def test(a,b):
g = (vsr.CGA(vsr.Mot(0,1,0,0,0,0,0,0)).comm(vsr.CGA(a)) * vsr.CGA(b) * 2.0)[0]
h = (a[1]* b[0] - a[0] * b[1]) * 2
print(h)
print(g)
i = (-a[0] * b[0] - a[1] * b[1] ) * 4.0
j = (vsr.CGA(vsr.Mot(0,1,0,0,0,0,0,0)).comm(vsr.CGA(vsr.Mot(0,1,0,0,0,0,0,0)).comm(vsr.CGA(a))) * vsr.CGA(b) * 4.0)[0]
print(i)
print(j)
def project(Y, M):
YM2 = Y * M
YM2[0] = 0.0
YM2[26] = 0.0
YM2[27] = 0.0
YM2[28] = 0.0
YM2[29] = 0.0
YM2[30] = 0.0
return vsr.CGA(vsr.MotRec(YM2 * M.rev()))
def cga_gp_tensor():
dim = 32
M = np.zeros((dim, dim))
mask = np.arange(1, dim + 1)
for i in range(dim):
for j in range(dim):
a = vsr.CGA(*[0] * 32)
b = vsr.CGA(*[0] * 32)
a[i] = 1.
b[j] = 1.
M[i, j] = np.dot(mask, np.array(a * b))
tensor = np.zeros((dim, dim, dim))
for k in range(dim):
for i in range(dim):
for j in range(dim):
val = M[i, j]
if abs(val) == k + 1:
tensor[k, i, j] = np.sign(val)
return tensor
a[i] = 1.
b[j] = 1.
# print(a * b)
M[i, j] = np.dot(mask, np.array(a * b))
tensor = np.zeros((dim, dim, dim))
for k in range(dim):
for i in range(dim):
for j in range(dim):
val = M[i, j]
if abs(val) == k + 1:
tensor[k, i, j] = np.sign(val)
return tensor
Gkij = cga_gp_tensor()
a = vsr.CGA(*np.arange(1, 33)) * 0.1
b = vsr.CGA(*np.arange(1, 33)) * 0.1
# print(a * b)
# print(vsr.CGA(*np.einsum('i,j,kij->k', a, b, Gkij)))
Gkij = ega_gp_tensor()
for i in range(8):
a = vsr.EGA(*np.arange(1, 9))
b = vsr.EGA(*[0] * 8)
b[i] = 1.0
c = a * b
d = vsr.EGA(*np.einsum('i,j,kij->k', a, b, Gkij))
print(c)
print(d)
Gkij = cga_gp_tensor()
def main1():
motor0 = create_motor()
motor = create_motor()
points = create_points(motor)
A, B, _ = points[0]
dM = vsr.CGA(A) * vsr.CGA(motor0).rev() * vsr.CGA(B) + \
vsr.CGA(A).rev() * vsr.CGA(motor0).rev() * vsr.CGA(B).rev()
# print(vsr.CGA(motor0))
proj = project(dM, vsr.CGA(motor0))
print(proj)
dM2 = vsr.CGA(motor0).rev() * vsr.CGA(A).spin(vsr.CGA(motor0)) * vsr.CGA(B) * 2.0
print(project(dM2, vsr.CGA(motor0)))
def err(points, mot):
err = 0.0
for A, B, _ in points:
err += (vsr.CGA(A.spin(mot)) * vsr.CGA(B) * -2.0)[0]
return err