EVA version :  1.24
enter Cl(p) or Cl(p,q) :  p+q number basis vectors up to 5  , p positive squares, q negative squares
 
> tutor0()
 
##### example : base functions : Run Script and call tutor0()   #####
Cl(3)
oriented volume :
j = e123
signature : (1,1,1)
 
a = 2e1+3e2-e3           # vector a
(0,2,3,-1,0,0,0,0)
 
b = e1+e2-3e3             # vector b
(0,1,1,-3,0,0,0,0)
 
gp(a,b)                      # a b = a.b + a^b
(8,0,0,0,-1,-5,-8,0)
 
inp(a,b)+outp(a,b)       # a.b + a^b =
(8,0,0,0,-1,-5,-8,0)
 
rnd(gp(a,inv1(a)))        # a 1/a = e0
(1,0,0,0,0,0,0,0)
 
rev(a)                         # a~ reverse involution
(0,2,3,-1,0,0,0,0)
 
invol(a)                       # a' grade involution
(0,-2,-3,1,0,0,0,0)
 
cj(a)=invol(rev(a))        # a" Clifford conjugation
(0,-2,-3,1,0,0,0,0)
 
dual1(a)                    # a* dual
(0,0,0,0,1,3,-2,0)
 
dual1(dual1(a))            # (a*)* = -a
(0,-2,-3,1,0,0,0,0)
 
dual1(outp(a,b))          # a x b = (a^b)*    cross product
(0,-8,5,-1,0,0,0,0)
 
(a^b)*=a.b*               # dual relationship outp vs inp
(0,-8,5,-1,0,0,0,0)
(0,-8,5,-1,0,0,0,0)
 
(a.b)*=a^b*               # dual relationship inp vs outp
(0,0,0,0,0,0,0,-8)
(0,0,0,0,0,0,0,-8)
 
c = e1+2e2+3e3+4e12+5e13+6e23+7e123  # multivector c
(0,1,2,3,4,5,6,7)
 
c=grade(c,0)+grade(c,1)+grade(c,2)+grade(c,3)
(0,1,2,3,4,5,6,7)
 
abs1(unit1(c))           # = 1
1
ab=gp(ab)                 # ab = a b
(8,0,0,0,-1,-5,-8,0)
 
arg1(ab)                  # angle(a,b)=arg1(ab)
0.87022
 
abs1(ab)                  # module(ab)=abs1(ab)
12.4097
 
polar1(ab)                # polar(ab)=abs(ab)*exp(unit(imag(ab))*arg(ab)
(8,0,0,0,-1,-5,-8,0)
 
inp(a,b)                   # inner product
(8,0,0,0,0,0,0,0)
 
inp(a,b)                     # left contraction
(8,0,0,0,0,0,0,0)
 
rc(a,b)                     # rightcontraction
(8,0,0,0,0,0,0,0)
 
doth(a,b)                 # Hesteness product
(8,0,0,0,0,0,0,0)
 
meet(A,B)                 # intersection of two planes A and B
(0,0.5,0.5,0,0,0,0,0)
>
    base functions