On Wednesday, November 19, 2014 11:17:24 PM UTC+1, Jason Moore wrote:
>
> Sachin Joglekar developed the vector package this past summer. I was his
> GSoC mentor on the project. You can check out this implemented of the
> Cartesian coordinate system:
>
> https://github.com/sympy/sympy/blob/master/sympy/vector/coordsysrect.py
>
In sympy.diffgeom coordinate systems are defined as instances of the
CoordSystem class, once more coordinate systems are defined, the
transformation rules are set using the *connect_to* method:
In [1]: from sympy.diffgeom import *
In [2]: r, theta, phi = symbols('r theta phi', positive=True)
In [4]: M = Manifold('M', 3)
In [5]: P = Patch('P', M)
In [7]: rect = CoordSystem('rect', P, ['x', 'y', 'z'])
In [8]: spherical = CoordSystem('spherical', P, ['r', 'theta', 'phi'])
In [9]: spherical.connect_to(rect, [r, theta, phi], [r*sin(phi)*cos(theta),
r*sin(phi)*sin(theta), r*cos(phi)], inverse=False)
I put *inverse=False* in the last line, because SymPy's solvers are unable
to reverse the spherical-to-rect transformation.
Manifold and Patch are some boilerplate, Manifold specifies the space
you're considering, while Patch is a connected subspace of the manifold.
Patch is used because on some manifolds there does not exist a
homeomorphism to a coordinate system (e.g. on the sphere).
I think that some algorithmic code could be shared between the vector and
the diffgeom modules.
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