Grade  
 
grade(a1 ^ a2 ^ ...^ ak) = k
grade(A ^ B) = grade(A) + grade(B)
an arbitrary multivector  can be decomposed into a sum of pure grade terms :
A = <A>0 + <A>1 + <A>2 + <A>3     (Cl3)
 
the grade operator grade(A,k) extract the k grade part of A
 
ex : A = 3e0 - e2 + 3e3 + 5e12 + 2e23    (Cl3)
grade(A,0) = 3e0
grade(A,1) = -e2 + 3e3
grade(A,2) = 2e23
grade(A,3) = 0                
 
grade(A,0) + grade(A,2) = 3e0 + 2e23       =  A+     (even part of A)
grade(A,0) + grade(A,3)  = complex numbers
grade(A,0) + grade(A,2)  = quaternions
grade(A,0) + grade(A,1)  = paravectors (over complex = 4D Minkowski SpaceTime)
 
 
 

                       
    grade(u, k)
FUNCTIONS
products
grade
involutions
dual
geometry
usual  functions
diff.  operators
utilities