Re: Imposing constraints on a system of equations

• To: mathgroup at smc.vnet.net
• Subject: [mg109390] Re: Imposing constraints on a system of equations
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Sat, 24 Apr 2010 04:03:39 -0400 (EDT)

```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 = Reduce[{eq1, eq2, eq3, r >= 0, h >= 0}, {r, h, x}, Reals]

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

Bobby

On Thu, 22 Apr 2010 02:31:16 -0500, Virgil Stokes <vs at it.uu.se> 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
>
>

--
DrMajorBob at yahoo.com

```

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