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():
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)
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)
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()
(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()
(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)
print(w)
uv = u ^ v
print(uv)
print(uv.is_blade())
uvw = u ^ v ^ w
print(uvw)
print(uvw.is_blade())
print(simplify((uv * uv).scalar()))
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
print w
uv = u^v
print uv
print uv.is_blade()
uvw = u^v^w
print uvw
print uvw.is_blade()
print simplify((uv*uv).scalar())
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
def_prec(locals())
print GAeval('eu^ev|ex',True)
print GAeval('eu^ev|ex*eu',True)
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)
def_prec(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
