implement the Hijikata trace formula

williamstein commented 12 years ago

This can be used for computing traces of Hecke operators acting on spaces of modular forms. In most cases, other methods are better, but this can still have value in that it can do things that are impossible with modular symbols.

My pari and Magma implementations are here: http://wstein.org/Tables/hijikata.html

Hijikata's article: http://projecteuclid.org/euclid.jmsj/1240435364

Component: modular forms

Keywords: trace formula, hijikata

Work Issues: documentation, tests

Author: William Stein

Branch/Commit: u/chapoton/12450v2 @ 4b867f8

Issue created by migration from https://trac.sagemath.org/ticket/12450

williamstein commented 12 years ago

Attachment: trac_12450-part1.patch.gz

part 1 -- this fully implements the algorithm, and includes many tests that pass (and I've tested extensively against my Magma implementation too).

williamstein commented 12 years ago

comment:1

Plan:

Implement the algorithm and make sure it passes a wide range of tests. Done.
Get coverage to 100% so it can be included in Sage.
Open a new ticket to rewrite key parts using Cython and more intelligent algorithms (in some cases), which should be dramatically faster, since most of the code is simple integer manipulation.

williamstein commented 12 years ago

Author: William Stein

williamstein commented 12 years ago

Changed keywords from none to trace formula, hijikata

fchapoton commented 11 years ago

add some doctests to easy functions

856887fc-c4a0-4392-a207-e1239ccef741 commented 10 years ago

comment:3

Attachment: trac_12450-part2-fc.patch.gz

fchapoton commented 10 years ago

Branch: u/chapoton/12450

fchapoton commented 10 years ago

Commit: d95adbc

fchapoton commented 10 years ago

comment:4

Here is a git branch

New commits:

`c9db839`	`trac 12450: implement the Hijikata trace formula`
`39caa01`	`trac #12450 more doc and tests`
`d95adbc`	`trac #12450 cosmetic details`

fchapoton commented 10 years ago

comment:5

The paper of Hijikata is freely available here : http://projecteuclid.org/euclid.jmsj/1240435364

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

Changed commit from d95adbc to 7cec65e

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

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

7cec65e trac #12450 oops, it was broken

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

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

`56dd25a`	`Merge branch 'u/chapoton/12450' of ssh://trac.sagemath.org:22/sage into 12450`
`a47cb63`	`trac #12450 comments on sigma`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

Changed commit from 7cec65e to a47cb63

fchapoton commented 10 years ago

Work Issues: documentation, tests

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

Changed commit from a47cb63 to f33416d

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

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

`e5122a4`	`Merge branch 'u/chapoton/12450' into 6.6.b0`
`f33416d`	`trac #12450 moving dedekind psi to arith.py`

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

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

8386515 trac #12450 better algo for root finding

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

Changed commit from f33416d to 8386515

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

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

63047d6 Merge branch 'u/chapoton/12450' into 6.6.b3

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

Changed commit from 8386515 to 63047d6

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

Changed commit from 63047d6 to 3d040d2

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

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

3d040d2 Merge branch 'u/chapoton/12450' into 6.7.b1

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

Changed commit from 3d040d2 to 7ae0512

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

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

7ae0512 Merge branch 'u/chapoton/12450' into 7.1.b4

fchapoton commented 8 years ago

Description changed:

--- 
+++ 
@@ -1 +1,5 @@
-This can be used for computing traces of Hecke operators acting on spaces of modular forms.  In most cases, other methods are better, but this can still have value in that it can do things that are impossible with modular symbols.    My pari and Magma implementations are here:  http://wstein.org/Tables/hijikata.html
+This can be used for computing traces of Hecke operators acting on spaces of modular forms.  In most cases, other methods are better, but this can still have value in that it can do things that are impossible with modular symbols.    
+
+My pari and Magma implementations are here:  http://wstein.org/Tables/hijikata.html
+
+Hijikata's article: http://projecteuclid.org/euclid.jmsj/1240435364

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

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

`d05a834`	`Merge branch 'u/chapoton/12450' into 7.2.rc2`
`ec3f295`	`trac 12450 restore the dedekind psi function`

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

Changed commit from 7ae0512 to ec3f295

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

Changed commit from ec3f295 to e5cd277

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

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

e5cd277 Merge branch 'u/chapoton/12450' in 7.3.rc0

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

Changed commit from e5cd277 to 749e83b

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

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

`e3193b7`	`Merge branch 'u/chapoton/12450' in 8.0.b2`
`749e83b`	`trac 12450 fix import`

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

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

ac3984c Merge branch 'u/chapoton/12450' in 8.1.b5

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

Changed commit from 749e83b to ac3984c

fchapoton commented 6 years ago

comment:24

I have made a fresh new branch.

New commits:

91e89a5 implement the Hijikata trace formula (refreshed branch)

fchapoton commented 6 years ago

Changed branch from u/chapoton/12450 to u/chapoton/12450v2

fchapoton commented 6 years ago

Changed commit from ac3984c to 91e89a5

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

Changed commit from 91e89a5 to da18dae

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

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

da18dae change import in doctest of Dedekind psi

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

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

3399755 some details

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

Changed commit from da18dae to 3399755

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

Changed commit from 3399755 to 29127d8

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

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

29127d8 implement the Hijikata trace formula (refreshed branch)

fchapoton commented 6 years ago

Dependencies: #26053

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

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

c59cf80 pyflakes fixup

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

Changed commit from 29127d8 to c59cf80

fchapoton commented 6 years ago

Changed dependencies from #26053 to none

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

Changed commit from c59cf80 to e7633bf

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

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

`9649d79`	`Merge branch 'u/chapoton/12450v2' in 8.4.rc1`
`e7633bf`	`some details`

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

Changed commit from e7633bf to 4b867f8

sagemath / sage

implement the Hijikata trace formula #12450