Re: JSH: Polynomial multiples
From: Matt Grime (mattgrime_at_o2.co.uk)
Date: 10/18/04
- Next message: Mark Mackey: "Re: Complicated least-squares problem"
- Previous message: Robin Chapman: "Re: the connection orthogonal expansions and stochastic processes"
- In reply to: James Harris: "JSH: Polynomial multiples"
- Next in thread: Randy Poe: "Re: JSH: Polynomial multiples"
- Messages sorted by: [ date ] [ thread ]
Date: Mon, 18 Oct 2004 14:49:52 GMT
On Sun, 17 Oct 2004 16:43:46 -0700, James Harris wrote:
> If you had even a basic math education then you learned about
> multiples of polynomials--you learned to divide them off.
>
> None of you have ever been taught that multiples of polynomials are
> varying functions that vary with the polynomial's variable, unless
> you're learning from sci.math'ers.
>
> Like P(x) = 4x^2 + 4x + 4 has a multiple of 4.
>
> If some freaking poster were arguing for years that the factors of
> P(m) have 4 divided off as function of x, would you be nodding along?
>
> No.
>
4 divides P(x) in this case in the ring of polynomials, and as such isn't
relevant to your discussion about divisibility in the ring of algebraic
integers.
After all, 2 divides x^2+x for all integer x in the integers (not in the
algebraic integers, just the integers), yet how it divides the factors x
and x+1 does depend on x.
6 also divides x(x-1)(x+1) for all integer x, again in the integers, want
explain how?
> But when yahoos argue with me, claiming that multiples of polynomials
> divide off as freaking functions of the polynomial variable, you
> nincompoops nod along, agree with them and call ME crazy.
>
- Next message: Mark Mackey: "Re: Complicated least-squares problem"
- Previous message: Robin Chapman: "Re: the connection orthogonal expansions and stochastic processes"
- In reply to: James Harris: "JSH: Polynomial multiples"
- Next in thread: Randy Poe: "Re: JSH: Polynomial multiples"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
