You can emulate this behavior with the diffgeom module on which I am
working (the version in master is out of date, you can check out the
pull request)

Vector fields are differential operators:

from sympy.diffgeom.Rn import R2 # the R^2 manifold
derivative_wrt_x = R2.e_x # the base vector along the x axis
more_complicated_derivative_op = (stuff*derivative_wrt_x)
some_expression = (cos(R2.x) + R2.y)
more_complicated_derivative_op(some_expression) == -stuff*sin(R2.x)

You even have a somewhat intelligent Commutator class inside the module.

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