This ticket's goal is to implement the q-bracket and related functions in order to verify the Bloch-Okounkov theorem. A reference about the subject is the paper by Zagier:

Partitions, quasimodular forms and the Bloch-Okounkov theorem, https://people.mpim-bonn.mpg.de/zagier/files/doi/10.1007/s11139-015-9730-8/bloch-okounkov.pdf

This ticket is part of the GSoC 2021 project about quasimodular forms, see the task ticket #31560.

This code will be marked as experimental, but a more formal, non-experimental, implementation shall be done in the future (using shifted symmetric polynomials).

The code of this ticket is located in the following new directory:

sage/combinat/shifted_symmetric_functions/

Depends on #32357

CC: @videlec @slel

Component: combinatorics

Keywords: quasimodular forms, Bloch-Okounkov

Author: David Ayotte

Branch/Commit: u/gh-DavidAyotte/block_okounkov @ c3e7136

Issue created by migration from https://trac.sagemath.org/ticket/32366

DavidAyotte commented 3 years ago

Changed keywords from none to quasi modular forms block okounkov

DavidAyotte commented 3 years ago

Branch: u/gh-DavidAyotte/block_okounkov

slel commented 3 years ago

Description changed:

--- 
+++ 
@@ -1,4 +1,4 @@
-This ticket's goal is to implement the q-bracket and related functions in order to verify the Block-Okounkov theorem. A reference about the subject is the paper by Zagier: 
+This ticket's goal is to implement the q-bracket and related functions in order to verify the Bloch-Okounkov theorem. A reference about the subject is the paper by Zagier: 

 *Partitions, quasimodular forms and the Bloch-Okounkov theorem*, 
 https://people.mpim-bonn.mpg.de/zagier/files/doi/10.1007/s11139-015-9730-8/bloch-okounkov.pdf

slel commented 3 years ago

Commit: ffded0a

slel commented 3 years ago

comment:3

Careful, it's Spencer Bloch, not Block.

http://www.math.uchicago.edu/~bloch/

Last 10 new commits:

`094d64a`	`New methods in ring.py: ngens, polynomial_ring, from_polynomial. New methods in element.py: to_polynomial, weights_list, is_homogeneous, weight, homogeneous_components.`
`c8fb9d1`	`fix some docstring. small fix.`
`6057a6f`	`fix failing doctests, pyflakes, block, tiple colon`
`c3307e4`	`first implementation of serre derivative`
`cfb6696`	`fix mistake`
`37610fc`	`added examples, fix computations over arbitrary base rings`
`91eb0a5`	`minor fix`
`a18d0ab`	`Merge branch 'derivative_of_modular_forms' into derivative_modform`
`6705fcc`	`implement derivative for graded forms and quasiforms`
`ffded0a`	`added Hn function`

slel commented 3 years ago

Changed keywords from quasi modular forms block okounkov to quasimodular forms, Bloch-Okounkov

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from ffded0a to 1763120

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

`77e8a3d`	`add congruence subgroups support`
`6884d6d`	`add input parsing for q-expansions in _element_constructor_`
`31432ae`	`fixed input parsing for q-expansion, added documentation to reference manual, added a bibliographical reference`
`5ef7767`	`Merge branch 't/31559/make_modularformrings_manipulate_formal_objects' into t/31512/implementation_of_the_graded_quasimodular_forms_ring`
`377d88b`	`resolved merge conflicts`
`100f079`	`added missing newline, fix capitalization of title`
`71ba9f0`	`fixed merge conflicts`
`4b3c890`	`Merge branch 'quasiform_to_from_polynomial' into derivative_modform`
`52584ab`	`fix docbuild errors`
`1763120`	`Merge branch 'derivative_modform' into block_okounkov`

DavidAyotte commented 3 years ago

comment:5

To make the commit history clear, I must mention that I added the q_bracket function in this commit:

https://github.com/sagemath/sagetrac-mirror/commit/cb29e98053fca6818e365a36a4c22fa46f7f1e3c

(Everything outside sage/combinat/shifted_symmetric_functions/ does not belong to this ticket).

Unfortunately, I don't think the code is correct because the output seems wrong when I test it for a shifted symmetric polynomial different than a generator of the ring of shifted symmetric polynomial.

For examples, this is correct:

sage: from sage.combinat.shifted_symmetric_functions.q_bracket import *
sage: P.<Q1, Q2, Q3, Q4> = QQ[]
sage: q_bracket(Q2)
-1/24*P
sage: q_bracket(Q4)
1/1152*P^2 + 1/2880*Q

(by correct, I mean that the computations are the same as the ones given in the Appendix of the paper by Zagier)

However, this is not correct:

sage: q_bracket(Q2^2)
1/576*P^2 + 1/1440*Q

By the table of Zagier, it should be equal to -1/576*P^2 + 1/288*Q. I would be really grateful if someone could help me figure out why my code return the wrong answer! Thanks!

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 2 years ago

Changed commit from 1763120 to c3e7136

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 2 years ago

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

`936b3b6`	`fix docbuild errors`
`782d722`	`Merge branch 'develop' into quasiform_to_from_polynomial`
`d4eb6cd`	`fix small error`
`9143312`	`Merge branch 'quasiform_to_from_polynomial' into derivative_modform`
`c3e7136`	`Merge branch 'derivative_modform' into block_okounkov`

sagemath / sage

Implementation of the q-bracket #32366