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MathGroup Archive 2000

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Re: Manipulating Equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25142] Re: [mg25064] Manipulating Equations
  • From: BobHanlon at aol.com
  • Date: Sun, 10 Sep 2000 03:15:00 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 9/7/2000 10:48:48 PM, chusseau at univ-montp2.fr writes:

>I have to simultaneously solve equations corresponding to a physical
>problem. Therefore most of my variables have a meaning only if they are
>real
>and positive. How can I say to Mathematica that it has to reject solutions
>not corresponding to these cases, and furthermore how to declare these
>variables so that their particular nature is used by Simplify or
>FullSimplify.
>

var = {x, y, z};

eqn = {(x + y)*z^2 == 1, x^2 == 3, y^2 == 3}; 

For real, positive variables the conditions are

cond = And @@ Join[Im[#] == 0 & /@ var, # > 0 & /@ var];

soln = Solve[eqn, var]

{{x -> -Sqrt[3], y -> -Sqrt[3], 
   z -> -(I/(Sqrt[2]*3^(1/4)))}, {x -> -Sqrt[3], 
   y -> -Sqrt[3], z -> I/(Sqrt[2]*3^(1/4))}, 
  {x -> Sqrt[3], y -> Sqrt[3], z -> -(1/(Sqrt[2]*3^(1/4)))}, 
  {x -> Sqrt[3], y -> Sqrt[3], z -> 1/(Sqrt[2]*3^(1/4))}}

Select[soln, cond /. # &]

{{x -> Sqrt[3], y -> Sqrt[3], z -> 1/(Sqrt[2]*3^(1/4))}}

Whenever you want to apply the conditions use

Simplify[expr, cond]

FullSimplify[expr, cond]

or define functions 

mySimplify[expr_] := Simplify[expr, cond];

myFullSimplify[expr_] := FullSimplify[expr, cond];


Bob Hanlon


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