def derivatives_in_rectangular_coordinates():
Print_Function()
X = (x, y, z) = symbols('x y z')
o3d = Ga('e_x e_y e_z', g=[1, 1, 1], coords=X)
(ex, ey, ez) = o3d.mv()
grad = o3d.grad
f = o3d.mv('f', 'scalar', f=True)
A = o3d.mv('A', 'vector', f=True)
B = o3d.mv('B', 'bivector', f=True)
C = o3d.mv('C', 'mv', f=True)
print 'f =', f
print 'A =', A
print 'B =', B
print 'C =', C
print 'grad*f =', grad * f
print 'grad|A =', grad | A
print 'grad*A =', grad * A
print '-I*(grad^A) =', -o3d.E() * (grad ^ A)
print 'grad*B =', grad * B
print 'grad^B =', grad ^ B
print 'grad|B =', grad | B
print 'grad<A =', grad < A
print 'grad>A =', grad > A
print 'grad<B =', grad < B
print 'grad>B =', grad > B
print 'grad<C =', grad < C
print 'grad>C =', grad > C
return
def derivatives_in_spherical_coordinates():
Print_Function()
X = (r,th,phi) = symbols('r theta phi')
s3d = Ga('e_r e_theta e_phi',g=[1,r**2,r**2*sin(th)**2],coords=X,norm=True)
(er,eth,ephi) = s3d.mv()
grad = s3d.grad
f = s3d.mv('f','scalar',f=True)
A = s3d.mv('A','vector',f=True)
B = s3d.mv('B','bivector',f=True)
print 'f =',f
print 'A =',A
print 'B =',B
print 'grad*f =',grad*f
print 'grad|A =',grad|A
print '-I*(grad^A) =',(-s3d.E()*(grad^A)).simplify()
print 'grad^B =',grad^B
