On Fri, 25 Apr 2008 20:59:30 +0100, Jack <jj@[EMAIL PROTECTED]
>
wrote in <news:EKqQj.251244$833.94482@[EMAIL PROTECTED]
> in
alt.algebra.help:
> "Brian M. Scott" <b.scott@[EMAIL PROTECTED]
> wrote in message
> news:7pjsntiqk3fs$.4eaycx81ywvj$.dlg@[EMAIL PROTECTED]
>> On Fri, 25 Apr 2008 18:52:36 +0100, Jack <jj@[EMAIL PROTECTED]
>
>> wrote in <news:EToQj.60181$_h7.47121@[EMAIL PROTECTED]
> in
>> alt.algebra.help:
>>> Take x and y to be integers. If we have a set P(m)
>>> comprising the first m primes beneath a value z, and a
>>> general subset J of of P(m), then I am constructing a
>>> matrix M_1 in which the members of J index the rows.
Do you really mean this, or do you mean that the only rows
of M_1 whose elements are defined (or non-empty, if you
think of M_1 as an array in a computer program, for
instance) are the ones indexed by the members of J?
>>> I am also constructing an array M_[x,y] comprising black
>>> cells and white cells. The number of black cells in a
>>> column is given by t(n,M_[x,y]). Will it be acceptable
>>> in a mathematical paper to devise a form of notation
>>> referencing an interval [x,y] in such a way that the
>>> values of t(n,M_[x,y]) over [x,y] conform precisely to
>>> the divisibility distribution that is exhibited in an
>>> interval [x,y] M_1?
>> I can't tell from this description just what you're trying
>> to do.
> Let a(J) be the product of all members of J.
> I'm trying to construct an array in which the black cells
> do not necessarily conform to the distribution of
> occupied matrix components in the matrix M_1.
What do you mean by 'conform to'? 'Occupied matrix
components' is also problematic, unless you're thinking of
M_1 as an array (e.g., in a computer program) whose cells
may or may not have defined contents rather than as a
(mathematical) matrix.
My best guess at this point is that you have a partially
populated array M_1 = [m(i, j)]. Now let
P = {(i, j) : m(i, j) is defined}; in other words, P
contains the addresses of the populated cells of M_1. You
now want to construct an array A = [a(i, j)] of black and
white cells; presumably it's an array of the same dimensions
as M_1. If B = {(i, j) : a(i, j) is black}, B is not
necessarily equal to P. (I've used A for simplicity; I
gather that this is your M_[x,y].)
> I am considering subintervals [x,y] in the interval that
> is the product of all members of J.
But the product of the members of J isn't an interval: it's
simply an integer. Do you mean subintervals of [1, a(J)],
or perhaps of [0, a(J)]?
> But I am also wondering if I can devise a form of
> notation in which I indicate that the distribution of
> black cells in my array, for some [x,y], do indeed
> conform to the distribution found for [x,y] in M_1.
> Ideally I want to have an array in which all the black
> cells in columns indexed by integers 0 to 2a(J) conform
> to the same distribution as do the occupied matrix
> components M_1.
This is still pretty opaque, because I've no idea how the
indexing works. But if I've guessed correctly what you mean
by 'conforms' in this context, you're asking whether there
is some notational way to indicate (in the notation that I
used above) that B = P.
> But I also want there to be other subintervals in the
> array such that this conformity does not apply. This
> will mean I don't have to keep switching between a matrix
> and an array.
This sounds like you're making some distinction between
'matrix' and 'array', but I can't tell what it is, unless
you just mean switching back and forth between M_1 and what
I called A. It is also not clear to me what you mean by a
'subinterval in the array'
> It's just that I don't know whether that sort of thing is
> done.
And I can't tell you, because I still haven't any real idea
of what you want to do. Perhaps I'm being uncommonly dense,
but I suspect that you don't realize how very much
background you're taking for granted. E.g., in the other
thread your answer to my final question is useless, because
I have no idea what the interval [x', y'] has to do with
anything that precedes that point.
At any rate we're not communicating: I still have only the
foggiest idea of what you're trying to do, let alone what
your question about it really is, and it's pretty clear that
I've not adequately conveyed the nature and extent of my
confusion(s). Since I've a small mountain of exams to mark
(and more to prepare), I should probably just bow out, but
if you want to try again with a more detailed explanation,
I'll try to make time to have one more go at it.
Brian
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