passagemath-symbolics 10.6.47

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 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-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