rotations
 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
 
> tutor1()
 
##### example : rotations : Run Script and call  tutor1()   #####
Cl(3)
oriented volume :
j = e123
signature : (1,1,1)
 
# sandwich operator RR(R,x) with  rotor R = R(B,theta) or  R(B)
 
#      y = RR(R,x)  ==>        y = R x/R
 
x=2e1+e2+7e3         # vector x
(0,2,1,7,0,0,0,0)
 
A=e12+2e23           # rotation plane
(0,0,0,0,1,0,2,0)
 
s1=R(A,90)          # rotor: plane A, rotation angle 90°
(0.7071,0,0,0,-0.3162,0,-0.6325,0)
 
y=RR(s1,x)           # rotate vector x by s1
(0,3.9528,-5.3666,3.0944,0,0,0,0)
 
gp(x,x)             # check that the length is preserved x x
(54,0,0,0,0,0,0,0)
 
gp(y,y)             # check that the length is preserved y y
(54,0,0,0,0,0,0,0)
 
B=unit1(A)*pi/4      # now,B encode the rotation plane and the 1/2 angle :|B|= pi/4
(0,0,0,0,0.351241,0,0.702481,0)
 
s2=R(B)              # compute the rotor s2 = R(B)
(0.9239,0,0,0,-0.1711,0,-0.3423,0)
 
z=RR(s2,x)           # rotate x : rotation plane B by angle |B|
(0,2.3867,-3.0876,6.2266,0,0,0,0)
 
gp(z,z)              # check that the length is preserved z z
(54,0,0,0,0,0,0,0)
 
tty=0
M1=M(s1)             # rotation matrice for s1
 
0.941423   0.316227   0.117157
-0.316227  0.707107   0.632457
0.117157   -0.632457  0.765686
 
M1=M(s2)            # rotation matrice for s2
 
0.941423   0.316227   0.117157
-0.316227  0.707107   0.632457
0.117157   -0.632457  0.765686
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