Date: Feb 24, 2012 6:01 AM
Author: Peter Pein
Subject: Re: Terrible algebraic system
Am 24.02.2012 11:17, schrieb deltaquattro@gmail.com:

> Hmmm! Tried following this approach, i.e. solving f(b)=0 with Netwon's and then plugging b in a=g(b), but it doesn't work. The solution doesn't satisfy the initial system. Try for example

>

> L=-1

> U=1

> p=0.0013498980316301

>

> I get

>

> a=-1

> b=1

>

> which clearly is wrong, i.e., a and b don't solve the initial system, even though f(b)=f(1)=0 and a=g(b)=g(1)=-1. I rewrite the initial system here:

>

> ((a-L)^2/a)*(2/(a+b))-p=0

> ((b-U)^2/b)*(2/(a+b))-p=0

>

> Am I doing something wrong, or is FriCAS/Derive solution wrong?

When L=-U, you probably want p>1 to get a real result for

a= (-2 U + 2 p U +/- sqrt((-1 + p) p^2 U^2))/((-2 + p) (-1 + p))