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Re: Re: Implementation rest modulo 2 needed

  • To: mathgroup at smc.vnet.net
  • Subject: [mg93896] Re: [mg93867] Re: [mg93789] Implementation rest modulo 2 needed
  • From: danl at wolfram.com
  • Date: Fri, 28 Nov 2008 05:06:31 -0500 (EST)
  • References: <200811251216.HAA03013@smc.vnet.net>

> Dear Daniel,
> One question more. If we will be have strictly matematical formula on
> adding numbers in binary system (not algorhitm but explicite formula)
> what will be changed in our difficult situation ?
> Best wishes
> Artur

You will have more equations: you'd get one per bit of the result. This
would be good, were they linear. But they're not. One small advantage, if
you use Groebner bases at this stage, is you could work modulo 2.

Daniel Lichtblau
Wolfram Research


> Daniel Lichtblau pisze:
>> Artur wrote:
>>> Dear Mathematica Gurus,
>>>
>>> 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]
>>>
>>> but to find divisors of 15=1111 wasn't necessary to use rest modulo 2
>>>
>>> How do that for e.g. 735 = 1011011111 where we have to uses rest
>>> modulo 2
>>>
>>> Any idea ?
>>>
>>> Best wishes
>>> Artur
>>> [...]




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