Re: Simplify and Abs in version 6.0

*To*: mathgroup at smc.vnet.net*Subject*: [mg78115] Re: Simplify and Abs in version 6.0*From*: Michael <mcauxeu at gmail.com>*Date*: Sat, 23 Jun 2007 07:09:13 -0400 (EDT)*References*: <200706210958.FAA27636@smc.vnet.net><f5gape$gc1$1@smc.vnet.net>

On Jun 22, 4:11 am, Andrzej Kozlowski <a... at mimuw.edu.pl> wrote: > It is a good think that mathemaica does not return the answer that > you suggest: > > {-\[ImaginaryI] a, \[ImaginaryI] a} > > because it would be completely wrong as in Mathematica {a,b} is an > ordered pair and not a set. Mathematica has no built in structures > corresponding to sets and has no way of expressing the answer you > (seem to) have in mind. You can get the answer with Sqrt[a^2] more > directly by: > > ComplexExpand[{I*Abs[a], (-I)*Abs[a]}, TargetFunctions -> {Re, Im}] > > {I*Sqrt[a^2], (-I)*Sqrt[a^2]} > > This, of course, can't be reduced any further without additional > information about a the sign of a. > > Andrzej Kozlowski > > On 21 Jun 2007, at 18:58, Michael wrote: > > > > > Hi, > > > In Mathematica version 6.0, I'm having difficulty trying to coax the > > input > > > In[1]:= FullSimplify[{\[ImaginaryI] Abs[a], -\[ImaginaryI] Abs[a]}, > > Element[a, Reals]] > > > to produce the set {-\[ImaginaryI] a, \[ImaginaryI] a}. > > Interestingly, this *does* result for > > > In[2]:= FullSimplify[{\[ImaginaryI] Abs[a], -\[ImaginaryI] Abs[a]}, a > >> = 0] > > > and > > > In[3]:= FullSimplify[{Sqrt[-1] Abs[a], -Sqrt[-1] Abs[a]}, a < 0] > > > Am I missing something here? I've tried Allan Hayes' suggestion in > > 2003, with > > > In[4]:= FullSimplify[{\[ImaginaryI] Abs[a], -\[ImaginaryI] Abs[a]}, > > Element[a,Reals],ComplexityFunction -> ((Count[#, _Abs, Infinity]) &)] > > Out[4]= {\[ImaginaryI] Sqrt[a^2], -\[ImaginaryI] Sqrt[a^2]} > > > to no avail; of course, I could just add a PowerExand@ to the above > > expression, but this seems like a lot to do, especially when > > Mathematica already has been explicitly told that "a" is a real > > number. > > > Any tricks or hints would be greatly appreciated! > > > Regards, > > > Michael- Hide quoted text - > > - Show quoted text - Hi, My apologies for assuming that my input was a set, and not an ordered pair. Everything now makes more sense, and my sincere thanks to Daniel, Andrzej, and Murray for their help and patience! Regards, Michael

**References**:**Simplify and Abs in version 6.0***From:*Michael <mcauxeu@gmail.com>