I have the following problem. Defining two simple functions in Mathematica, say, foo[x_]:= x, and bar[y_]:=y, I would expect that the expression foo[x]^(-bar[y])-(1/foo[x])^(bar[y]) will be evaluated to zero. However, I find (oddly) that Mathematica insists rather on keeping this thing "in a symbolic fashion", not willing to simplify at all. Tried many things to overcome this behaviour but they all failed. Any help much appreciated :)
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Simon Righley
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You have to tell Mathematica that x>0:
Simplify[foo[x]^(-bar[y]) - (1/foo[x])^(bar[y]), x > 0]
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FJRA
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`foo[x]^(-bar[y]) - (1/foo[x])^(bar[y]) /. {y -> 1/2, x -> -1/2}` – ssch Nov 21 '13 at 18:00
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Yep, OK, but it's not really a very generic solution. For instance, why does it work for `x>0` but it doesn't if I assume `x<0`? More generally, if I have a very complicated function, I would not like waste time trying all possible combinations of assumptions. Trying with other silly examples (e.g., a^(-b)*c^(b)), you will soon realize (again) that in order to get the expected behaviour, you need to assume something very specific. Why is that? Is there a (more general) way of "enforcing" what simply stands to reason? – Simon Righley Nov 21 '13 at 18:09
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That's because simplifying it for x<0 is not valid in general terms. Mathematica knows it, and without a value or assumption only simplifies all it is allowed by the most general rules. – FJRA Nov 22 '13 at 19:43