Opened 5 years ago

Closed 5 years ago

#16883 closed enhancement (fixed)

Modular forms for the theta subgroup (as part of Hecke triangle groups)

Reported by: jj Owned by:
Priority: minor Milestone: sage-6.4
Component: modular forms Keywords: theta subgroup modular forms hecke triangle
Cc: mraum Merged in:
Authors: Jonas Jermann Reviewers: Martin Raum
Report Upstream: N/A Work issues:
Branch: 05e551d (Commits) Commit: 05e551d292500c1928d08361207703dab8a89043
Dependencies: Stopgaps:

Description (last modified by jj)

Complete support for modular forms for the Hecke triangle group corresponding to n=infinity (the theta subgroup) with corresponding + further doctests/documentation.

The situation is slightly different since there are now two cusps with two corresponding generators.

In particular the limit of the generator f_rho tends to 1 and the generator for n=infinity is instead E4 which is the limit of f_rhon.

Note that only functions which are meromorphic and meromorphic at the cusps are considerd. E.g. E4 is the 8th power of theta, but smaller powers are no longer meromorphic at -1. Also note that limits of functions/coefficients as n tends to infinity are usually given by the corresponding function in the theta subgroup.

Additionally the ticket adds support for experimental rationalization of series, refactoring of code which in particular provides more robust numerical Fourier expansions and Eisenstein series of arbitrary weight for n=3,4,6.

The ticket also fixes a mistake from #16839 and has some other small changes.

Attachments (1)

eisenstein_series_zz.diff (10.1 KB) - added by jj 5 years ago.
An optional change to make EisensteinSeries? more consistent with the rest

Download all attachments as: .zip

Change History (24)

comment:1 Changed 5 years ago by git

  • Commit changed from 988bdadce2f5a50af09f8b7a668c3e9e4f7a6a46 to b73a0d6bd3581a586ad5e7c844f1c78aabcd83a6

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

b73a0d6support much more arguments for actions and/or evaluations without raising an error (which was a very common issue before), support for orders of functions at certain points != infinity, do precise function evaluation at these points in the trivial cases

comment:2 Changed 5 years ago by git

  • Commit changed from b73a0d6bd3581a586ad5e7c844f1c78aabcd83a6 to ff9f4a8ae72ba9eaead6e22be3bcd7e682f5966c

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

ff9f4a8support taking power 0 of homogeneous elements

comment:3 Changed 5 years ago by git

  • Commit changed from ff9f4a8ae72ba9eaead6e22be3bcd7e682f5966c to 3d46db2825c6e5364897613293fb482293a41dab

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

3d46db2Complete support for the theta subgroup:

comment:4 Changed 5 years ago by jj

  • Description modified (diff)

comment:5 Changed 5 years ago by jj

  • Status changed from new to needs_review

comment:6 Changed 5 years ago by jj

  • Dependencies changed from 16839 to #16839
  • Description modified (diff)

comment:7 Changed 5 years ago by jj

  • Description modified (diff)

comment:8 Changed 5 years ago by git

  • Commit changed from 3d46db2825c6e5364897613293fb482293a41dab to 65eb97e15d05a2af8e631f8252485bc48a1bc23c

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

65eb97eexperimental support for turning numerical laurent series into exact series and using it to cosntruct forms based on numerical series (no success garantuees)

comment:9 Changed 5 years ago by git

  • Commit changed from 65eb97e15d05a2af8e631f8252485bc48a1bc23c to 1de64b82dbbcfc94ef7ab49b4e633b0b82187ee2

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

1de64b8A large refactoring of code:

comment:10 Changed 5 years ago by jj

  • Description modified (diff)

comment:11 Changed 5 years ago by git

  • Commit changed from 1de64b82dbbcfc94ef7ab49b4e633b0b82187ee2 to 6cdde65492fe21fe9adc5897ccf97f53bc8ca481

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

6cdde65documentation fix, use get_d and get_q, also support to get the polynomial variable d with get_d

comment:12 Changed 5 years ago by git

  • Commit changed from 6cdde65492fe21fe9adc5897ccf97f53bc8ca481 to 3660bea9865f6982fc60974c82f24b1c1b825726

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

3660beaconstruction of elements based on numerical coefficients works (sometimes), so we might as well doctest it

comment:13 Changed 5 years ago by git

  • Commit changed from 3660bea9865f6982fc60974c82f24b1c1b825726 to 13ea3d8ecceea61173b0a8308ccafabe2769b208

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

13ea3d8- Support for Eisenstein series of all weights in the arithmetic cases n=3, 4, 6

comment:14 Changed 5 years ago by jj

  • Description modified (diff)

comment:15 Changed 5 years ago by git

  • Commit changed from 13ea3d8ecceea61173b0a8308ccafabe2769b208 to 9f7ab3c343a66a4a6050d21a0bcf2ba99f3b47cd

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

9f7ab3ccheck by default whether the constructed element has the same initial (rationalized) laurent series

Changed 5 years ago by jj

An optional change to make EisensteinSeries? more consistent with the rest

comment:16 Changed 5 years ago by git

  • Commit changed from 9f7ab3c343a66a4a6050d21a0bcf2ba99f3b47cd to e8df685493dcdb323aeb7a1906de8a6fc7c1bee7

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

e8df685simplify/reorder the basis such that the quasi part matrix corresponds to the quasi part generators

comment:17 Changed 5 years ago by mraum

  • Branch changed from u/jj/theta_group to u/mraum/ticket/16883
  • Created changed from 08/26/14 16:17:24 to 08/26/14 16:17:24
  • Modified changed from 09/02/14 01:42:25 to 09/02/14 01:42:25

comment:18 Changed 5 years ago by jj

  • Branch changed from u/mraum/ticket/16883 to u/jj/theta_group
  • Commit changed from e8df685493dcdb323aeb7a1906de8a6fc7c1bee7 to 05e551d292500c1928d08361207703dab8a89043

comment:19 Changed 5 years ago by mraum

  • Dependencies #16839 deleted

This looks good. I have reviewed the changes originally introduced in #16839, too. Several corrections to the latter have been made. I.e. #16839 should be closed as invalid or similar after this.

As soon as the buildbot has run this, this can be changed to positive review.

comment:20 Changed 5 years ago by mraum

  • Status changed from needs_review to positive_review

comment:21 Changed 5 years ago by vbraun

  • Status changed from positive_review to needs_work

Reviewer name

comment:22 Changed 5 years ago by jj

  • Reviewers set to Martin Raum
  • Status changed from needs_work to positive_review

Martin Raum is the reviewer.

comment:23 Changed 5 years ago by vbraun

  • Branch changed from u/jj/theta_group to 05e551d292500c1928d08361207703dab8a89043
  • Resolution set to fixed
  • Status changed from positive_review to closed
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