passagemath-libecm 10.6.4

passagemath: Elliptic curve method for integer factorization using GMP-ECM

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.

For the Linux aarch64 (ARM) platform, some third-party packages are still missing wheels; see the instructions for building them from source.

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-3.13.x.

About this pip-installable distribution package

This pip-installable package passagemath-libecm provides interfaces to GMP-ECM, the implementation of the Elliptic Curve Method for integer factorization.

What is included

• Python interface to the ECM program

• Cython interface to the libecm library

• The binary wheels published on PyPI include a prebuilt copy of GMP-ECM (executable and library).

Examples

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

In [1]: from sage.libs.libecm import ecmfactor

In [2]: N = 11 * 43570062353753446053455610056679740005056966111842089407838902783209959981593077811330507328327968191581

In [3]: ecmfactor(N, 100, verbose=True)
Performing one curve with B1=100
Found factor in step 1: 11
Out[3]: (True, 11, ...)

In [4]: ecmfactor(N//11, 100, verbose=True)
Performing one curve with B1=100
Found no factor.
Out[4]: (False, None)

Available as extras, from other distributions

pip install passagemath-libecm[pari] additionally makes PARI available (for primality testing)