zetalib 0.4.5

computing zeta functions of groups, algebras, and modules

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Introduction

Zeta provides methods for computing local and topological zeta functions arising from the enumeration of subalgebras, ideals, submodules, and representations of suitable algebraic structures as well as some other types of zeta functions.

This package is an experimental fork of Zeta, turning it into a pip-installable SageMath package. You can check this temporary link for the full documentation.

Please also check the original homepage of Zeta by Tobias Rossmann.

Installation

Dependencies

We assume SageMath version 8.3, or higher, is used.

The wheel packaging standard is needed at installation time. It can be installed by running:

$ sage -pip install wheel

Zeta will try to invoke the programs count (a part of LattE integrale) and normaliz (a part of Normaliz). They can be installed by running:

$ sage -i latte_int
$ sage -i normaliz

See the full documentation how to use other versions of these programs.

Install from PyPI

The easiest way to obtain Zeta is to run:

$ sage -pip install zetalib

Local install from source

Download the source from the git repository:

$ git clone https://gitlab.com/mathzeta2/zetalib.git

For convenience this package contains a Makefile with some often used commands. To build the C extensions, install and test you should change to the root directory and run:

$ make

Alternatively, you can do it in separate steps:

$ make build
$ make test
$ sage -pip install --upgrade --no-index -v . # or `make install`

To uninstall you can run:

$ sage -pip uninstall zetalib # or `make uninstall`

If you want to use another version of SageMath you have installed, you can modify the SAGE variable when calling make:

$ make SAGE=/path/to/sage build

Usage

Once the package is installed, you can use it in Sage with:

sage: import zetalib
sage: M = zetalib.Algebra(rank=3, operators=[ [[1,1,-1], [0,1,1], [0,0,1]] ])
sage: zetalib.topological_zeta_function(M)
1/((3*s - 2)*(2*s - 1)*s)

See the documentation for further details.

Packaging

All packaging setup is internally done through setup.py. To create a “source package” run:

$ sage setup.py sdist

To create a binary wheel package run:

$ sage setup.py bdist_wheel

Or use the shorthand:

$ make build_wheel

Documentation

The source files of the documentation are located in the docs/source directory, and are written in Sage’s Sphinx format.

Generate the HTML documentation by running:

$ cd docs
$ sage -sh -c "make html"

Or using the shorthand:

$ make doc

Then open docs/build/html/index.html in your browser.

Acknowledgements

• The Sage Sample Package was used for the initial package structure.

License

See the LICENSE file. This fork of Zeta is released under GPL-3.0-or-later, like the original version, as quoted in the original documentation:

Copyright 2014, 2015, 2016, 2017 Tobias Rossmann.

Zeta is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

Zeta is distributed in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Zeta. If not, see http://www.gnu.org/licenses.