       Re: Imposing constraints on a system of equations

• To: mathgroup at smc.vnet.net
• Subject: [mg109367] Re: Imposing constraints on a system of equations
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 23 Apr 2010 03:50:28 -0400 (EDT)

```Just use Reduce instead of Solve:

sols =
Reduce[eq1 && eq2 && eq3 && r >= 0 && h >= 0, {r, h, x}, Reals,
Backsubstitution -> True]

(a == 0 && r == 0 && h == 0) || (a == 0 && r == 0 &&
h > 0 && x == 0) || (a > 0 &&
r == Sqrt[a]/Sqrt[6*Pi] &&
h == Sqrt[2/(3*Pi)]*Sqrt[a] &&
x == -(Sqrt[a]/(2*Sqrt[6*Pi])))

On 22 Apr 2010, at 16:31, Virgil Stokes wrote:

> A very simple question on imposing conditions/constraints.
>
> I know that a, r, and h must be real and non-negative in the following
> system of equations:
>
> eq1=Pi*r^2+2*Pi*r*x==0;
> eq2=2*Pi*r*h+(2*Pi*h+4*Pi*r)*x==0;
> eq3=2*Pi*r^2+2*Pi*r*h-a==0;
> sols=Solve[{eq1,eq2,eq3},{r,h,x}]
>
> How can I impose conditions on this system such that only real solutions
> are obtained, and r and h are non-negative?
>
> Thank you,
> --V
>
>

```

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