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how implement a rule

• To: mathgroup at smc.vnet.net
• Subject: [mg112568] how implement a rule
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Mon, 20 Sep 2010 05:43:34 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• Reply-to: murray at math.umass.edu

I want to define a function abs (mimicking Abs) with various properties. 
One part of the definition is:

   abs[c_ z_ /; c \[Element] Reals] = Abs[c] abs[z]

Given that, how might I express that abs[z] is always real in such a way 
that the result of

   abs[1/abs[z]^2]

will be 1/abs[z]^2 -- WITHOUT explicitly introducing, say:

   abs/: abs[1/abs[z_]^2] =  1/abs[z]^2

?

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305