GAlgebra
Symbolic Geometric Algebra/Calculus package for SymPy.
Development Status
brombo/galgebra was originally written by Alan Bromborsky, but was no longer actively maintained, and as of 2019-11-25 no longer exists.
pygae/galgebra is a community fork, maintained by Pythonic Geometric Algebra Enthusiasts.
The fork supports Python 3, increases test coverage, sets up CI and linters, maintains releases to PyPI, improves docs and has many bug fixes, see Changelog.
For information on how GAlgebra is used in other projects, see Used by.
[!IMPORTANT] Readers of Prof. Alan Macdonald’s Linear and Geometric Algebra and Vector and Geometric Calculus, please check out **Migrating guide for readers of LAGA&VAGC** below.
If you are coming from sympy.galgebra or brombo/galgebra (unlikely nowadays), please check out section the old Migration Guide.
Features
Geometric Algebra
Arbitrary Vector Basis and Metric
Scalar, Vector, Bivector, Multivector, Pseudoscalar, Spinor, Blade
Basic Geometic Algebra Operations
Sum Difference
Geometric Product
Outer and Inner Products
Left and Right Contractions
Reverse, Dual, Exponential
Commutator
Projection, Reflection, Rotation
Reciprocal Frames
Inspecting Base/Blade Representation
Symbolic Manipulations
expand
,factor
,simplify
,subs
,trigsimp
etc.
Overloaded Python operators for basic GA operations:
Geometric Calculus
Geometric Derivative
Submanifolds
Linear Transformations
Differential Operators
The various derivatives of a multivector function is accomplished by multiplying the gradient operator vector with the function:
Tip: an example for getting grad
and rgrad
of a 3-d Euclidean geometric algebra in rectangular coordinates:
from sympy import symbols
from galgebra.ga import Ga
o3d = Ga('e', g=[1,1,1], coords=symbols('x,y,z',real=True))
(grad,rgrad) = o3d.grads()
Printing
Enhanced Console Printing
Latex Printing
out-of-the-box support for Jupyter Notebook
PDF generation and croping support if you have
pdflatex
/pdfcrop
installed
Getting Started
After installing GAlgebra (see section Installing GAlgebra below), in a Jupyter Notebook:
from sympy import symbols
from galgebra.ga import Ga
from galgebra.printer import Format
Format(Fmode = False, Dmode = True)
st4coords = (t,x,y,z) = symbols('t x y z', real=True)
st4 = Ga('e',
g=[1,-1,-1,-1],
coords=st4coords)
M = st4.mv('M','mv',f = True)
M.grade(3).Fmt(3,r'\langle \mathbf{M} \rangle _3')
You will see:
You may also check out more examples here.
For detailed documentation, please visit https://galgebra.readthedocs.io/ .
Installing GAlgebra
Prerequisites
Works on Linux, Windows, Mac OSX
Python >= 3.8
0.5.0 was the last supported release for Python 3.5-3.7
0.4.x was the last supported release series for Python 2.7
SymPy >= 1.3
Only SymPy 1.12 is tested via CI, see
.github/workflows/ci.yml
for more details0.5.0 was the last supported release for SymPy 1.7
Installing GAlgebra From PyPI (Recommended for users)
pip install galgebra
Then you are all set!
Installing GAlgebra From Source (Recommended for developers)
To install from the latest source code of GAlgebra:
git clone https://github.com/pygae/galgebra.git
cd galgebra
pip install -e .
Note that the optional -e
argument is used here for a developer install so modifying the source will take effect immediately without the need of reinstallation.
Now you may run tests to verify the installation, run from the root of the repository:
pip install pytest
pytest test
Further, to run the complete test suite including the ones using nbval, just run:
pip install nbval
pytest --nbval examples/ipython/ --nbval examples/primer/ test --nbval-current-env --nbval-sanitize-with test/.nbval_sanitize.cfg
This could take more than 10 minutes, please be patient.
Migration Guide
Migrating guide for readers of LAGA&VAGC
Readers of Linear and Geometric Algebra and Vector and Geometric Calculus might be guided by GAlgebra Primer (version November 29, 2022, accessed May, 2024) to download GAfiles.zip and copy gprinter.py
, lt.py
, mv.py
, and ``GAlgebraInit.py``¸ into where GAlgebra is installed.
These steps are NO LONGER NEEDED since GAlgebra 0.6.0 as they are merge into GAlgebra with tests, copying these files will cause conflicts and regressions of fixed bugs. Instead, you may follow the following steps:
pip uninstall galgebra
pip install git+https://github.com/pygae/galgebra.git
GAlgebra will be installed as 0.6.0-dev
as 0.6.0
has not yet been finalized and published to PyPI.
For minor differences to those files, please check out the change log for GAlgebra 0.6.0. Also please note that:
GAlgebraInit.py
is renamed toprimer.py
and can be imported likefrom galgebra.primer import *
but it’s usage is discouraged, although it saves some boilerplate code, this is not part of GAlgebra’s maintained API, GAlgebra might remove it in future.Some notebooks from the zip are included in GAlgebra in
examples/primer
.
Bundled Resources
Note that in the doc/books directory there are:
BookGA.pdf
which is a collection of notes on Geometric Algebra and Calculus based of “Geometric Algebra for Physicists” by Doran and Lasenby and on some papers by Lasenby and Hestenes.galgebra.pdf
which is the original main doc of GAlgebra in PDF format, while the math part is still valid, the part describing the installation and usage of GAlgebra is outdated, please read with caution or visit https://galgebra.readthedocs.io/ instead.Macdonald
which contains bundled supplementary materials for Linear and Geometric Algebra and Vector and Geometric Calculus by Alan Macdonald, see here and here for more information.Particularly,
GAlgebraPrimer.pdf
is an archived version of GAlgebra Primer by Alan Macdonald, last updated on November 29, 2022.
Star History
Contributors
Made with contrib.rocks.
Citing This Library
For citation information, see our ``CITATION.md` file <https://github.com/pygae/galgebra/blob/master/CITATION.md>`_.