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MathGroup Archive 2007

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Re: Re: Weird result in Mathematica 6

I failed to notice that your input was nonsensical since:

  ComplexExpand[x - Conjugate[x] > 0, {x}]
  2*I*Im[x] > 0

which is certainly not the same as Im[x]>0.

Nevertheless the advice to use ComplexExpand seems to me still good.

Andrzej Kozlowski

On 24 May 2007, at 23:18, Andrzej Kozlowski wrote:

>  Applying ComplexExpand[] to real assumptions and ComplexExpand[ , 
> {x}] to complex ones will normally avoid such problems:
> Simplify[Im[x], Assumptions -> {ComplexExpand[x - Conjugate[x] > 0,  
> {x}]}]
>  Im(x)
> Andrzej Kozlowski
> On 24 May 2007, at 19:18, Sebastian Meznaric wrote:
>> Another related effect can be used to actually derive contradictions
>> in Mathematica. Try this
>> Simplify[Im[x],Assumptions->{x-Conjugate[x]>0}]
>> It returns 0. The assumption was that Im[x]>0 so here Mathematica
>> clearly contradicts the assumption.
>> Obviously this suggests one should be very careful when using
>> inequalities with complex quantities. I think this sort of bugs  
>> should
>> really be fixed considering how much trouble Mathematica usually goes
>> into to ensure that real quantities are not assumed in expressions.

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