############ fgb_sage ############

.. image:: https://readthedocs.org/projects/fgb-sage/badge/?version=latest :target: https://fgb-sage.readthedocs.io/en/latest/?badge=latest :alt: Documentation Status

A Sage interface for FGb

This package is a SageMath <SAGE_> interface to FGb and can be installed as a Python package for use with Sage. It provides a simple link between the C-interface of FGb and polynomials and ideals in Sage.

FGb is a C-library by J. C. Faugère for Gröbner basis computations, with support for:

• Gröbner bases over ℚ and finite prime fields
• parallel computations (over finite fields)
• elimination/block orders (degree-reverse-lexicographic, only)

Examples

See the examples and documentation at https://fgb-sage.readthedocs.io <fgb_sage_rdt_>_.

Installation

Requirements: Linux with a recent version of Sage <SAGE_>_ (tested with Sage 9.5.rc0 on Ubuntu 20.04 as well as with Sage 9.6 from Arch Linux).

First, clone the repository from GitHub <fgb_sage_gh_>_ and then compile and run the tests::

git clone https://github.com/mwageringel/fgb_sage.git && cd fgb_sage
sage setup.py test

After the tests passed successfully, run the following command to install the package for use with Sage::

sage -python -m pip install --upgrade --no-index -v .

Alternatively, to install into the Python user install directory (no root access required), run::

sage -python -m pip install --upgrade --no-index -v --user .

Installing into a virtual environment, assuming Sage is installed system-wide::

python -m venv --system-site-packages ./sage-venv  # assumes that sage and python-setuptools are available system-wide
source ./sage-venv/bin/activate                    # redefines `python` and `pip` using virtual environment
python -m pip install --upgrade --no-index -v .
cd sage-venv && python -m IPython                  # changing directory is important

    In [1]: from sage.all import *
    In [2]: R = PolynomialRing(QQ, 5, 'x', order="degrevlex(2),degrevlex(3)")
    In [3]: I = sage.rings.ideal.Cyclic(R)
    In [4]: import fgb_sage
    In [5]: gb = fgb_sage.groebner_basis(I)

Packaged versions of Sage

If Sage was installed by the package manager of your Linux distribution, you may need to install a few more dependencies in order to compile this package. For example, on

• Arch Linux::

  pacman -S --asdeps cython python-pkgconfig

• Ubuntu::

  libgsl-dev liblinbox-dev libsingular4-dev libntl-dev libflint-dev libmpfr-dev libpari-dev python3-ipywidgets

Alternatively, you can download a Sage binary <https://www.sagemath.org/download.html>, use Sage via Docker <https://hub.docker.com/r/sagemath/sagemath> or install Sage from source. See also issue #2 <https://github.com/mwageringel/fgb_sage/issues/2>_.

Issues

• macOS: Support for macOS has been dropped for the time being due to difficulties in compiling this package with -fopenmp since Sage version 8.8. Compiling the entirety of Sage with GCC support might make this work, but this was not tested. See issue #3 <https://github.com/mwageringel/fgb_sage/issues/3>_.

• Memory leaks: The underlying FGb program leaks memory, which can be a problem when computing many Gröbner bases in a single long-lived process. In this case, it might be better to split the computation into several processes or use a different Gröbner basis algorithm available in Sage <sage_docs_gb_>_.

.. _SAGE: https://www.sagemath.org/ .. _FGb: https://www-polsys.lip6.fr/~jcf/FGb/index.html .. _fgb_sage_gh: https://github.com/mwageringel/fgb_sage .. _fgb_sage_rdt: https://fgb-sage.readthedocs.io/en/latest/#module-fgb_sage .. _sage_docs_gb: https://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/multi_polynomial_ideal.html#sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal.groebner_basis