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

Select[soln, cond /. # &]

{{x -> Sqrt, y -> Sqrt, z -> 1/(Sqrt*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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