Monday, October 20, 2008
JSH: Explaining for the "angry idiots"
I'm noticing some posters replying negatively in some of my recent threads in a way that shows they don't have a clue, so because I'm trying to get a few answers quickly I thought I'd remind those who I call angry idiots, how things work here:
I'd tried to get away from posting hoping I'd finished things out as I'm feeling kind of tired, but turns out there is more to re-working binary quadratic Diophantine equations than I first thought!
After all, I thought I was done weeks ago, but am still refining theory, God help me, and still making new discoveries, damn it. Sick of new discoveries. Tired of discovering new math. Wish it would all just stop so I can spend more time chasing women.
Ok, but I digress.
Seems that non-rationals have no real role at all with Pell's Equation but only come in because of one of those weird things where non-rationals can behave a lot like the relation group:
x^2 + Dy^2 = F
means that
(x-Dy)^2 + D(x+y)^2 = F*(D+1)
which is just one of those things as the D just stays there like with non-rationals, say 1+sqrt(2), the sqrt(2) keeps hanging around as you raise that to higher powers and a lot of math history turned on that one thing.
But understanding the RATIONAL explanation allows you to do cool things, like have a general solution method.
And, oh, you wackies know damn well that even with JUST the general solution to equations of the form
c_1^x^2 + c_2*xy + c_3*y^2 = c_4 + c_5*x + c_6*y
I've advanced the state of the art as no one had a simple, direct, general way to do it before but just quirky more roundabout ways which readers can verify at MathWorld:
http://mathworld.wolfram.com/DiophantineEquation2ndPowers.html
Just looked at the page and puzzled at it a bit where the important point is that the equation is not directly and generally handled when I almost trivially do so with my Quadratic Diophantine Theorem.
But it gets better as if this latest insight holds then I've figured out how to determine how long it will take before continued fractions will give a solution based on when -D is not a quadratic residue modulo (D+1), where
x^2 + Dy^2 = F
in general so you can have F=1. That could be HUGE as not only would it allow you to know exactly WHY a continued fraction solution takes as long as it does, I've figured out a general technique for getting the answer.
Putting it all together it's really exciting, which is why I'm stuck posting still as I work through it all, which leaves me also seeing posts from the angry idiots. If any of you can get some of these nitwits off my back it'd be appreciated. I'm finally getting tired of them. They're so, angry, and so, idiotic.
IN any event, waiting to see how this latest research plays out, and posting just to sci.math because you are the home of the angry idiots! So you people need EXTRA explaining as otherwise you're too goddamn stupid to get things on your own.
Have I mentioned I'm getting tired of the angry idiots?
Some of you need to think about trying to put more of a leash on these people, or better yet, a muzzle, or no, as I'm a free speech advocate. AT least let them know that they know no math, speak no math, should not pride themselves on their ape behavior in the face of their godawful ignorance of what is actually going on.
Freaking apes. I feel like I can see the human species devolving when I come on this newsgroup.
Some of these people should be back swinging in the trees versus ranting and raving, and throwing crap words, like chimps throw feces, at discoverers trying to work in the only environment available because, yup, because it's a stupid world.
- I post when I'm working on problems, as I toss ideas out there, as part of brainstorming which is part of what I call extreme mathematics.
- You do not know what is going on based on how you think people should reply to me, how you see people reply to me, or think you see people reply to me, but only from the mathematical content.
- There is always significant mathematical content lurking in there somewhere.
I'd tried to get away from posting hoping I'd finished things out as I'm feeling kind of tired, but turns out there is more to re-working binary quadratic Diophantine equations than I first thought!
After all, I thought I was done weeks ago, but am still refining theory, God help me, and still making new discoveries, damn it. Sick of new discoveries. Tired of discovering new math. Wish it would all just stop so I can spend more time chasing women.
Ok, but I digress.
Seems that non-rationals have no real role at all with Pell's Equation but only come in because of one of those weird things where non-rationals can behave a lot like the relation group:
x^2 + Dy^2 = F
means that
(x-Dy)^2 + D(x+y)^2 = F*(D+1)
which is just one of those things as the D just stays there like with non-rationals, say 1+sqrt(2), the sqrt(2) keeps hanging around as you raise that to higher powers and a lot of math history turned on that one thing.
But understanding the RATIONAL explanation allows you to do cool things, like have a general solution method.
And, oh, you wackies know damn well that even with JUST the general solution to equations of the form
c_1^x^2 + c_2*xy + c_3*y^2 = c_4 + c_5*x + c_6*y
I've advanced the state of the art as no one had a simple, direct, general way to do it before but just quirky more roundabout ways which readers can verify at MathWorld:
http://mathworld.wolfram.com/DiophantineEquation2ndPowers.html
Just looked at the page and puzzled at it a bit where the important point is that the equation is not directly and generally handled when I almost trivially do so with my Quadratic Diophantine Theorem.
But it gets better as if this latest insight holds then I've figured out how to determine how long it will take before continued fractions will give a solution based on when -D is not a quadratic residue modulo (D+1), where
x^2 + Dy^2 = F
in general so you can have F=1. That could be HUGE as not only would it allow you to know exactly WHY a continued fraction solution takes as long as it does, I've figured out a general technique for getting the answer.
Putting it all together it's really exciting, which is why I'm stuck posting still as I work through it all, which leaves me also seeing posts from the angry idiots. If any of you can get some of these nitwits off my back it'd be appreciated. I'm finally getting tired of them. They're so, angry, and so, idiotic.
IN any event, waiting to see how this latest research plays out, and posting just to sci.math because you are the home of the angry idiots! So you people need EXTRA explaining as otherwise you're too goddamn stupid to get things on your own.
Have I mentioned I'm getting tired of the angry idiots?
Some of you need to think about trying to put more of a leash on these people, or better yet, a muzzle, or no, as I'm a free speech advocate. AT least let them know that they know no math, speak no math, should not pride themselves on their ape behavior in the face of their godawful ignorance of what is actually going on.
Freaking apes. I feel like I can see the human species devolving when I come on this newsgroup.
Some of these people should be back swinging in the trees versus ranting and raving, and throwing crap words, like chimps throw feces, at discoverers trying to work in the only environment available because, yup, because it's a stupid world.
# posted by James Harris @ 23:44 
