- To: mathgroup at smc.vnet.net
- Subject: [mg32034] Re: Simplify
- From: "Alan Mason" <swt at austin.rr.com>
- Date: Wed, 19 Dec 2001 04:29:23 -0500 (EST)
- References: <firstname.lastname@example.org>
- Sender: owner-wri-mathgroup at wolfram.com
<Matthias.Bode at oppenheim.de> wrote in message
news:9vmrje$hh7$1 at smc.vnet.net...
> Dear Colleagues,
> why should I not expect MATHEMATICA to (Full)Simplify
> (a^b)^(1/b) or a^b^(1/b) to a?
the reason is because they are not equal for general complex-valued a, b, c.
The following notebook illustrates how to make a rule to enforce the desired
simplification (which is correct only for a, b, c real), and also gives a
case where equality fails. z^w is defined as Exp[w Log[z]], and Log has a
branch cut; this complication is the reason for the failure.
test = (a^b)^(1/b)
test2 = (a^b)^c
rule = Power[Power[a_, b_], c_]\[RuleDelayed] Power[a, b c]
\!\(\((a_\^b_)\)\^c_ \[RuleDelayed] a\^\(b\ c\)\)
test /. rule
test2 /. rule
a = 2 + 3 I;b = 3 +I; c = -2-4I;
\!\(4.240023659792295`*^-7 - 7.75911100859049`*^-7\ \[ImaginaryI]\)
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