passagemath-symbolics 10.8.4

passagemath: Symbolic calculus

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-symbolics is a distribution of a part of the Sage Library. It provides a small subset of the modules of the Sage library (“sagelib”, passagemath-standard).

What is included

• Symbolic Calculus

• Pynac (fork of GiNaC)

• Arithmetic Functions, Elementary and Special Functions (via sagemath-categories)

• Asymptotic Expansions

• SageManifolds: Topological, Differentiable, Pseudo-Riemannian, Poisson Manifolds

• Hyperbolic Geometry

Examples

Using SageManifolds:

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

In [1]: from passagemath_symbolics import *

In [2]: M = Manifold(4, 'M', structure='Lorentzian'); M
Out[2]: 4-dimensional Lorentzian manifold M

In [3]: X = M.chart(r"t r:(0,+oo) th:(0,pi):\theta ph:(0,2*pi):\phi")

In [4]: t,r,th,ph = X[:]; m = var('m'); assume(m>=0)

In [5]: g = M.metric(); g[0,0] = -(1-2*m/r); g[1,1] = 1/(1-2*m/r); g[2,2] = r**2; g[3,3] = (r*sin(th))**2; g.display()
Out[5]: g = (2*m/r - 1) dt⊗dt - 1/(2*m/r - 1) dr⊗dr + r^2 dth⊗dth + r^2*sin(th)^2 dph⊗dph

In [6]: g.christoffel_symbols_display()
Out[6]:
Gam^t_t,r = -m/(2*m*r - r^2)
Gam^r_t,t = -(2*m^2 - m*r)/r^3
Gam^r_r,r = m/(2*m*r - r^2)
Gam^r_th,th = 2*m - r
Gam^r_ph,ph = (2*m - r)*sin(th)^2
Gam^th_r,th = 1/r
Gam^th_ph,ph = -cos(th)*sin(th)
Gam^ph_r,ph = 1/r
Gam^ph_th,ph = cos(th)/sin(th)

Available as extras, from other distributions

pip install "passagemath-symbolics[fricas]"

Computer algebra system FriCAS, via passagemath-fricas

pip install "passagemath-symbolics[giac]"

Computer algebra system Giac, via passagemath-giac

pip install "passagemath-symbolics[primecount]"

Prime counting function implementation primecount, via primecountpy

pip install "passagemath-symbolics[sympy]"

Python library for symbolic mathematics / computer algebra system SymPy

pip install "passagemath-symbolics[plot]"

Plotting facilities