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GeometricAlgebra

Guides

  • Dual numbers
  • Geometric Algebra
  • Matrix Gateway

Tech Notes

  • Conformal Geometry
  • Dual numbers
  • Geometric Numbers
  • Matrix Gateway
  • Operator Duality
  • Projective Geometry
  • Spinors

Symbols

  • ConvertGeometricAlgebra
  • GeometricAlgebra
  • GeometricProduct
  • Grade
  • Multivector
Wolfram`GeometricAlgebra`
Grade
​
Grade
[v,n]
gives a
th
n
grade of a
Multivector
v
or converts a list to a multivector.
​
​
Grade[v,n,g]
specify a GeometricAlgebra
g
.
​
Examples  
(1)
Basic Examples  
(1)
Construct multivectors of a given grade:
In[1]:=
Grade
[{x,y,z},1]
Out[1]=
x
e
1
+y
e
2
+z
e
3
In[2]:=
Grade
[{x,y,z},2]
Out[2]=
x
e
12
+y
e
13
+z
e
23
Specify Geometric Algebra:
In[3]:=
Grade
[{x,y,z},3,{3,1}]
Out[3]=
x
e
123
+y
e
12
1
+z
e
13
1
Extract a particular grade from a
Multivector
:
In[4]:=
Grade
[RandomMultivector[],1]
Out[4]=
0.627576
e
1
+0.809571
e
2
+0.281425
e
3
SeeAlso
Multivector
RelatedGuides
▪
Geometric Algebra
""

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