Hilbert Modular Groups

This repository contains a python package hilbert_modgroup that implements algorithms for Hilbert modular groups, in particular a reduction algorithm. The implementation is written in Python and is dependent on SageMath.

Requirements

• SageMath v9.6+ (https://www.sagemath.org/) (Tested on v9.6, v9.7, v10.0 and v10.2)

Installation

Using sage pip

This package needs to be installed in the virtual environment provided by SageMath, and it is therefore necessary to run the following command

$ sage -pip install --no-build-isolation hilbert-modular-group

Note: The --no-build-isolation is necessary as the compiler needs access to certain library files from the sage installation and SageMath itself is too large to be required as a build dependency. As an alternative to this flag you can also specify the environment variable SAGE_LIB explicitly.

From git source

If the SageMath executable sage is in the current path you can install from source using the Makefile

$ git clone https://github.com/fredstro/hilbertmodgroup.git
$ cd hilbertmodgrup
$ make install

Docker

If you do not have SageMath installed, but you have docker you can use install this package in a docker container built and executed using e.g. make docker-sage or make docker-examples

Usage

The package can be imported and used as any other package. For example, to find the reduction of the point given by [1+i,1+i] in H^2 with respect to the Hilbert modular group of Q joint by square-root of 5 write:

sage: from hilbert_modgroup.all import *
sage: H1=HilbertModularGroup(5)
sage: P1=HilbertPullback(H1)
sage: z = UpperHalfPlaneProductElement([1+I,1+I])
sage: P1.reduce(z)
[1.00000000000000*I, 1.00000000000000*I]
sage: z = UpperHalfPlaneProductElement([0.25+I/2,1+I])
sage: P1.reduce(z) # abs tol 1e-10
[0.694427190999916 + 0.611145618000168*I, -0.309016994374947 + 1.30901699437495*I]
sage: P1.reduce(z, return_map=True)[1]
[-1/2*a + 1/2  1/2*a + 1/2]
[-1/2*a + 1/2            0]

For more examples see the embedded doctests (search for EXAMPLES) as well as the /examples directory which contains Jupyter notebook with more extensive examples corresponding to the paper "Reduction Algorithms for Hilbert Modular Groups" by F. Stromberg. (Reference to appear)

Examples

The directory /examples contains Jupyter notebooks with example code to illustrate the interface and functionality of this package. You can either open them manually from SageMath or run one of the following commands: make examples make docker-examples which will start up a Jupyter notebook server from sagemath either locally or in a docker container.

Community Guidelines

How to Contribute?

• Open an issue on GitHub and create a pull / merge request against the develop branch.

How to report an issue or a problem?

• First check if the issue is resolved in the develop branch. If not, open an issue on GitHub.

How to seek help and support?

• Contact the maintainer, Fredrik Stromberg, at: [email protected] (alternatively at [email protected])

Development and testing

The make file Makefile contains a number of useful commands that you can run using

$ make <command>

The following commands are run in your local SagMath environment:

1. build -- builds the package in place (sometimes useful for development).
2. sdist -- create a source distribution in /sdist (can be installed using sage -pip install sdist/<dist name>)
3. install -- build and install the package in the currently active sage environment
4. clean -- remove all build and temporary files
5. test -- run sage's doctests (same as sage -t src/*)
6. examples -- run a Jupyter notebook with the SageMath kernel initialised at the /examples directory.
7. tox -- run sage -tox with all environments: doctest, coverage, pycodestyle, relint, codespell Note: If your local SageMath installation does not contain tox this will run sage -pip install tox.

The following commands are run in an isolated docker container and requires docker to be installed and running:

1. docker -- build a docker container with the tag hilbertmodgroup-{GIT_BRANCH}
2. docker-rebuild -- rebuild the docker container without cache
3. docker-test -- run SageMath's doctests in the docker container
4. docker-examples -- run a Jupyter notebook with the SageMath kernel initialised at the /examples directory and exposing the notebook at http://127.0.0.1:8888. The port used can be modified by
5. docker-tox -- run tox with all environments: doctest, coverage, pycodestyle, relint, codespell.
6. docker-shell -- run a shell in a docker container
7. docker-sage -- run a sage interactive shell in a docker container

The following command-line parameters are available

• NBPORT -- set the port of the notebook for examples and docker-examples (default is 8888)
• TOX_ARGS -- can be used to select one or more of the tox environments (default is all)
• REMOTE_SRC -- set to 0 if you want to use the local source instead of pulling from gitHub (default 1)
• GIT_BRANCH -- the branch to pull from gitHub (used if REMOTE_SRC=1)

Example usage

Run tox coverage on the branch main from gitHub:

make docker-tox REMOTE_SRC=1 GIT_BRANCH=main TOX_ARGS=coverage

Run doctests on the local source with local version of sage:

make tox TOX_ARGS=doctest

Run relint on the local source with docker version of sage:

make docker-tox REMOTE_SRC=0 TOX_ARGS=relint

Development

GitHub Workflow

• There are two long-lived branches main and develop.
• The develop branch is used for development and can contain new / experimental features.
• Pull-requests should be based on develop.
• Releases should be based on main.
• The main branch should always be as stable and functional as possible. In particular, merges should always happen from develop into main.
• Git-Flow is enabled (and encouraged) with feature branches based on develop and hotfixes based on main.

GitHub Actions

Each commit is tested and checked using gitHub actions with tox running:

• doctest -- run all doctests
• coverage -- ensure that all functions and classes are documented
• pycodestyle-minimal -- ensure PEP8 style guide is followed (except we allow max line length 99)
• relint -- relint against some patterns taken from the SageMath source (config file .relint.yaml)
• codespell -- spellchecker

To make sure that your commit passes all tests you should make tox or make docker-tox REMOTE_SRC=0 on the command line.

Versions

Versioning of this project is managed by setuptools_scm. To bump the version create a git tag x.y.z and the file src/hilbert_modgroup/version.py will then be automatically updated to contain

version = 'x.y.z.???'
version_tuple = (x, y, z, '???')

where ??? depends on the state of the current directory. If you are creating a new version to release the source directory should be clean.

PyPi

To upload new versions to PyPi:

1. make sdist -- creates a source distribution dist/hilbert_modular_group-x.y.z
2. twine check dist/hilbert_modular_group-x.y.z
3. twine upload --repository pypi dist/hilbert_modular_group-z.y.z

References:

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