geometry :  project(u,B)   reject(u,B)  reflect(u,B)
             RR(u,B,theta)   R(B,theta)   R(B)
 
project(u,B)  
prj =  u.B/B
 
reject(u,B)      
rjt = u - u.B/B  = u - project(u,B)
 
reflect(u,B)    
 B u 1/B                                   if B+ (even grade)        
 invol(B) u 1/B                           if B- (odd grade)
 
RR(u, B, theta)           rotate u around an axis (dual B)  by an angle theta degree
                                     B the rotation plane  
                                     RR = exp1(-B*theta/2) u exp1(B*theta/2)
                                     u -> RR u
RR(u, B)                     rotate u around an axis (dual B)  by an angle abs(B) radian
                                     u -> RR u
 
R(B, theta)                  define a rotor R = exp( -B theta/2 )
                                     rotate u around an axis (dual B) by an angle theta degree
                                     u -> R u rev(R)
 
R(B)                            define a rotor R = exp( -B theta/2 )
                                     rotate u around an axis (dual B) by an angle abs(B) radian
                                     u -> R u rev(R)
 
reciprocal(u1,u2,u3)        return reciprocal frame [r1,r2,r3 ]      (Cl3)
u1, u2, u3 form a non orthogonal frame for 3 dimensional space. r3 is formed by constructing the u1 ^ u2 plane and forming the vector perpenducular to this frame :
 
r3 = dual1 (u1 ^ u2)
r2 = dual1 (u3 ^ u1)
r1 = dual1 (u2 ^ u3)
 
orthogonal(u1,u2,u3)        return orthogonall frame [o1,o2,o3 ]     (Cl3)
 
o1 = u1
o2 = (u2 ^ o1)/o1
o3 = (u3 ^ o1 ^ o2)/(o1 ^ o2)
 

cplot(B,s=1)      (only on Spacetime version)
graphical representation for constant blades (not available with Eigenmath) :
 
scalar   = point  [0,0,0]
vector   = line segment
bivector = disk (s=1)
             = square (s!=1)
trivector = sphere
 
graphical representation for parametric blades :
 
ex : plot1 (3u*e1 + 5u*e2)                                               one parameter u        ==> a  line
      plot1 (3u*e1 + sin(u)*e2 + u*e3)
      plot1 (3u*e12 + (u*sin(v) + v*cos(u))*e23)              two parameter u, v    ==> a  surface
FUNCTIONS
products
grade
involutions
dual
geometry
usual  functions
diff.  operators
utilities