CyPari 2
========
.. image:: https://readthedocs.org/projects/cypari2/badge/?version=latest
:target: https://cypari2.readthedocs.io/en/latest/?badge=latest
:alt: Documentation Status
A Python interface to the number theory library `PARI/GP <http://pari.math.u-bordeaux.fr/>`_.
Installation
------------
From a distribution package (GNU/Linux, conda-forge)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
A package might be available in your package manager, see
https://repology.org/project/python:cypari2/versions or
https://doc.sagemath.org/html/en/reference/spkg/cypari for
installation instructions.
From a pre-built wheel from PyPI
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Requirements:
- Python >= 3.9
- pip
Install cypari2 via the Python Package Index (PyPI) via
::
$ pip install cypari2 [--user]
(the optional option *--user* allows to install cypari2 for a single user
and avoids using pip with administrator rights).
From source with pip
^^^^^^^^^^^^^^^^^^^^
Requirements:
- PARI/GP >= 2.9.4 (header files and library); see
https://doc.sagemath.org/html/en/reference/spkg/pari#spkg-pari
for availability in distributions (GNU/Linux, conda-forge, Homebrew, FreeBSD),
or install from source.
- Python >= 3.9
- pip
- `cysignals <https://pypi.python.org/pypi/cysignals/>`_ >= 1.11.3
- Cython >= 3.0
Install cypari2 via the Python Package Index (PyPI) via
::
$ pip install --no-binary cypari2 cypari2 [--user]
(the optional option *--user* allows to install cypari2 for a single user
and avoids using pip with administrator rights).
`pip` builds the package using build isolation. All Python build dependencies
of the package, declared in pyproject.toml, are automatically installed in
a temporary virtual environment.
If you want to try the development version, use
::
$ pip install git+https://github.com/sagemath/cypari2.git [--user]
Usage
-----
The interface as been kept as close as possible from PARI/GP. The following
computation in GP
::
? zeta(2)
%1 = 1.6449340668482264364724151666460251892
? p = x^3 + x^2 + x - 1;
? modulus = t^3 + t^2 + t - 1;
? fq = factorff(p, 3, modulus);
? centerlift(lift(fq))
%5 =
[ x - t 1]
[x + (t^2 + t - 1) 1]
[ x + (-t^2 - 1) 1]
translates into
::
>>> import cypari2
>>> pari = cypari2.Pari()
>>> pari(2).zeta()
1.64493406684823
>>> p = pari("x^3 + x^2 + x - 1")
>>> modulus = pari("t^3 + t^2 + t - 1")
>>> fq = p.factorff(3, modulus)
>>> fq.lift().centerlift()
[x - t, 1; x + (t^2 + t - 1), 1; x + (-t^2 - 1), 1]
The object **pari** above is the object for the interface and acts as a
constructor. It can be called with basic Python objects like integer
or floating point. When called with a string as in the last example
the corresponding string is interpreted as if it was executed in a GP shell.
Beyond the interface object **pari** of type **Pari**, any object you get a
handle on is of type **Gen** (that is a wrapper around the **GEN** type from
libpari). All PARI/GP functions are then available in their original names as
*methods* like **zeta**, **factorff**, **lift** or **centerlift** above.
Alternatively, the pari functions are accessible as methods of **pari**. The
same computations be done via
::
>>> import cypari2
>>> pari = cypari2.Pari()
>>> pari.zeta(2)
1.64493406684823
>>> p = pari("x^3 + x^2 + x - 1")
>>> modulus = pari("t^3 + t^2 + t - 1")
>>> fq = pari.factorff(p, 3, modulus)
>>> pari.centerlift(pari.lift(fq))
[x - t, 1; x + (t^2 + t - 1), 1; x + (-t^2 - 1), 1]
The complete documentation of cypari2 is available at http://cypari2.readthedocs.io and
the PARI/GP documentation at http://pari.math.u-bordeaux.fr/doc.html
Contributing
------------
CyPari 2 is maintained by the SageMath community.
Open issues or submit pull requests at https://github.com/sagemath/cypari2
and join https://groups.google.com/group/sage-devel to discuss.
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