coolest identity competition WAS sqrt(x)*sqrt(x)

Maybe we should have a coolest identity competition.  I have one that I 
like.  It comes from pw.mac.  I worked it out one day and it's enshrined in 
pw.mac.  I know it is lame but at least I can follow it.  I can usually 
follow stuff I think of myself.

between(x, a, b) = ((signum(b - a) + 1) * unit_pulse(x/(b-a) + a/(a-b)))/2

That is really lame because you have to know that between() is 1 when x >= a 
or x <= b and zero otherwise.  unit_pulse(x) is 1 from 0 to 1 and 0 
everywhere else.

Well, I like it.

Rvh






-----Original Message----- 
From: Steve Haflich
Sent: Friday, February 11, 2011 9:37 PM
To: Gary Pajer
Cc: maxima at math.utexas.edu ; Michel Talon
Subject: Re: [Maxima] sqrt(x)*sqrt(x)

Gary Pajer <gary.pajer at gmail.com> wrote:

   Don't we have better things to discuss, like revolution in Egypt or
   basketball losing streaks?  Bye for now!

But to keep discussion within the realm of Maxima, I was intrigued with
Richard's earlier comment: "It depends on whether you believe in
negative numbers."

Richard: Do you really think it might be practical to disbelieve
negative numbers?  That belief would obviously simplify and unclutter
huge swaths of the Maxima implementation.  Indeed, it would also
simplify and unclutter huge swaths of mathematics itself, at least those
small parts of mathematics that would remain.

I need to think more deeply about this notion.
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