       Re: Re: Weird result in Mathematica 6

• To: mathgroup at smc.vnet.net
• Subject: [mg76630] Re: [mg76432] Re: [mg76393] Weird result in Mathematica 6
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 25 May 2007 06:23:41 -0400 (EDT)
• References: <200705211001.GAA10071@smc.vnet.net> <EB6D3224-597F-4DD6-B05D-08B9F6A05D2D@mimuw.edu.pl> <200705220648.CAA19836@smc.vnet.net> <63B2BBD7-455D-42F6-AFB2-63F7D37D62D3@mimuw.edu.pl> <465461D4.5000109@wolfram.com> <1FA17BCB-CFF6-4C96-BC81-F5C84629F61C@mimuw.edu.pl> <5B668FAB-4950-497D-9CCF-E7C37A9D5A5E@mimuw.edu.pl> <46556952.5000205@wolfram.com>

```On 24 May 2007, at 19:30, Adam Strzebonski wrote:

> Now, x*Conjugate[x]>1 is different, because it actually is
> a valid formula for arbitrary complex x. But other syntactically
> similar formulas, like (x^2+1)*Conjugate[x]>1, are not valid for
> arbitrary complex x and the sets of complex numbers for which they
> are well defined are rather complicated.

Well, I agree. I think it may be worth pointing out that Conjugate[x]
itsef is trated as a non-algebraic fucntions so that for example:

Simplify[Re[x], Conjugate[x] > 1]
Re(x)

even though the asumption actually implies that x is real. It is the
presence of x in x*Conjugate[x] that causes:

Simplify[Re[x], x*Conjugate[x] > 1]
x

From the point of view of "usual mathematics" these two answers
ought to be exactly the wrong way round!

One more solution, not so far mentioned,  that seems to (normally)
solve such problems is wrapping ComplexExpand[] around "real
assumptions" and ComplexExpand[ ,{x}] around complex ones. Thus in
the above:

Simplify[Re[x], ComplexExpand[Conjugate[x] > 1]]
x

Simplify[Re[x], ComplexExpand[x*Conjugate[x] > 1, {x}]]
Re(x)

which are now the right way round.

Andrzej Kozlowski

```

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