passagemath-pari 10.8.4

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 2005-2026 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 from binary wheels, - this major project was started in May 2020 in the Sage codebase and completed in passagemath 10.5.29 (May 2025),

• 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 WebAssembly (Pyodide, emscripten-forge) for serverless deployment with Javascript,

• developing a native Windows port - passagemath 10.6.1 (July 2025) published the first pip-installable wheel packages for native Windows on x86_64, - passagemath packages became available in the [MSYS2 software distribution](https://packages.msys2.org/search?t=pkg&q=passagemath) in November 2025.

Moreover, the passagemath project:

• provides a stable, frequently updated version of the Sage distribution,

• integrates additional mathematical software, notably Macaulay2, a full set of GAP packages, and the Combinatorial Matrix Recognition library,

• curates a library of Sage user packages.

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, ARM) 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-10.8.x series are 3.11.x-3.14.x; the passagemath-10.6.x series (EOL 2026-10) still supports Python 3.10.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]"