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Simplify and Abs in version 6.0

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  • Subject: [mg78034] Simplify and Abs in version 6.0
  • From: Michael <mcauxeu at>
  • Date: Thu, 21 Jun 2007 05:58:26 -0400 (EDT)


In Mathematica version 6.0, I'm having difficulty trying to coax the

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]


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

Any tricks or hints would be greatly appreciated!



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