sympy.vector.express doesn't express field in spherical coordinates

[Mantabit]

Hello

I am using the vector module to define a field in Cartesian coordinates and I want to get an expression for that field in spherical coordinates:

from sympy.vector import CoordSys3D, express

C=CoordSys3D('C')
S=C.create_new('S',transformation="spherical")

testfield=C.x*C.i+C.y*C.j+C.z*C.k

print(S.base_scalars())
print(S.base_vectors())
print(express(testfield,S,variables=True))

However, this code will result in the output:

(S.r, S.theta, S.phi)
(S.i, S.j, S.k)
S.rS.i + S.thetaS.j + S.phi*S.k

Not quite sure what's the issue here?

[friyaz]

It looks like scalar_map() does not work correctly when system is defined with help of transformation equation.

>>> S.scalar_map(C)
{S.r: C.x, S.phi: C.z, S.theta: C.y}

[Mantabit]

I also get an incorrect result if I pass a lambda expression as the argument for transformation:

from sympy.vector import CoordSys3D, express
from sympy import sin,cos

C=CoordSys3D('C')
S=C.create_new('S',transformation=lambda r,phi,theta: (r*sin(theta)*cos(phi),r*sin(theta)*sin(phi),r*cos(theta)),variable_names=("r","phi","theta"))

testfield=C.x*C.i+C.y*C.j+C.z*C.k

print(S.base_scalars())
print(S.base_vectors())
print(express(testfield,S,variables=True))

This results in the output:

(S.r, S.phi, S.theta)
(S.i, S.j, S.k)
S.r * S.i + S.phi * S.j + S.theta * S.k

[friyaz]

I think rotation_matrix is to blame here.
rotation_matrix does not change when transformation equations are used to define a new system.

>>> from sympy.vector import CoordSys3D, express
>>> C = CoordSys3D('C')
>>> S = C.create_new('S',transformation="spherical")
>>> S.rotation_matrix()
Matrix([
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]])

>>> B = C.create_new('B', transformation=lambda x,y,z: (x*sin(y), x*cos(y), z))
>>> B.rotation_matrix()
Matrix([
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]])

Can you have a look @smichr .

[friyaz]

ping @jksuom

[jksuom]

It seems to me that express was designed to work with rectilinear coordinate systems only.

[Mantabit]

It seems to me that express was designed to work with rectilinear coordinate systems only.

True. As far as I can tell, there's also no way to get the unit vectors of a spherical coordinate system which would be required to transform a vectorial expression.