.. ipython::
:doctest:
In [138]: from clifford.g3 import * # import GA for 3D space
In [138]: import math
In [138]: a = e1 + 2*e2 + 3*e3 # vector
In [138]: R = math.e**(math.pi/4*e12) # rotor
@doctest
In [138]: R*a*~R # rotate the vector
Out[138]: (2.0^e1) - (1.0^e2) + (3.0^e3)
This module implements Geometric Algebras (a.k.a. Clifford algebras). Geometric Algebra (GA) is a universal algebra which subsumes complex algebra, quaternions, linear algebra and several other independent mathematical systems. Scalars, vectors, and higher-grade entities can be mixed freely and consistently in the form of mixed-grade multivectors.
.. toctree::
:maxdepth: 3
:hidden:
installation
api/index
predefined-algebras
changelog
issues
.. toctree::
:maxdepth: 1
:caption: Tutorials
:hidden:
tutorials/g2-quick-start
tutorials/g3-algebra-of-space
tutorials/euler-angles
tutorials/space-time-algebra
tutorials/InterfacingOtherMathSystems
tutorials/PerformanceCliffordTutorial
tutorials/cga/index
tutorials/linear-transformations
tutorials/apollonius-cga-augmented
.. toctree::
:maxdepth: 1
:caption: Other resources
:hidden:
resources
bibliography