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Re: Implementation rest modulo 2 needed

  • To: mathgroup at smc.vnet.net
  • Subject: [mg93875] Re: Implementation rest modulo 2 needed
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Thu, 27 Nov 2008 05:34:05 -0500 (EST)

On 11/26/08 at 5:10 AM, grafix at csl.pl (Artur) wrote:

>I want to construct algorhitm finding two divisors of numbers
>(without FactorIneteger and with uses only Reduce, GroebnerBasis
>etc.)

>e.g. for divisors of number 15 in binary system these will be

>Reduce[{x a == 1 && y a + x b == 1 && y b + x c == 1 && y c =
== 1 &&
>x (x - 1) == 0 && y (y - 1) == 0 && c (c - 1) == 0 && b (b - 1=
) == 0
>&& a (a - 1) == 0}, {x, y, a, b, c}, Integers]

You are making things more complex than necessary here. Doing

Reduce[a b == 15, {a, b}, Integers]

will return a list of all possible pairs of integers that when
multiplied together will be 15. If you want this restricted to
non-trivial positive solutions then

Reduce[a b == 15 && a>1 && b>1, {a, b}, Integers]

will work. Another alternative would be

FindInstance[
  a b == 15 && {a, b} \[Element] Integers && a > 1, {a, b}]

However, it may well be using Reduce here simply masks an
internal call to FactorInteger  And using a different
Mathematica function to solve a problem really isn't what I
would refer to as constructing an algorithm.

Why is it you don't want to use FactorInteger?


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