Re: Unexpected behavior of Simplify

*To*: mathgroup at smc.vnet.net*Subject*: [mg63261] Re: Unexpected behavior of Simplify*From*: Adam Strzebonski <adams at wolfram.com>*Date*: Tue, 20 Dec 2005 23:35:46 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Some transformations used by Simplify, like partial factorization, depend on the order of variables. Simplify does not try all variable orders, because first it does not know in general what the "variables" are, and second trying all orders would multiply the computation time of Simplify by Factorial[number of variables]. Here is a simple implementation of a variable order independent Simplify. (A FullSimplify variant of the code was posted at http://forums.wolfram.com/mathgroup/archive/2005/Jan/msg00237.html see also the accompanying discussion.) In[1]:= VOISimplify[vars_, expr_, assum_:True] := Module[{perm, ee, best}, perm=Permutations[vars]; ee=(Simplify@@({expr, assum}/.Thread[vars->#]))&/@perm; best=Sort[Transpose[{LeafCount/@ee, ee, perm}]][[1]]; best[[2]]/.Thread[best[[3]]->vars]] In[2]:= expr = c^4*b^2 + a^4*b^2 + c^2*a^2*(1 - 2*b^2) ; In[3]:= VOISimplify[{a, b, c}, expr] 2 2 2 2 2 2 Out[3]= a c + b (a - c ) In[4]:= VOISimplify[{a, b, c}, expr/.{a -> b, b -> a}]/. {a -> b, b -> a} 2 2 2 2 2 2 Out[4]= a c + b (a - c ) Best Regards, Adam Strzebonski Wolfram Research