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CGAlgebra

Symbols

  • Arco
  • Centere
  • circle3D
  • Dual
  • GeometricProduct
  • GFactor
  • Grade
  • GradeQ
  • I5
  • InnerProduct
  • Involution
  • Magnitude
  • MultiplicationTable
  • MultivectorInverse
  • OuterProduct
  • Radio
  • Reversion
  • Rotation
Jlaragonvera`CGAlgebra`
Grade
​
Grade[m,r]
returns the r-vector part of the multivector m.
​
Details and Options

Examples  
(2)
Basic Examples  
(1)
Return the terms of grade 2 of the multivector:
In[1]:=
mv=(-x2y1+x3y1+x1y2-x3y2-x1y3+x2y3)e[1,2]+(-x2z1+x3z1+x1z2-x3z2-x1z3+x2z3)e[1,3]+(-y2z1+y3z1+y1z2-y3z2-y1z3+y2z3)e[2,3]+(-x2y1+x3y1+x1y2-x3y2-x1y3+x2y3)e[0,1,2,∞]+(-x2z1+x3z1+x1z2-x3z2-x1z3+x2z3)e[0,1,3,∞]+(-y2z1+y3z1+y1z2-y3z2-y1z3+y2z3)e[0,2,3,∞]+(-x3y2z1+x2y3z1+x3y1z2-x1y3z2-x2y1z3+x1y2z3)e[1,2,3,∞];
In[2]:=
Grade
[mv,2]
Out[2]=
-x2y1e[1,2]+x3y1e[1,2]+x1y2e[1,2]-x3y2e[1,2]-x1y3e[1,2]+x2y3e[1,2]-x2z1e[1,3]+x3z1e[1,3]+x1z2e[1,3]-x3z2e[1,3]-x1z3e[1,3]+x2z3e[1,3]-y2z1e[2,3]+y3z1e[2,3]+y1z2e[2,3]-y3z2e[2,3]-y1z3e[2,3]+y2z3e[2,3]
Applications  
(1)

SeeAlso
GradeQ
▪
GFactor
""

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