Re: from range restriction to domain restriction

• To: mathgroup at smc.vnet.net
• Subject: [mg72602] Re: from range restriction to domain restriction
• From: Peter Pein <petsie at dordos.net>
• Date: Thu, 11 Jan 2007 05:24:55 -0500 (EST)
• References: <eo4o86\$mgn\$1@smc.vnet.net>

Chris Chiasson schrieb:
> If I wanted to ensure that Sqrt[x] was always a real number, perhaps
> as a condition on Piecewise, I would say Im@Sqrt@x==0 (or
> Element[Sqrt@x,Reals], but Mathematica doesn't like to simplify that).
> In my real case, x isn't a symbol - and it comes from the output of
> some other commands. However, I also know that Element[x,Reals], so I
> was wondering if there is a way to make Mathematica do the following:
>
> (part of) input:
> Im@Sqrt@x==0
>
> output:
> x>0
>
> If someone knows how to do this (other than the obvious Cases +
> pattern transformation), I would appreciate being told how. Thank you.
>

Hi Chris,

is Reduce[ComplexExpand[Im[Sqrt[x]], x] == 0, x]
--> x >= 0
acceptable?

You would have to do sth. like

expr/.{Assuming[a_,ex_]:>Reduce[...],Simplify[ex_,a_]:>... and so on}

I guess I would use the Menu->Find->Find... to replace all "Im@Sqrt@==" with
"0<=" ;-)

Sorry, I've got no better idea :-(

Peter

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