>
> sage: from sage.symbolic.function import function
> sage: var('r,kappa', ns=1)
> (r, kappa)
> sage: psi = function('psi', 1)(r); psi
> psi(r)
> sage: g = 1/r^2*(2*r*psi.diff(r,1) + r^2*psi.diff(r,2)); g
> (2*psi(1,r)*r + psi(2,r)*r^2)*r^(-2)
> sage: g.expand()
> psi(2,r) + 2*psi(1,r)*r^(-1)
> sage: g.coeff(psi.diff(r,2))
> 1
> sage: g.coeff(psi.diff(r,1))
> 2*r^(-1)
I implemented the same interface to sympy:
http://code.google.com/p/sympy/issues/detail?id=979
In [1]: var('r, kappa')
Out[1]: (r, κ)
In [2]: psi = Function("psi")
In [3]: g = 1/r**2 * (2*r*psi(r).diff(r, 1) + r**2 * psi(r).diff(r, 2))
In [4]: g.coeff(psi(r).diff(r))
Out[4]:
2
─
r
In [5]: g.coeff(psi(r).diff(r, 2))
Out[5]: 1
It will be in the next release.
Ondrej
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