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Re: Bug in Mathematica ?

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  • Subject: [mg109319] Re: Bug in Mathematica ?
  • From: David Bailey <dave at>
  • Date: Wed, 21 Apr 2010 07:47:53 -0400 (EDT)
  • References: <hqmd2g$pro$>

slawek wrote:
> In[1] := Im[a] ^= 0; Conjugate[a b]
> Out[1] := Conjugate[a b]
> It is not funny, Mathematica 6 properly evaluates the result 
> a Conjugate[b]
> What happens?
> slawek
There are several points here:

1)  The answer from 7.0.1 is not wrong - just not in the form you desired.

2)  Your code assumed that Conjugate called Im internally - this is the 
sort of assumption that may vary from one version to the next.

3)  Using the code:

FullSimplify[Conjugate[a b], Im[a] == 0]

solves the problem, but in a possibly unreliable way because (a 
Conjugate[b]) is actually no simpler than Conjugate[a b]

Ideally, you need to find a  way to tell Mathematica that a is Real, and 
what kind of expression you prefer, for example:

In[8]:= complexity[expr_] := LeafCount[expr] +
            10*Count[expr, Conjugate[x_ y_], {0, Infinity}];

FullSimplify[Conjugate[a b], Im[a] == 0,
  ComplexityFunction -> complexity]

Out[9]= a Conjugate[b]

Note that although that looks like a lot of work, you can wrap the 
process up in a function that you define at startup, or in a package, 
and then use as required.

David Bailey

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