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I re-ran your code, replacing ϕ withphi. After :
f = function('f')(x,y,z) == phi_t.expand();
we have :
sage: f
f(x, y, z) == k*q/(a^2 + x^2 + y^2 + 2*a*z + z^2) + k*q/(a^2 + x^2 + y^2 - 2*a*z + z^2) - 2*k*q/(x^2 + y^2 + z^2)
meaning that f is a Python variable whose value is an equality. Probably not what you wanted.
I am guessing that your intent was :
sage: reset("f")
sage: f(x,y,z) = phi_t.expand(); f
(x, y, z) |--> k*q/(a^2 + x^2 + y^2 + 2*a*z + z^2) + k*q/(a^2 + x^2 + y^2 - 2*a*z + z^2) - 2*k*q/(x^2 + y^2 + z^2)
f is now (a Python variable whose value is) a symbolic function (a. k. a. a callable symbolic expression).
sage: f(x, y, z).subs(z^2+x^2+y^2+w0==r^2+w0)
k*q/(a^2 + r^2 + 2*a*z) + k*q/(a^2 + r^2 - 2*a*z) - 2*k*q/(x^2 + y^2 + z^2)
which seems to be closer to what you seem to want.
But writing yourself your conversion functions may be unnecessary : you may be interested by this tutorial, then by this one, using this (large) Sage module.
HTH,
