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
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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"description": "CyPari 2\n========\n\n.. image:: https://readthedocs.org/projects/cypari2/badge/?version=latest\n :target: https://cypari2.readthedocs.io/en/latest/?badge=latest\n :alt: Documentation Status\n\nA Python interface to the number theory library `PARI/GP <http://pari.math.u-bordeaux.fr/>`_.\n\nInstallation\n------------\n\nFrom a distribution package (GNU/Linux, conda-forge)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\nA package might be available in your package manager, see\nhttps://repology.org/project/python:cypari2/versions or\nhttps://doc.sagemath.org/html/en/reference/spkg/cypari for\ninstallation instructions.\n\n\nFrom a pre-built wheel from PyPI\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\nRequirements:\n\n- Python >= 3.9\n- pip\n\nInstall cypari2 via the Python Package Index (PyPI) via\n\n::\n\n $ pip install cypari2 [--user]\n\n(the optional option *--user* allows to install cypari2 for a single user\nand avoids using pip with administrator rights).\n\n\nFrom source with pip\n^^^^^^^^^^^^^^^^^^^^\n\nRequirements:\n\n- PARI/GP >= 2.9.4 (header files and library); see\n https://doc.sagemath.org/html/en/reference/spkg/pari#spkg-pari\n for availability in distributions (GNU/Linux, conda-forge, Homebrew, FreeBSD),\n or install from source.\n- Python >= 3.9\n- pip\n\nInstall cypari2 via the Python Package Index (PyPI) via\n\n::\n\n $ pip install --no-binary cypari2 cypari2 [--user]\n\n(the optional option *--user* allows to install cypari2 for a single user\nand avoids using pip with administrator rights).\n\n`pip` builds the package using build isolation. All Python build dependencies\nof the package, declared in pyproject.toml, are automatically installed in\na temporary virtual environment.\n\nIf you want to try the development version, use\n\n::\n\n $ pip install git+https://github.com/sagemath/cypari2.git [--user]\n\n\nUsage\n-----\n\nThe interface as been kept as close as possible from PARI/GP. The following\ncomputation in GP\n\n::\n\n ? zeta(2)\n %1 = 1.6449340668482264364724151666460251892\n\n ? p = x^3 + x^2 + x - 1;\n ? modulus = t^3 + t^2 + t - 1;\n ? fq = factorff(p, 3, modulus);\n ? centerlift(lift(fq))\n %5 =\n [ x - t 1]\n\n [x + (t^2 + t - 1) 1]\n\n [ x + (-t^2 - 1) 1]\n\ntranslates into\n\n::\n\n >>> import cypari2\n >>> pari = cypari2.Pari()\n\n >>> pari(2).zeta()\n 1.64493406684823\n\n >>> p = pari(\"x^3 + x^2 + x - 1\")\n >>> modulus = pari(\"t^3 + t^2 + t - 1\")\n >>> fq = p.factorff(3, modulus)\n >>> fq.lift().centerlift()\n [x - t, 1; x + (t^2 + t - 1), 1; x + (-t^2 - 1), 1]\n\nThe object **pari** above is the object for the interface and acts as a\nconstructor. It can be called with basic Python objects like integer\nor floating point. When called with a string as in the last example\nthe corresponding string is interpreted as if it was executed in a GP shell.\n\nBeyond the interface object **pari** of type **Pari**, any object you get a\nhandle on is of type **Gen** (that is a wrapper around the **GEN** type from\nlibpari). All PARI/GP functions are then available in their original names as\n*methods* like **zeta**, **factorff**, **lift** or **centerlift** above.\n\nAlternatively, the pari functions are accessible as methods of **pari**. The\nsame computations be done via\n\n::\n\n >>> import cypari2\n >>> pari = cypari2.Pari()\n\n >>> pari.zeta(2)\n 1.64493406684823\n\n >>> p = pari(\"x^3 + x^2 + x - 1\")\n >>> modulus = pari(\"t^3 + t^2 + t - 1\")\n >>> fq = pari.factorff(p, 3, modulus)\n >>> pari.centerlift(pari.lift(fq))\n [x - t, 1; x + (t^2 + t - 1), 1; x + (-t^2 - 1), 1]\n\nThe complete documentation of cypari2 is available at http://cypari2.readthedocs.io and\nthe PARI/GP documentation at http://pari.math.u-bordeaux.fr/doc.html\n\nContributing\n------------\n\nCyPari 2 is maintained by the SageMath community.\n\nOpen issues or submit pull requests at https://github.com/sagemath/cypari2\nand join https://groups.google.com/group/sage-devel to discuss.\n",
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