Re: Log[Exp[r]] <> r?

*To*: mathgroup at smc.vnet.net*Subject*: [mg39279] Re: Log[Exp[r]] <> r?*From*: "Kevin J. McCann" <KevinMcCann!kjm at uunet.uu.net>*Date*: Sun, 9 Feb 2003 04:50:17 -0500 (EST)*References*: <b22jou$6bh$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

It is because the log is a multivalued function. I believe that Log gives the principle branch, i.e. -Pi < Arg[Log[z]] < Pi; equivalently, the branch cut is chosen to go from 0 to -Infinity (real). This may be illustrated by Log[Exp[2+4.5*Pi*I]] which returns 2.0+1.5708I. it does not return 2+4.5*Pi*I, rather 2+0.5*Pi*I which is in the principle branch. Kevin "Jonathan Greenberg" <greenberg at ucdavis.edu> wrote in message news:b22jou$6bh$1 at smc.vnet.net... > Hi there, why is it when I enter Log[Exp[r]] (or use Simplify or > FullSimplify) I don't get r? If I do Log[Exp[2]] I get 2! > > --j > > -- > Jonathan Greenberg > Graduate Group in Ecology, U.C. Davis > http://www.cstars.ucdavis.edu/~jongreen > http://www.cstars.ucdavis.edu > AIM: jgrn307 or jgrn3007 > MSN: jgrn307 at msn.com or jgrn3007 at msn.com > >