Metadata-Version: 2.1
Name: passagemath-symbolics
Version: 10.5.8
Summary: passagemath: Symbolic calculus
Author-email: The Sage Developers <sage-support@googlegroups.com>
Maintainer: Matthias Köppe, passagemath contributors
License: GNU General Public License (GPL) v2 or later
Project-URL: release notes, https://github.com/passagemath/passagemath/releases
Project-URL: repo (upstream), https://github.com/sagemath/sage
Project-URL: repo, https://github.com/passagemath/passagemath
Project-URL: documentation, https://doc.sagemath.org
Project-URL: homepage (upstream), https://www.sagemath.org
Project-URL: discourse, https://passagemath.discourse.group
Project-URL: tracker (upstream), https://github.com/sagemath/sage/issues
Project-URL: tracker, https://github.com/passagemath/passagemath/issues
Classifier: Development Status :: 6 - Mature
Classifier: Intended Audience :: Education
Classifier: Intended Audience :: Science/Research
Classifier: License :: OSI Approved :: GNU General Public License v2 or later (GPLv2+)
Classifier: Operating System :: POSIX
Classifier: Operating System :: MacOS :: MacOS X
Classifier: Programming Language :: Python :: 3 :: Only
Classifier: Programming Language :: Python :: 3.9
Classifier: Programming Language :: Python :: 3.10
Classifier: Programming Language :: Python :: 3.11
Classifier: Programming Language :: Python :: 3.12
Classifier: Programming Language :: Python :: Implementation :: CPython
Classifier: Topic :: Scientific/Engineering :: Mathematics
Requires-Python: <3.13,>=3.9
Description-Content-Type: text/x-rst
Requires-Dist: gmpy2~=2.1.b999
Requires-Dist: cypari2>=2.1.1
Requires-Dist: cysignals>=1.10.2
Requires-Dist: cysignals<1.12,>=1.10.2
Requires-Dist: numpy>=1.19
Requires-Dist: numpy>=1.22.4
Requires-Dist: passagemath-categories~=10.5.8.0
Requires-Dist: passagemath-ecl~=10.5.8.0
Requires-Dist: passagemath-environment~=10.5.8.0
Requires-Dist: passagemath-flint~=10.5.8.0
Requires-Dist: passagemath-maxima~=10.5.8.0
Requires-Dist: passagemath-modules~=10.5.8.0
Requires-Dist: passagemath-ntl~=10.5.8.0
Requires-Dist: passagemath-conf~=10.5.8.0
Requires-Dist: sympy<2.0,>=1.6
Provides-Extra: test
Requires-Dist: passagemath-repl; extra == "test"
Provides-Extra: axiom
Provides-Extra: giac
Requires-Dist: passagemath-giac; extra == "giac"
Provides-Extra: ginac
Provides-Extra: maxima
Provides-Extra: ntl
Provides-Extra: primecount
Requires-Dist: primecountpy; extra == "primecount"
Provides-Extra: pynac
Provides-Extra: singular
Provides-Extra: sympy
Provides-Extra: plot
Requires-Dist: passagemath-plot; extra == "plot"

===========================================================
 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 <https://doc.sagemath.org/html/en/reference/calculus/index.html>`_

* `Pynac <http://pynac.org/>`_ (fork of GiNaC)

* Arithmetic Functions, `Elementary and Special Functions <https://doc.sagemath.org/html/en/reference/functions/index.html>`_
  (via `sagemath-categories <https://doc.sagemath.org/html/en/reference/spkg/sagemath_categories.html>`_)

* `Asymptotic Expansions <https://doc.sagemath.org/html/en/reference/asymptotic/index.html>`_

* `SageManifolds <https://sagemanifolds.obspm.fr/>`_: `Topological, Differentiable, Pseudo-Riemannian, Poisson Manifolds <https://doc.sagemath.org/html/en/reference/manifolds/index.html>`_

* `Hyperbolic Geometry <https://doc.sagemath.org/html/en/reference/hyperbolic_geometry/index.html>`_


Examples
--------

Using `SageManifolds <https://sagemanifolds.obspm.fr/>`_::

    $ 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 <https://doc.sagemath.org/html/en/reference/spkg/giac.html>`_, via `passagemath-giac <https://doc.sagemath.org/html/en/reference/spkg/sagemath_giac.html>`_

`pip install "passagemath-symbolics[primecount]"`
 `Prime counting function <https://doc.sagemath.org/html/en/reference/functions/sage/functions/prime_pi.html>`_
 implementation `primecount <https://doc.sagemath.org/html/en/reference/spkg/primecount.html>`_, via `primecountpy <https://doc.sagemath.org/html/en/reference/spkg/primecountpy.html>`_

`pip install "passagemath-symbolics[sympy]"`
 Python library for symbolic mathematics / computer algebra system `SymPy <https://doc.sagemath.org/html/en/reference/spkg/sympy.html>`_

`pip install "passagemath-symbolics[plot]"`
 Plotting facilities
