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Topic: Terrible algebraic system
Replies: 18   Last Post: Mar 8, 2012 4:26 AM

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Peter Pein

Posts: 1,147
Registered: 5/4/05
Re: Terrible algebraic system
Posted: Feb 24, 2012 6:01 AM
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Am 24.02.2012 11:17, schrieb
> 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))

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