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There is no general algorithm able to decide whether a symbolically defined function is positive. Note that, when Sage outputs False it means False or Unknown. When Sage is able to prove (f1>f2), it outputs True, otherwise, it will output False.

There is no general algorithm able to decide whether a symbolically defined function is positive. positive, see for example this paper. Note that, when Sage outputs False it means False or Unknown. When Sage is able to prove (f1>f2), it outputs True, otherwise, it will output False.

There is no general algorithm able to decide whether a symbolically defined function is positive, positive even in a single variable, see for example this paper. Note that, when Sage outputs False it means False or Unknown. When Sage is able to prove (f1>f2), it outputs True, otherwise, it will output False.

There is no general algorithm able to decide whether a symbolically defined function is positive even in a single variable, and using only log2, exp(x), pi, sin(x), x, +, - , *, o, see for example this paper.

Note that, when Sage outputs False it means False or Unknown. When Sage is able to prove (f1>f2), it outputs True, True, otherwise, it will output False.. This means that when Sage outputs "False", it means "False or Unknown".

Now, if you have a concrete example, someone may help you to decide in that particular case.