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
 
> tutor6()
 
##### example : operators nabla & diff : Run Script and call tutor6()   #####
Cl(3)
oriented volume :
j = e123
signature : (1,1,1)
 
x = x1*e1 + x2*e2 + x3*e3
(0,x1,x2,x3,0,0,0,0)
 
nabla(x,x)
(3,0,0,0,0,0,0,0)
 
a=e1+2e2+3e3
(0,1,2,3,0,0,0,0)
 
nabla(inp(x,a),x)                  # nabla(x.a,x)
(0,1,2,3,0,0,0,0)
 
nabla(outp(x,a),x)                # nabla(x^a,x)
(0,-2,-4,-6,0,0,0,0)
 
nabla(gp(x,a),x)                   # nabla(x a,x) = nabla(x.a,x) + nabla(x^a,x)
(0,-1,-2,-3,0,0,0,0)
 
xx =  gp(x,x)                        # xx = x^2 -->  a scalar function
(x1^2 + x2^2 + x3^2,0,0,0,0,0,0,0)
 
nabla(xx,x)                           #  gradient(xx)
(0,2 x1,2 x2,2 x3,0,0,0,0)
 
nabla(nabla(xx,x),x)                #  laplacian(xx)
(6,0,0,0,0,0,0,0)
 
x12 = x1*sin(x2)*e1 + x2*cos(x1)*e2
(0,x1 sin(x2),x2 cos(x1),0,0,0,0,0)
 
n12=nabla(x12,x)
(1 cos(x1) + 1 sin(x2),0,0,0,1 x1 cos(x2) + 1 x2 sin(x1),0,0,0)
# nabla x12 = nabla . x12 + nabla ^ x12 =  divergence(x12)*e0 + curl(x12)*e12
 
# grade0 = divergence
(1 cos(x1) + 1 sin(x2),0,0,0,0,0,0,0)
 
# grade2 = curl
(0,0,0,0,1 x1 cos(x2) + 1 x2 sin(x1),0,0,0)
 
nabla(abs1(x)*e0,x)            # = x/abs1(x)    with abs1(x) = sqrt(x1^2 + x2^2 + x3^2)
(0,1 x1 / ((x1^2 + x2^2 + x3^2)^0.5),1 x2 / ((x1^2 + x2^2 + x3^2)^0.5),1 x3 / ((x1^2 + x2^2 + x3^2)^0.5),0,0,0,0)
 
x/abs1(x)
(0,x1 / ((x1^2 + x2^2 + x3^2)^(1/2)),x2 / ((x1^2 + x2^2 + x3^2)^(1/2)),x3 / ((x1^2 + x2^2 + x3^2)^(1/2)),0,0,0,0)
 
nabla(abs1(x)^3*e0,x) = 3abs1(x) x1*e1 + 3abs1(x) x2*e2 + 3abs1(x) x3*e3
(0,3 x1 (x1^2 + x2^2 + x3^2)^0.5,3 x2 (x1^2 + x2^2 + x3^2)^0.5,3 x3 (x1^2 + x2^2 + x3^2)^0.5,0,0,0,0)
 
diff(x,a,x)                                        # directional derivative a*dx(x)= a
(0,1,2,3,0,0,0,0)
 
diff(inp(x,b),a,x)                                 # directional derivative a*dx(x.b)= a.b
(3,0,0,0,0,0,0,0)
 
inp(a,b)
(3,0,0,0,0,0,0,0)
 
diff(e0*abs1(x)^3,a,x)                         # directional derivative a*dx(|x|^3)= 3(a.x)|x|
(3 x1 (x1^2 + x2^2 + x3^2)^(1/2) + 6 x2 (x1^2 + x2^2 + x3^2)^(1/2) + 9 x3 (x1^2 + x2^2 + x3^2)^(1/2),0,0,0,0,0,0,0)
 
3*inp(a,x)*abs1(x)
(3 x1 (x1^2 + x2^2 + x3^2)^(1/2) + 6 x2 (x1^2 + x2^2 + x3^2)^(1/2) + 9 x3 (x1^2 + x2^2 + x3^2)^(1/2),0,0,0,0,0,0,0)
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    differential operators