# Tag Info

## New answers tagged assumptions

2

You cannot use Except in $Assumptions like you do. Just use ComplexExpand which assumes that are variables are real. E.g.: conj = TrigToExp@ComplexExpand@Conjugate@# &; Then conj[ Exp[-I*a]*a + Exp[-I*b]*b ] gives a*E^(I*a) + b*E^(I*b) 2 I have isolated a simplified instance of the bug: a = Exp[-(ux - uy) (vx - vy)] ((ux - uy) (vx - vy))^2; i1 = Integrate[a, {vy, 0, vx}]; Assuming[ux > 0, i2a = Integrate[i1, {vx, 0, 1}, {uy, 0, ux}]; i2b = Integrate[Integrate[i1, {uy, 0, ux}], {vx, 0, 1}]; i2b - i2a // FullSimplify ] which gives 4 I \[Pi] (incorrect) rather than 0 (correct). We ... 2 It's a bug, of course. Mathematica gets dizzy by the "hanging" integration order (I believe). As simple as it is, it was tough to find out but it gives the right result if you just change the order of limits:$Assumptions = {ρ > 0, L > 0}; limits = Sequence[{ux, 0, L}, {uy, 0, ux}, {vx, 0, L}, {vy, 0, vx}]; (* instead of limits = Sequence[{ux, 0, ...

4

This code should give you some insight as to why you are seeing this behavior: Manipulate[Plot[(a - Sqrt[a^2 + x])/(a^2 - a*Sqrt[a^2 - x]), {x, -1, 1}], {a, -3, 3}] When Assumptions -> {a > 0} is used, you get the correct limit. But when no assumptions are placed, Mathematica tries to evaluate the limit for a general complex $a$. This second ...

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