def main():
Eprint()
X = (x, y, z) = symbols('x y z', real=True)
(o3d, ex, ey, ez) = Ga.build('e_x e_y e_z', g=[1, 1, 1], coords=(x, y, z))
A = x * (ey ^ ez) + y * (ez ^ ex) + z * (ex ^ ey)
print 'A =', A
print 'grad^A =', (o3d.grad ^ A).simplify()
print
f = o3d.mv(1 / sqrt(x**2 + y**2 + z**2))
print 'f =', f
print 'grad*f =', (o3d.grad * f).simplify()
print
B = f * A
print 'B =', B
print
Curl_B = o3d.grad ^ B
print 'grad^B =', Curl_B.simplify()
return
def main():
Get_Program(True)
#ga_print_on()
Eprint()
basic_multivector_operations()
check_generalized_BAC_CAB_formulas()
derivatives_in_rectangular_coordinates()
derivatives_in_spherical_coordinates()
rounding_numerical_components()
noneuclidian_distance_calculation()
conformal_representations_of_circles_lines_spheres_and_planes()
properties_of_geometric_objects()
extracting_vectors_from_conformal_2_blade()
reciprocal_frame_test()
#ga_print_off()
return
def main():
Eprint()
(o3d, ex, ey, ez) = Ga.build('e*x|y|z', g=[1, 1, 1])
u = o3d.mv('u', 'vector')
v = o3d.mv('v', 'vector')
w = o3d.mv('w', 'vector')
print u
print v
uv = u ^ v
print uv
print uv.is_blade()
exp_uv = uv.exp()
print 'exp(uv) =', exp_uv
return
def main():
Get_Program()
Eprint()
Mv_setup_options()
return
def main():
Eprint()
(o3d, ex, ey, ez) = Ga.build('e*x|y|z', g=[1, 1, 1])
(r, th, phi, alpha, beta, gamma) = symbols('r theta phi alpha beta gamma',
real=True)
(x_a, y_a, z_a, x_b, y_b, z_b, ab_mag,
th_ab) = symbols('x_a y_a z_a x_b y_b z_b ab_mag theta_ab', real=True)
I = ex ^ ey ^ ez
a = o3d.mv('a', 'vector')
b = o3d.mv('b', 'vector')
c = o3d.mv('c', 'vector')
ab = a - b
print('a =', a)
print('b =', b)
print('c =', c)
print('ab =', ab)
ab_norm = ab / ab_mag
print('ab/|ab| =', ab_norm)
R_ab = cos(th_ab / 2) + I * ab_norm * cos(th_ab / 2)
R_ab_rev = R_ab.rev()
print('R_ab =', R_ab)
print('R_ab_rev =', R_ab_rev)
e__ab_x = R_ab * ex * R_ab_rev
e__ab_y = R_ab * ey * R_ab_rev
e__ab_z = R_ab * ez * R_ab_rev
print('e_ab_x =', e__ab_x)
print('e_ab_y =', e__ab_y)
print('e_ab_z =', e__ab_z)
R_phi = cos(phi / 2) - (ex ^ ey) * sin(phi / 2)
R_phi_rev = R_phi.rev()
print(R_phi)
print(R_phi_rev)
e_phi = (R_phi * ey * R_phi.rev())
print(e_phi)
R_th = cos(th / 2) + I * e_phi * sin(th / 2)
R_th_rev = R_th.rev()
print(R_th)
print(R_th_rev)
e_r = (R_th * R_phi * ex * R_phi_rev * R_th_rev).trigsimp()
e_th = (R_th * R_phi * ez * R_phi_rev * R_th_rev).trigsimp()
e_phi = e_phi.trigsimp()
print('e_r =', e_r)
print('e_th =', e_th)
print('e_phi =', e_phi)
return
Bh = B / NB
ap = ebar - ((ebar ^ Bh) * Bh)
a1 = ap + (ap * Bh)
a2 = ap - (ap * Bh)
#print '#a1 = ',a1
#print '#a2 = ',a2
return [a1, a2]
def norm(X):
Y = sqrt((X * X).scalar())
return Y
Get_Program(True)
Eprint()
g = '1 0 0 0, \
0 1 0 0, \
0 0 0 2, \
0 0 2 0'
c2d = Ga('e_1 e_2 n \\bar{n}', g=g)
(e1, e2, n, nbar) = c2d.mv()
global n, nbar, I
def F(x):
global n, nbar
Fx = ((x * x) * n + 2 * x - nbar) / 2
def main():
Get_Program()
Eprint()
coefs_test()
return