Quick Start (G2)¶
This notebook gives a terse introduction to using the clifford
module, using a two-dimensional geometric algebra as the context.
Setup¶
First, import clifford and instantiate a two-dimensional algebra (G2),
In [1]:
from numpy import e,pi
import clifford as cf
layout, blades = cf.Cl(2) # creates a 2-dimensional clifford algebra
Inspect blades.
In [2]:
blades
Out[2]:
{'e1': (1^e1), 'e2': (1^e2), 'e12': (1^e12)}
Assign blades to variables
In [3]:
e1 = blades['e1']
e2 = blades['e2']
e12 = blades['e12']
Basics¶
In [4]:
e1*e2 # geometric product
Out[4]:
(1.0^e12)
In [5]:
e1|e2 # inner product
Out[5]:
0
In [6]:
e1^e2 # outer product
Out[6]:
(1.0^e12)
Reflection¶
In [7]:
a = e1+e2 # the vector
n = e1 # the reflector
-n*a*n.inv() # reflect `a` in hyperplane normal to `n`
Out[7]:
-(1.0^e1) + (1.0^e2)
Rotation¶
In [8]:
from numpy import pi
R = e**(pi/4*e12) # enacts rotation by pi/2
R
Out[8]:
0.70711 + (0.70711^e12)
In [9]:
R*e1*~R # rotate e1 by pi/2 in the e12-plane
Out[9]:
-(1.0^e2)