passagemath-symbolics 10.4.60

passagemath: Symbolic calculus

About SageMath

“Creating a Viable Open Source Alternative to

Magma, Maple, Mathematica, and MATLAB”

Copyright (C) 2005-2024 The Sage Development Team

https://www.sagemath.org

SageMath fully supports all major Linux distributions, recent versions of macOS, and Windows (Windows Subsystem for Linux).

See https://doc.sagemath.org/html/en/installation/index.html for general installation instructions.

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

• Binary wheels on PyPI contain prebuilt copies of Maxima and Embeddable Common Lisp

Examples

Starting Maxima from the command line:

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-symbolics" sage -maxima

Using the pexpect interface to Maxima:

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

In [1]: from sage.interfaces.maxima import maxima

In [2]: maxima('1+1')
Out[2]: 2

Using the library interface to Maxima:

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

In [1]: from sage.interfaces.maxima_lib import maxima_lib

In [2]: F = maxima_lib('x^5 - y^5').factor()

In [3]: F.display2d()
Out[3]:
                           4      3    2  2    3      4
               - (y - x) (y  + x y  + x  y  + x  y + x )

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