Simplify[] and Sign[]

*To*: mathgroup at smc.vnet.net*Subject*: [mg48529] Simplify[] and Sign[]*From*: thom.covert at gmail.com (Thomas R. Covert)*Date*: Fri, 4 Jun 2004 04:49:55 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

I have a handful of 5-variable algebraic expressions that I am pretty sure have constant signs (I make this assumption based on many tests using random numbers). By hand, I've been able to prove that a few of them do indeed have a constant sign, but the others have eluded me so far. Supposing I have, for example, F[w,a,b,c,d,e] = some rational function in {w,a,b,c,d,e} where the variables w,a,b,c,d,e are strictly positive. By hand, I can manipulate some of the partial derivatives of F in such a manner that I am sure that they have unambiguous signs. However, for the rest, Simplify[Sign[D[F,c],{w>0,a>0,b>0,c>0,d>0,e>0}] just returns: Sign[D[F,c]] (using c as an example). My question is two-fold: should I give FullSimplify[] a try in this case? or is there a better way of doing this? If I can somehow "guide" Simplify[] into manipulating these expressions as I did for the first one then I will be ok. Perhaps there is a way to step-through the Simplify[] process? -Thomas R. Covert