In article <3cXUj.2019$KQ4.1186@[EMAIL PROTECTED]
>, Jack <jj@[EMAIL PROTECTED]
>
wrote:
[...]
> Ah, but I really need to know the precise wording I should use. So far
my
> best guess is "We shall be constructing arrays comprising entries of
ones
> and zeroes, in which the first column, containing exclusively ones, is
> indexed by zero."
How about "We shall construct binary matrices whose first column
consists only of 1's and whose other entries are determined by certain
divisibility properties"? It is OK to be a little vague at this stage.
I still think it is a mistake to have the exceptional first column. If
you really, really need it you could do something like
"Let p(2) < ... < p(m + 1) be the first m primes and let p(1) = 1. Let
x = x(1) < ... < x(n) = y (or x(n) = x + a - see below) be consecutive
integers. Let M_1 be the m + 1 by n matrix (m(i,j)) where m(i,j) = 1 if
p(i) divides x(j) and m(i,j) = 0 otherwise."
If you want to get fancy, there is a function div(d,n) which is 1 if d
divides n and 0 otherwise. Mathematica implements it with the function
"divides"; I think it is fairly obscure but you do have
m(i,j) = div(p(i),x(j)) which is kind of pretty.
> > Your paragraph quoted above is a little too vague for me to be of any
> > help. Are you going to change m's or intervals or both or none of the
> > above. How many changes at one time are you going to want to make?
> >
>
> Generally my argument takes the pattern: "For any given m, and for all
> intervals of length y-x+1..."
I read this to say that m is fixed and all intervals have the same
length. If that is so then all you need to do is say, somewhere near
the start, "Let m and a be positive integers." If you do that,
subsequently you will only need to reference the starting points of
your intervals - the intervals will be [x, x + a] (or maybe
[x, x + a + 1] if you prefer) for your various x's. With m and a fixed
your M_1 could be instead M_x which would convey all the needed
information. Also, if you prefer, m(i,j) = div(p(j),(x - 1) + j).
[...]
--
Paul Sperry
Columbia, SC (USA)
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