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assumption, supposition?

  • To: mathgroup at
  • Subject: [mg15331] assumption, supposition?
  • From: Erk Jensen <Erk.Jensen at>
  • Date: Fri, 8 Jan 1999 04:15:20 -0500
  • Sender: owner-wri-mathgroup at

Probably I'm looking up the wrong keyword in Mathematica help, but I
can't find what I'm looking for. Maybe that's because I've learned
those expressions in german...

My problem:

I want Mathematica to assume that a certain condition is satisfied for
the following algebraic transformations. More specifically: Let rho
describe a radius coordinate. I know it is not negative real. So, for
transformations of expressions containing rho, e.g.  Sqrt[rho^2], I
want assure Mathematica that 0 <= rho is in fact satisfied, and that it
is consequently allowed to replace Sqrt[rho^2] by rho. How do I do

My solution was 

Unprotect[Sqrt]; Sqrt[rho_^2] := rho/; 0 <= rho; Protect[Sqrt]; 

rho /: 0 <= rho = True;

and this seems to work, but I wonder whether this is really the proper
way. Since the TagSet I'm using here assigns the whole statement to
rho, and ?rho results in

rho /: 0 <= rho = True

so I still have my doubts ...

Can some of you experts enlighten me?

Thanks in advance

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