Re: Re: verification

*To*: mathgroup at smc.vnet.net*Subject*: [mg74768] Re: [mg74724] Re: verification*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Wed, 4 Apr 2007 04:08:35 -0400 (EDT)*References*: <eunpso$772$1@smc.vnet.net> <200704021057.GAA08445@smc.vnet.net>

On 2 Apr 2007, at 19:57, David W.Cantrell wrote: > "dimitris" <dimmechan at yahoo.com> wrote: >> Hello. >> >> foo = {ArcTan[8/(1 - Sqrt[-15 - 4*I])] + ArcTan[8/(1 + Sqrt[-15 - >> 4*I])] + ArcTan[8/(1 - Sqrt[-15 + 4*I])] + >> ArcTan[8/(1 + Sqrt[-15 + 4*I])], ArcTan[3] + ArcTan[5] + >> ArcTan[41/3] + ArcTan[21], 2*Pi - ArcTan[1/4] - ArcTan[5/12]}; >> >> The elements of foo list are equal >> >> Chop[N[foo, 30]] >> {5.64341552435296080601310475496,5.64341552435296080601310475496,5.\ >> 64341552435296080601310475496} >> >> Block[{Message}, FullSimplify[foo[[2]] == foo[[3]]]] >> Block[{Message}, FullSimplify[foo[[1]] == foo[[3]]]] >> Block[{Message}, FullSimplify[foo[[1]] == foo[[2]]]] >> >> True > > OK, so you easily showed that foo[[2]] and foo[[3]] are the same. > Here's > the easiest way I know to show that foo[[1]] and foo[[3]] are the > same: > > In[4]:= FullSimplify[TrigToExp[foo[[1]]]] == FullSimplify[foo[[3]]] > > Out[4]= True > > What really disturbs me is that I can also "show" that foo[[1]] and > foo[[3]] are NOT the same: > > In[6]:= FullSimplify[TrigToExp[foo[[1]]] == foo[[3]]] > > messages regarding Internal precision limit snipped > > Out[6]= False > > It seems that Mathematica is asserting that two _equal_ expressions > are _not equal_. What am I missing?! (Of course, if Mathematica had > merely > left the logical expression unevaluated, I wouldn't have been > disturbed...) I get the same result which certainly suggests some curious problems in FullSimplify. However, in general and for several good reasons it is better in such situations to use: FullSimplify[TrigToExp[foo[[1]]] -foo[[3]]] 0 On my 1 gigaretz PowerBook the above took a very long time (I forgot to use Timing but now I do want to run it again). Andrzej Kozlowski

**References**:**Re: verification***From:*"David W.Cantrell" <DWCantrell@sigmaxi.net>