passagemath-symbolics 10.5.49

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 2005-2025 under the motto “Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, and MATLAB”.

The passagemath fork was created in October 2024 with the following goals:

• providing modularized installation with pip, thus completing a major project started in 2020 in the Sage codebase,

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

• giving clear attribution of upstream projects,

• providing independently usable Python interfaces to upstream libraries,

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

• inviting collaborations with upstream projects,

• building a professional, respectful, inclusive community,

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

• developing a native Windows port.

Full documentation is available online.

passagemath attempts to support all major Linux distributions and recent versions of macOS. Use on Windows currently requires the use of Windows Subsystem for Linux or virtualization.

Complete sets of binary wheels are provided on PyPI for Python versions 3.9.x-3.12.x. Python 3.13.x is also supported, but some third-party packages are still missing wheels, so compilation from source is triggered for those.

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 sage.all__sagemath_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[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