Assumptions on symbolic functions

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None at the moment, as far as I know.

Note however that :

• maxima has such a facility (see maxima.declare?) ;
• similarly, Sympy has such a facility (it even has two, the newer progressively replacing the older) ;
• there are some reported bugs pointing the the way sage handles assumptions and tests thereof, and these bugs are worked on.

You might try to isolate the part of your computations where you need such a handling, do them in maxima or Sympy, and reimport the relevant results.

Note also that you can

assume(f(x)>0)

But that won't do a thing about bool(f(2*x+1)>0)...