Simplify and Abs in version 6.0

*To*: mathgroup at smc.vnet.net*Subject*: [mg78034] Simplify and Abs in version 6.0*From*: Michael <mcauxeu at gmail.com>*Date*: Thu, 21 Jun 2007 05:58:26 -0400 (EDT)

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

**Follow-Ups**:**Re: Simplify and Abs in version 6.0***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>