Re: Math question [polynomial division]

From: Mok-Kong Shen (mok-kong.shen_at_t-online.de)
Date: 12/29/03 

Date: Mon, 29 Dec 2003 21:28:59 +0100

Tom St Denis wrote:
>
[snip]
> The problem now is that division cannot always be computed in the first
> instance [as I understand it, and well as I understand math isn't saying
> much]. Say you have
>
> p(x) = 3x^2 + 4x + 1
> and
> q(x) = 7x + 9
>
> If you attempt to divide p(x)/v(x) over Z^k[x] there is no solution since
> you have to multiply q(x) by (3/7)x and subtract that out to clear the x^2
> term. Since 3/7 == 0 over Z you cannot complete this operation for all
> polynomials.
[snip]

In this case you can't express p(x) as a(x)*q(x)+r(x)
with a(x) and r(x) having integer coefficients. But
what is the practical 'consequence' of that for you?
(What are the applications demanding such expressions?)

M. K. Shen

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