passagemath-pari 10.6.47

passagemath: Computational Number Theory with PARI/GP

passagemath is open source mathematical software in Python, released under the GNU General Public Licence GPLv2+.

It is a fork of SageMath, which has been developed 2005-2025 under the motto “Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, and MATLAB”.

The passagemath fork uses the motto “Creating a Free Passage Between the Scientific Python Ecosystem and Mathematical Software Communities.” It was created in October 2024 with the following goals:

• providing modularized installation with pip,

• establishing first-class membership in the scientific Python ecosystem,

• giving clear attribution of upstream projects,

• providing independently usable Python interfaces to upstream libraries,

• offering platform portability and integration testing services to upstream projects,

• inviting collaborations with upstream projects,

• building a professional, respectful, inclusive community,

• empowering Sage users to participate in the scientific Python ecosystem by publishing packages,

• developing a port to Pyodide for serverless deployment with Javascript,

• developing a native Windows port.

Full documentation is available online.

passagemath attempts to support and provides binary wheels suitable for all major Linux distributions and recent versions of macOS.

Binary wheels for native Windows (x86_64) are are available for a subset of the passagemath distributions. Use of the full functionality of passagemath on Windows currently requires the use of Windows Subsystem for Linux (WSL) or virtualization.

The supported Python versions in the passagemath 10.6.x series are 3.10.x-3.14.x.

About this pip-installable distribution package

This pip-installable distribution passagemath-pari is a small distribution that provides modules that depend on PARI/GP, the computer algebra system designed for fast computations in number theory: factorizations, algebraic number theory, elliptic curves, modular forms, L-functions…

What is included

• integer factorization

• finite fields

• much of the p-adics functionality of the Sage library

• discrete valuations

• parts of the quadratic forms functionality of the Sage library

• various other modules with dependencies on PARI/GP, see MANIFEST

• the cypari2 API

• the pari-jupyter kernel

• the binary wheels on PyPI ship a prebuilt copy of PARI/GP

• the binary wheels on PyPI ship XEUS-GP, another Jupyter kernel for PARI/GP

Examples

Starting the GP calculator from the command line:

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-pari" sage -gp
GP/PARI CALCULATOR Version 2.17.2 (released)
...

Using the pexpect interface to the GP calculator:

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-pari[test]" ipython

In [1]: from sage.interfaces.gp import gp

In [2]: E = gp.ellinit([1,2,3,4,5])

In [3]: E.ellglobalred()
Out[3]: [10351, [1, -1, 0, -1], 1, [11, 1; 941, 1], [[1, 5, 0, 1], [1, 5, 0, 1]]]

Using the cypari2 library interface:

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-pari" python

>>> 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]

Available as extras, from other distributions

PARI/GP data packages

See https://pari.math.u-bordeaux.fr/packages.html for detailed descriptions.

pip install "passagemath-pari[elldata]"

pip install "passagemath-pari[galdata]"

pip install "passagemath-pari[galpol]"

pip install "passagemath-pari[nflistdata]"

pip install "passagemath-pari[nftables]"

pip install "passagemath-pari[seadata]"

pip install "passagemath-pari[seadata-big]"

pip install "passagemath-pari[seadata-small]"