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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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