Inverse of Polynomial Function -- Mathematics Help

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Subject: Inverse of Polynomial Function

Author:
tnewton

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Date Posted: 17:40:43 02/17/04 Tue

What I would really like to do is find the coefficients of INV(f(x)) from the coefficients of f(x) of an nth degree polynomial (1-variable).

f(x)= SUM(ai * x^i) for i = 0..n)
INV(f(x)) = ???

Any and all help is greatly appreciated. Thanks!

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Replies:

[> Subject: Re: Inverse of Polynomial Function

Author:
QUITTNER
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Date Posted: 10:22:18 04/23/04 Fri

>>>What I would really like to do is find the coefficients of INV(f(x)) from the coefficients of f(x) of an nth degree polynomial (1-variable).<<<

>>> f(x)= SUM(ai * x^i) for i = 0..n)
>INV(f(x)) = ??? <<<
..... As I remember it, if y is a function of the sum of various degrees of x, then the inverse is (simply - oh yeah?) x as a function of y. That may be quite difficult to find is many cases involving higher than the 3rd degree of x.

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[> [> Subject: Re: Inverse of Polynomial Function

Author:
tnewton
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Date Posted: 19:39:51 05/04/04 Tue

Yes, that's the definition of inverse, but it requires you to know the order of the function first in order to solve. I believe there may be some algorithm to find the reverse coefficients regardless of degree, and may require very deep recursion (related to the polynomial order); at least that's the direction I seem to keep finding myself heading. I've seen a process that finds the solution to the inverse function; it's a little tough to follow and I haven't been able to use it as a basis for determining the coefficients. Maybe if I figure this out I'll get my name in the history books...
>>>>What I would really like to do is find the
>coefficients of INV(f(x)) from the coefficients of
>f(x) of an nth degree polynomial (1-variable).<<<
>
>>>> f(x)= SUM(ai * x^i) for i = 0..n)
>>INV(f(x)) = ??? <<<
>..... As I remember it, if y is a function of the sum
>of various degrees of x, then the inverse is (simply -
>oh yeah?) x as a function of y. That may be quite
>difficult to find is many cases involving higher than
>the 3rd degree of x.

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[> [> [> Subject: Re: Inverse of Polynomial Function
Author: QUITTNER [ Edit \| View ]	Date Posted: 10:42:17 05/06/04 Thu tnewton, unfortunately I can't help you with that. But maybe you'll come up with some useful solution(s). Good luck, and keep well! [ Post a Reply to This Message ]