def main():
enhance_print()
X = (x, y, z) = symbols('x y z')
(ex, ey, ez, grad) = MV.setup('e_x e_y e_z', metric='[1,1,1]', coords=(x, y, z))
A = x*(ey ^ ez) + y*(ez ^ ex) + z*(ex ^ ey)
print('A =', A)
print('grad^A =', (grad ^ A).simplify())
print()
f = MV('f', 'scalar', fct=True)
f = (x**2 + y**2 + z**2)**(-1.5)
print('f =', f)
print('grad*f =', (grad*f).expand())
print()
B = f*A
print('B =', B)
print()
Curl_B = grad ^ B
print('grad^B =', Curl_B.simplify())
def Symplify(A):
return(factor_terms(simplify(A)))
print(Curl_B.func(Symplify))
return
def main():
Get_Program(True)
with GA_Printer():
enhance_print()
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()
return
def main():
Get_Program(True)
with GA_Printer():
enhance_print()
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()
return
def main():
enhance_print()
(ex, ey, ez) = MV.setup('e*x|y|z', metric='[1,1,1]')
u = MV('u', 'vector')
v = MV('v', 'vector')
w = MV('w', 'vector')
print(u)
print(v)
uv = u ^ v
print(uv)
print(uv.is_blade())
exp_uv = uv.exp()
exp_uv.Fmt(2, 'exp(uv)')
return
def main():
enhance_print()
coords = symbols('x y z')
(ex, ey, ez, grad) = MV.setup('ex ey ez', metric='[1,1,1]', coords=coords)
mfvar = (u, v) = symbols('u v')
eu = ex + ey
ev = ex - ey
(eu_r, ev_r) = ReciprocalFrame([eu, ev])
oprint('Frame', (eu, ev), 'Reciprocal Frame', (eu_r, ev_r))
print('eu.eu_r =', eu | eu_r)
print('eu.ev_r =', eu | ev_r)
print('ev.eu_r =', ev | eu_r)
print('ev.ev_r =', ev | ev_r)
eu = ex + ey + ez
ev = ex - ey
(eu_r, ev_r) = ReciprocalFrame([eu, ev])
oprint('Frame', (eu, ev), 'Reciprocal Frame', (eu_r, ev_r))
print('eu.eu_r =', eu | eu_r)
print('eu.ev_r =', eu | ev_r)
print('ev.eu_r =', ev | eu_r)
print('ev.ev_r =', ev | ev_r)
print('eu =', eu)
print('ev =', ev)
define_precedence(locals())
print(GAeval('eu^ev|ex', True))
print(GAeval('eu^ev|ex*eu', True))
return
def main():
Get_Program(True)
enhance_print()
MV_setup_options()
return
def main():
Get_Program(True)
enhance_print()
MV_setup_options()
return