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),
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from numpy import e,pi
import clifford as cf
layout, blades = cf.Cl(2) # creates a 2-dimensional clifford algebra
Inspect blades.
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blades
Assign blades to variables
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e1 = blades['e1']
e2 = blades['e2']
e12 = blades['e12']
Basics¶
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e1*e2 # geometric product
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e1|e2 # inner product
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e1^e2 # outer product
Reflection¶
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a = e1+e2 # the vector
n = e1 # the reflector
-n*a*n.inv() # reflect `a` in hyperplane normal to `n`
Rotation¶
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from numpy import pi
R = e**(pi/4*e12) # enacts rotation by pi/2
R
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R*e1*~R # rotate e1 by pi/2 in the e12-plane