Re: ComplexityFunction affects set of transformations tried by Simplify

*To*: mathgroup at smc.vnet.net*Subject*: [mg71530] Re: ComplexityFunction affects set of transformations tried by Simplify*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Wed, 22 Nov 2006 05:22:12 -0500 (EST)*References*: <200611202311.SAA18396@smc.vnet.net><ejuqdp$htk$1@smc.vnet.net>

$VersionNumber 5.2 I got also the same results; Regards Dimitris Andrzej Kozlowski wrote: > 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

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