Re: JSH:Understanding constant terms

From: I.M.Davidson (sttscitrans_at_tesco.net)
Date: 12/01/04 

Date: 1 Dec 2004 01:23:17 -0800

magidin@math.berkeley.edu (Arturo Magidin) wrote in message news:<coi0o6$rg0$1@agate.berkeley.edu>...
> In article <5ff8565f.0411291642.1abb7b90@posting.google.com>,
> I.M.Davidson <sttscitrans@tesco.net> wrote:
> >magidin@math.berkeley.edu (Arturo Magidin) wrote in message news:<cofc0a$nh$1@agate.berkeley.edu>...
>
> [.snip.]
>
> >> >> You were assuming that the g_i(x) were polynomials, and that the
> >> >> product of the g_i(x) was equal to P(x). Then your statement "if and
> >> >> only if the g's are monic polys" was about the statement that each
> >> >> g_i(0) divides, in the algebraic integers, P(0).
> >> >
> >> >According to Harris, the g_i(x) are algebraic integers
> >> >whenever x is ( his "algebraic integer functions").
> >> >Clearly g_i(0) has to be an algebraic
> >> >integer and so the constant term of g_i(x)has to be an
> >> >algerbaic integer.
> >> >
> >> >You say that the gi can be "ANY polynominal".
> >>
> >> Please note that I was not addressing James's argument. I was
> >> addressing your restriction to the g_i being polynomials, and your
> >> assertion, ->under that further restriction<-, that each g_i(0) would
> >> divide P(0) in the ring of all algebraic integers if and only if the
> >> g_i(x) were "monic". ->That<- assertion is false.
> >
> >Yes, I agree
> >
> >> >This is clearly not the case. For example pi*x +1.
> >> >Are you saying that p1*1 +1 is an alegebraic integer ?
> >>
> >> No. I am saying that if g(x)=pi*x + 1, then it is entirely possible
> >> for g(0) to divide P(0) in the ring of all algebraic integers, EVEN
> >> THOUGH g(x) is not a monic polynomial.
> >
> >Yes, but we now know that the g_i(x)
> >must meet another condition.
> >
> >What I said prev. was incorrect,
> >but your statement that "ANY polyno."
> >would do is crassly passe in the light
> >of new revelations.
>
> So... I addressed your comment as written. Since that comment, you
> have now changed your mind about what the g_i(x) should be; based on
> that change of heart, you complain that my correction was wrong,
> because it failed to meet your newfound and not-previously asserted
> conditions on the g_i(x).
>
> How... interesting...

The disingenuousness of your attempted
exculpation is breathtaking.
I am unversed in exegesising the
pronouncements of the Supreme Coprolocutor.
You, however, analyse His productions with
monomaniacal intensity. Therefore,
to claim that the conditions on the g_i(x),
although new to me, were unknown to you
is sophistry of the most egregious kind.
A simple admission of your trivial error would bring
the catharsis and ultimate peace of mind
you yearn for.

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