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from range restriction to domain restriction

• To: mathgroup at smc.vnet.net
• Subject: [mg72590] from range restriction to domain restriction
• From: "Chris Chiasson" <chris at chiasson.name>
• Date: Thu, 11 Jan 2007 03:16:39 -0500 (EST)

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.

-- 
http://chris.chiasson.name/