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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>