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confirming my comment.. Integrate[ Sqrt[ 1 + a (x - 1) ] , {x, -1, 1}], Integrate[ Sqrt[ 1 + a (x - 1) ] , {x, -1, 1}, Assumptions -> True] Integrate[ Sqrt[ 1 + a (x - 1) ] , {x, -1, 1}, GenerateConditions -> True] Integrate[ Sqrt[ 1 + a (x - 1) ] , {x, -1, 1}, Assumptions -> {y == 3}] Integrate[ Sqrt[ 1 + a (x - 1) ] , {x, -1, 1}, ...


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Rule {Complex[re_, im_] :> Complex[re, -im]} seems to convert complex expressions which contain symbols which are meant to be real. Rule {I -> -I} does not, even on simple example: 2 I /.{I -> -I} 2 I the reason being that symbol I is automatically translated by Mathematica to Complex[0, 1] and rule above is interpreted ...


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Try this also: g[y__] := Simplify[y, Assumptions :> (First@Cases[y, f[__], -1]) > 0] g[f[x]+3==0] (*False*) g[f[a,b,c]+4==0] (*False*)


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There is another alternative which you could look into: dynamically creating your assumptions. I will try to show it with the simple example you have given. Basically, when you call Simplify[f[a,b,c]+4==0] then you can easily extract the expressions matching your pattern with Cases. For instance Cases[Hold[Simplify[f[a, b, c] - f[x] == 0]], f[__], Infinity] ...


2

I'll assume that your function has no other definitions associated with it, and you only want to make it behave like a positive function when added to other expressions. This is how I would do it: ClearAll[f] Plus[f[x__], r__] ^:= Plus[Exp[Abs[Log[f[x]]]], r] Simplify[f[x] + 3 == 0] (* ==> False *) Simplify[f[a, b, c] + 4 == 0] (* ==> False *) ...



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