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

[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_rho^n.

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.

[git]

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

​b73a0d6

support 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

[git]

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

​ff9f4a8

support taking power 0 of homogeneous elements

[git]

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

​3d46db2

Complete support for the theta subgroup:

[git]

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

​65eb97e

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

[git]

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

​1de64b8

A large refactoring of code:

[git]

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

​6cdde65

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

[git]

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

​3660bea

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

[git]

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

[git]

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

​9f7ab3c

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

[jj]

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

[git]

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

​e8df685

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

[mraum]

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.

[vbraun]

Reviewer name

[jj]

Martin Raum is the reviewer.