CoCalc -- 1933.sagews

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Path: pub / 1901-2001 / 1933.sagews

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c=11
s=13
Ms = Matrix([[10,0,1],[0,10,0],[0,0,1]])
Mr = Matrix([[c,-s,0],[s,c,0],[0,0,1]])
Mt = Matrix([[1,0,50],[0,1,10],[0,0,1]])

print Mt*Mr*Ms

[ 110 -130   61]
[ 130  110   23]
[   0    0    1]

print Mt*Mr*Ms*vector([0,0,0])

(0, 0, 0)

Ry=matrix([[1/sqrt(2),0,1/sqrt(2)],[0,1,0],[-1/sqrt(2),0,1/sqrt(2)]])

Rz=matrix([[1/sqrt(2),-1/sqrt(2),0],[1/sqrt(2),1/sqrt(2),0],[0,0,1]])

N=Ry*Rz
print N

[        1/2        -1/2 1/2*sqrt(2)]
[1/2*sqrt(2) 1/2*sqrt(2)           0]
[       -1/2         1/2 1/2*sqrt(2)]

M=N.inverse()

A=matrix([[1,0,0],[0,1/2,-1/2*sqrt(3)],[0,1/2*sqrt(3),1/2]])

print N*A*M

[1/8*(sqrt(2) + sqrt(3))*sqrt(2) - 1/8*sqrt(2)*sqrt(3) + 3/8             1/8*(sqrt(2)*sqrt(3) - 1)*sqrt(2) + 1/4*sqrt(2) 1/8*(sqrt(2) + sqrt(3))*sqrt(2) + 1/8*sqrt(2)*sqrt(3) - 3/8]
[                                  1/8*sqrt(2) - 1/4*sqrt(3)                                                         3/4                                  -1/8*sqrt(2) - 1/4*sqrt(3)]
[1/8*(sqrt(2) - sqrt(3))*sqrt(2) - 1/8*sqrt(2)*sqrt(3) - 3/8             1/8*(sqrt(2)*sqrt(3) + 1)*sqrt(2) - 1/4*sqrt(2) 1/8*(sqrt(2) - sqrt(3))*sqrt(2) + 1/8*sqrt(2)*sqrt(3) + 3/8]

def Rx(t):
   t=t*pi/180
   return matrix([[1,0,0],[0,cos(t),-sin(t)],[0,sin(t),cos(t)]])

def Ry(t):
   t=t*pi/180
   return matrix([[cos(t),0,sin(t)],[0,1,0],[-sin(t),0,cos(t)]])

def Rz(t):
   t=t*pi/180
   return matrix([[cos(t),-sin(t),0],[sin(t),cos(t),0],[0,0,1]])

#{{1/12*(3*sqrt(2/3)*sqrt(2)*cos(-arcsin(1/3*sqrt(3))) + sqrt(2)*sqrt(3)*sin(-arcsin(1/3*sqrt(3))))*sqrt(2) + 1/2, -1/2*sqrt(2/3)*sqrt(2)*sin(-arcsin(1/3*sqrt(3))) + 1/6*sqrt(2)*sqrt(3)*cos(-arcsin(1/3*sqrt(3))), -1/12*(3*sqrt(2/3)*sqrt(2)*cos(-arcsin(1/3*sqrt(3))) + sqrt(2)*sqrt(3)*sin(-arcsin(1/3*sqrt(3))))*sqrt(2) + 1/2},{1/12*(3*sqrt(2/3)*sin(-arcsin(1/3*sqrt(3))) + 2*sqrt(3)*cos(-arcsin(1/3*sqrt(3))))*sqrt(2) - 1/4*sqrt(2/3)*sqrt(2)*sqrt(3),1/2*sqrt(2/3)*cos(-arcsin(1/3*sqrt(3))) - 1/3*sqrt(3)*sin(-arcsin(1/3*sqrt(3))), -1/12*(3*sqrt(2/3)*sin(-arcsin(1/3*sqrt(3))) + 2*sqrt(3)*cos(-arcsin(1/3*sqrt(3))))*sqrt(2) - 1/4*sqrt(2/3)*sqrt(2)*sqrt(3)}, {-1/12*(3*sqrt(2/3)*sqrt(2)*cos(-arcsin(1/3*sqrt(3))) - 2*sqrt(2)*sqrt(3)*sin(-arcsin(1/3*sqrt(3))))*sqrt(2),1/2*sqrt(2/3)*sqrt(2)*sin(-arcsin(1/3*sqrt(3))) + 1/3*sqrt(2)*sqrt(3)*cos(-arcsin(1/3*sqrt(3))), 1/12*(3*sqrt(2/3)*sqrt(2)*cos(-arcsin(1/3*sqrt(3))) - 2*sqrt(2)*sqrt(3)*sin(-arcsin(1/3*sqrt(3))))*sqrt(2)}}
phi = asin(1/sqrt(3)) * 180/pi
theta = -45
Ru=Ry(-theta)*Rz(phi)*Rx(60)*Rz(-phi)*Ry(theta)
for row in Ru:    
   for column in row:
      help(column)

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