# What am I missing on this part of the documentation?

In the documentation for FullSimplify, under Options > Assumptions it is stated that:

When assumptions are given as an argument, $Assumptions is used as well: Assuming[x > 0, FullSimplify[E^(LogGamma[x] + LogGamma[y]), y > 0]] (* Gamma[x] Gamma[y] *)  Specifying assumptions as an option value prevents FullSimplify from using$Assumptions:

Assuming[x > 0, FullSimplify[E^(LogGamma[x] + LogGamma[y]), Assumptions -> y > 0]]
(* Gamma[x] Gamma[y] *)


The resuls are just the same. What is the point?

$Version (* 10.1.0 for Microsoft Windows (64-bit) (March 24, 2015) *)  • Try FullSimplify[E^(LogGamma[x] + LogGamma[y])] without assumptions. – Michael E2 Jun 12 '15 at 17:14 • I get the same result. – Giovanni F. Jun 12 '15 at 17:17 • So the assumptions are irrelevant, since the simplification is valid more generally. – Michael E2 Jun 12 '15 at 17:20 • This documentation example just adds nothing then. – Giovanni F. Jun 12 '15 at 17:23 • Yes, it's strange. I wonder if it has changed since some version. – Michael E2 Jun 12 '15 at 17:26 ## 1 Answer It's a badly written example. What it is trying to show is something like the following behavior, where the local Assumptions option overrides the global $Assumptions.

$Assumptions = x == -1; FullSimplify[E^(LogGamma[x] + LogGamma[y])]  FullSimplify::infd : "Expression LogGamma[x] + LogGamma[y] simplified to ∞. ∞  FullSimplify[E^(LogGamma[x] + LogGamma[y]), Assumptions -> x == 1]  Gamma[y]  However, Assumming only adds to $Assumptions, so

Assuming[x == 1, FullSimplify[E^(LogGamma[x] + LogGamma[y])]]


produces

\$Assumptions::cas : Warning : contradictory assumption (s) x == 1 && x == -1 encountered. >>

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