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

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Posts: 1,245
Registered: 4/26/08
Re: Terrible algebraic system
Posted: Feb 24, 2012 5:35 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply 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?

Here are two cases solved numerically on Derive 6.10. I am employing
NSOLUTIONS rather than SOLUTIONS to avoid the solution of the quartic in
terms of radicals. Because the solutions are very close-spaced here, I
calculate with 50 decimal digits, but display only 20.







Maxima should allow to do the same.


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