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