Re: FullSimplify regress?

*To*: mathgroup at smc.vnet.net*Subject*: [mg81408] Re: FullSimplify regress?*From*: Adam Strzebonski <adams at wolfram.com>*Date*: Sat, 22 Sep 2007 03:27:22 -0400 (EDT)*References*: <52E282C5-DA4D-4206-95DB-DEB5AEBA0958@mimuw.edu.pl>*Reply-to*: adams at wolfram.com

Andrzej Kozlowski wrote: > *This message was transferred with a trial version of CommuniGate(tm) Pro* > In Mathematica 5.2: > > > FullSimplify[ComplexExpand[ArcTan[Cos[Arg[z w]-Arg[z]- > Arg[w]],Sin[Arg[z w]-Arg[z]-Arg[w]]],{z,w},TargetFunctions->{Re,Im}]] > > > 0 > > > In Mathematica 6.01: > > FullSimplify[ComplexExpand[ > ArcTan[Cos[Arg[z*w] - Arg[z] - Arg[w]], > Sin[Arg[z*w] - Arg[z] - Arg[w]]], {z, w}, > TargetFunctions -> {Re, Im}]] > > ArcTan[Cos[ArcTan[Re[w], Im[w]] + ArcTan[Re[z], > Im[z]] - ArcTan[Re[w]*Re[z] - Im[w]*Im[z], > Re[z*Im[w] + w*Im[z]]]], > -Sin[ArcTan[Re[w], Im[w]] + ArcTan[Re[z], Im[z]] - > ArcTan[Re[w]*Re[z] - Im[w]*Im[z], > Re[z*Im[w] + w*Im[z]]]]] > > > This looks like a bit of a regress to me. > > Andrzej Kozlowski > Since FullSimplify always works with the simplest form found so far, adding simplification rules may result in preventing other rules from working for some expressions. In V5.2 FullSimplify did not simplify the following expressions: In[1]:= Re[x]+Re[y]//FullSimplify Out[1]= Re[x] + Re[y] In[2]:= Im[z]*Re[w] + Im[w]*Re[z]//FullSimplify Out[2]= Im[z] Re[w] + Im[w] Re[z] in V6.0 it does In[1]:= Re[x]+Re[y]//FullSimplify Out[1]= Re[x + y] In[2]:= Im[z]*Re[w] + Im[w]*Re[z]//FullSimplify Out[2]= Re[z Im[w] + w Im[z]] However, for the particular expression from your example, simplifying a sum of real parts prevents another, more useful in this case, simplification. If you explicitly apply TrigToExp before FullSimplify, V6.0 can simplify the expression to zero. In[3]:= FullSimplify[TrigToExp[ComplexExpand[ ArcTan[Cos[Arg[z*w] - Arg[z] - Arg[w]], Sin[Arg[z*w] - Arg[z] - Arg[w]]], {z, w}, TargetFunctions -> {Re, Im}]]] Out[3]= 0 Best Regards, Adam Strzebonski Wolfram Research