Comment #14 on issue 2205 by [email protected]: "Undefined functions"
http://code.google.com/p/sympy/issues/detail?id=2205
We need this to represent functions and possibly their derivatives.
Things like "f(x)", "f(0)", "f'(x)".
Yes, time is ripe for it. (issue 1620)
I can add what is needed more:
issue 1660
>>> f(g(x)).diff(x, point=a)
f'(g(a))*g'(a)
or more complicated (I even don't know how it is must represented):
>>> f(g(x, y)).diff(x, a)
f_g(g(a, y))*g_x(a, y)
Various partial derivatives's representations:
E.g. on _latex_ now only options are `\frac{\partial}{\partial x} f(x)` or
`\partial_x f(x)`, but sometimes more convenient `f_xyy(x, y)` or
`f_{12}(x, y)`.
Abstract function substitution, very usfull:
>>> f = AbstractFunction()
>>> f(2)**2
f(2)**2
>>> _.subs(f, sin)
sin(2)**2
>>> f = AbstractFunction(nargs=2)
>>> f(x, y)**2
f(x, y)**2
>>> _.subs(f, sin)
ValueError:
Assumptions about analyticity:
>>> f = Function("f", analyticity=False)
About series I do not even speak now. Just mention that operators could be
handling with functions (but it is related rather with operator's engine)
I think it would be better to keep all aims in one place. It is more
convenient to construct this object in a right way if the spectrum of the
problems and aims will be present, at least to do not forget something or
some little details.
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