Re: Re: Strange behavior of Simplify

*To*: mathgroup at smc.vnet.net*Subject*: [mg40180] Re: Re: Strange behavior of Simplify*From*: Selwyn Hollis <selwynh at earthlink.net>*Date*: Tue, 25 Mar 2003 03:04:06 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Thanks, Bob. This is actually a good example to illustrate the ComplexityFunction option. expr = Exp[2*n^2*(Log[1 + t] - Log[1 - t])]; LeafCount[expr] 20 newexpr = (1 + t)^(2*n^2)/(1 - t)^(2*n^2); LeafCount[newexpr] 21 So with the default ComplexityFunction->LeafCount, expr is already "simpler" than "newexpr". However... Depth[expr] 8 Depth[newexpr] 5 So with ComplexityFunction->Depth, newexpr is "simpler" than expr; thus... Simplify[expr, ComplexityFunction->Depth] (1 + t)^(2*n^2)/(1 - t)^(2*n^2) Very cool! On Monday, March 24, 2003, at 04:28 AM, Bob Hanlon wrote: > $Version > > 4.2 for Mac OS X (August 22, 2002) > > expr = Exp[2*n^2*(Log[1 + t] - Log[1 - t])]; > > expr // ExpandAll // Simplify > > (1 + t)^(2*n^2)/(1 - t)^(2*n^2) > > FullSimplify[expr, ComplexityFunction -> Length] > > (1 + t)^(2*n^2)/(1 - t)^(2*n^2) > > > Bob Hanlon > > In article <b5jtgf$mah$1 at smc.vnet.net>, Selwyn Hollis > <selwynh at earthlink.net> > wrote: > > << Subject: Strange behavior of Simplify > From: Selwyn Hollis <selwynh at earthlink.net> To: mathgroup at smc.vnet.net > To: mathgroup at smc.vnet.net > Date: Sun, 23 Mar 2003 09:07:27 +0000 (UTC) > > I've just run across the following strange behavior of Simplify. > (Using Mathematica 4.1.5, Mac OS X). > > These first two commands work as expected: > > Simplify[Exp[2*n*(Log[1 + t] - Log[1 - t])]] > > (1 - t)^(-2*n) (1 + t)^(2*n) > > Simplify[Exp[n^2*(Log[1 + t] - Log[1 - t])]] > > (1 - t)^(-n^2) (1 + t)^(n^2) > > But Simplify refuses to do anything with this: > > Simplify[Exp[2*n^2*(Log[1 + t] - Log[1 - t])]] > > Exp[2*n^2*(Log[1 + t] - Log[1 - t])] > > Can anyone shed some light here? By the way, FullSimplify does the > same thing. >><BR><BR> >