Re: ComplexityFunction affects set of transformations tried by Simplify

*To*: mathgroup at smc.vnet.net*Subject*: [mg71509] Re: [mg71492] ComplexityFunction affects set of transformations tried by Simplify*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Tue, 21 Nov 2006 07:05:06 -0500 (EST)*References*: <200611202311.SAA18396@smc.vnet.net>

On 21 Nov 2006, at 08:11, Schochet wrote: > Oops! I originally sent this as a reply to an unrelated thread. > Please reply only to this new version. > > As part of a large computation, I wanted Mathematica to > simplify expressions of the form Sqrt[c + d/k](c k + d)2, > where k is positive, to (c k + d)^(5/2)/Sqrt[k] > > Note that Mathematica knows that the two expressions > are equivalent: > > In[1]:=expr1 = Sqrt[c + d/k](c k + d)2; > expr2 = (c k + d)^(5/2)/Sqrt[k]; > Simplify[expr1 == expr2, k > 0] > > Out[1]=True Rather unlikely, I would say. Consider that my Mathematica 5.1 gives: expr1 = Sqrt[c + d/k]*(d + c*k)*2; expr2 = (d + c*k)^(5/2)/Sqrt[k]; Simplify[expr1 == expr2, k > 0] (d + c*k - 2)*Sqrt[d + c*k] == 0 furthermore expr1 /. {d -> 1, c -> 0, k -> 1} 2 expr2 /. {d -> 1, c -> 0, k -> 1} 1 It kind of makes the rest of the message less interesting but... > > However Simplify with LeafCount as the ComplexityFunction > leaves expr1 unchanged, while Simplify with Depth as the > ComplexityFunction changes expr1 to expr2: > > In[3]:=Simplify[expr1, k > 0, > ComplexityFunction -> LeafCount] // InputForm > > Out[3]//InputForm=Sqrt[c + d/k]*(d + c*k)2 > > In[4]:=Simplify[expr1, k > 0, > ComplexityFunction -> Depth] // InputForm > > Out[4]//InputForm=(d + c*k)^(5/2)/Sqrt[k] > > What explains this difference in behavior? Changing the order > of calculations 3 and 4 has no effect. Since calculation 2 > shows that the form expr2 would be preferred if it were tried, > while calculation 4 shows that the form expr2 is tried when > the ComplexityFunction is Depth, it seems that the choice of > ComplexityFunction affects the set of transformations tried > by Simplify. Here I get: In[4]:= Simplify[expr1, k > 0, ComplexityFunction -> LeafCount] Out[4]= (2*(d + c*k)^(3/2))/Sqrt[k] In[6]:= Simplify[expr1, k > 0, ComplexityFunction -> Depth] Out[6]= (2*(d + c*k)^(3/2))/Sqrt[k] So, the way I see it there are two possibilities. One is, that there was something funny with the state of your Mathematica when you got those results. If not, then I am pleased that I have not upgraded from version 5.1 to 5.2 ;-) Andrzej Kozlowski Tokyo, Japan

**Follow-Ups**:**Re: Re: ComplexityFunction affects set of transformations tried by Simplify***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**References**:**ComplexityFunction affects set of transformations tried by Simplify***From:*"Schochet" <schochet@netvision.net.il>