Integer factorization, etc.
in [Math]
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From: Pubkeybreaker on 8 Apr 2008 08:32 On Apr 7, 5:27 pm, Risto Lankinen <rlank...(a)gmail.com> wrote: > On 7 huhti, 20:00, Nick Wedd <n...(a)maproom.co.uk> wrote: > > > > > I think what he means is "Fermat's factorisation method can only be used > > to factorise natural numbers". He is interested in factorising Gaussian > > integers. > > Nope. I'm using gaussian integers to factor natural numbers. They are Polynomial time equivalent. > Inverting a number multiplied by itself is called a square root. Duh! Finding square roots is EASY. You want (a +bi)^2 = c + di. Expand, equate real and imaginary parts and solve the simultaneous 2-variable system of equations that arises. If a and b are not integers then c+di has no integral square root. This is TRIVIAL. Go learn some basic, high school level mathematics.
From: Risto Lankinen on 8 Apr 2008 15:21 On 8 huhti, 15:32, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > > Finding square roots is EASY. You want (a +bi)^2 = c + di. Expand, > equate real and imaginary parts and solve the simultaneous 2-variable > system > of equations that arises. If a and b are not integers then c+di has > no integral > square root. This is completely different to my method. Apparently you do not see any value in the opportunity for insight thru two completely different viewpoints of the same problem. I am truly sorry about that, while I hope I never stop learning. Hang loose! - Risto -
From: Pubkeybreaker on 9 Apr 2008 08:08 On Apr 8, 3:21 pm, Risto Lankinen <rlank...(a)gmail.com> wrote: > On 8 huhti, 15:32, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > > > > > Finding square roots is EASY. You want (a +bi)^2 = c + di. Expand, > > equate real and imaginary parts and solve the simultaneous 2-variable > > system > > of equations that arises. If a and b are not integers then c+di has > > no integral > > square root. > > This is completely different to my method. Apparently you > do not see any value in the opportunity for insight thru two > completely different viewpoints of the same problem. I am > truly sorry about that, while I hope I never stop learning. Now you are sounding like a true crank. I happen to know enough mathematics to realize when something is a dead end. The fact that you claim a new "method" is irrelevant. Finding the square root of a complex number is a trivial problem that is easily solved by high school level mathematics. The work that you have done only OBFUSCATES, rather than clarifies the problem. You can *start* learning by listening to an expert on primality testing and integer factorization. Another hallmark of a crank is refusing to take the advice of an expert when the expert tells you that something is a dead end.
From: Risto Lankinen on 9 Apr 2008 12:59 On 9 huhti, 15:08, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > > Now you are sounding like a true crank. I happen to know enough > mathematics > to realize when something is a dead end. Could you please tell me _WHY_ you think my approach is a dead end? Based on your own claim, you never dug into the code I sent. Respectfully, - Risto -
From: Pubkeybreaker on 9 Apr 2008 13:08
On Apr 9, 12:59 pm, Risto Lankinen <rlank...(a)gmail.com> wrote: > On 9 huhti, 15:08, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > > > > > Now you are sounding like a true crank. I happen to know enough > > mathematics > > to realize when something is a dead end. > > Could you please tell me _WHY_ you think my approach is > a dead end? Based on your own claim, you never dug into > the code I sent. (1) Presenting code only serves to obfuscate the underlying method. If you want to present an algorithm then do so. (2) Computing square roots of any complex number is a trivial and fast process via ***elementary algebra***. Your method is far more complicated. The world does not need a complicated way of doing something that is already very simple. You are trying to reinvent the wheel by giving us a square wheel. (3) You wouldn't try to invent a new surgical procedure would you? Unless one is a doctor, trying to do so is hopeless. Your trying to invent a new algorithm is analagous. You simply lack the skills and knowledge to do so. The difference between the two cases is that you are aware that you lack the medical skills. |