Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #326 20130725 06:05:03#327 20130725 13:06:21
Re: Define the intersection points of polynomialsThat I do not know offhand but I tend to disagree. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #328 20130725 17:05:35
Re: Define the intersection points of polynomialsI didnt know that this information would be helpful. From my point of I retstated the same question in a way that would be more familiar to you. Last edited by Herc11 (20130725 17:20:47) #329 20130725 17:31:03
Re: Define the intersection points of polynomialsWas anyone else able to provide a solution? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #330 20130725 17:34:23
Re: Define the intersection points of polynomialsNo. only one answer there was. #331 20130725 17:38:30
Re: Define the intersection points of polynomials
I read several answers. One of them said it was unsolvable as you posted it. I am inclined to agree. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #332 20130725 17:42:36#333 20130725 17:50:15
Re: Define the intersection points of polynomials
In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #334 20130725 17:51:00#335 20130725 17:55:32
Re: Define the intersection points of polynomialsFirst of all he says
There is something wrong with your understanding of the problem and how it is related to the so called GF.
A prime field should have been adequate to answer this question. It was not. I tried GF(113) Gf(2^16), Gf(2^32) all without a single solution that I could find. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #336 20130725 18:02:54
Re: Define the intersection points of polynomials
I thought that the filed plays a significant role to the solution of the system. And he says that it plays a role but not in the ways that I think. #337 20130725 18:11:25
Re: Define the intersection points of polynomials
I did not choose anything that is what the multiplications from your formula produced. I asked what you wanted to do next on those coefficients. I would have used a modulo on them to bring them into the set. You had no answer.
Your set or any prime field is nothing but a subset of the integers. If there was no intersection over the integers how can there be one over a subset of the integers? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #338 20130725 18:21:46
Re: Define the intersection points of polynomialsI used the field 2^128 and also polynomial representation basis. Therefore, addition multiplication and division is not defined as it were on real numbers. I have tested it many times that these operations never return negative elements. It is not possible. My problem is that I dont have an algorithm to solve the second problem. I have the definitions of the operations but I cannot solve a system of 4 equations with 4 unknowns. I am not sure that there is a solution but I think tha there is. I do I do not avoid any possibility but I think that believing that there is no solution is the easy but unhopefully the wrong way. Last edited by Herc11 (20130725 18:24:29) #339 20130725 18:33:24
Re: Define the intersection points of polynomials
Modulo would have brought them into your field. There still would not have been a solution.
Solve what? I do not like when people give offhand information like "this is a linear system" but provide no solution. How is that a representation of 4 quadratics? What am I solving for? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #340 20130725 18:41:30
Re: Define the intersection points of polynomialsOk. I understand that I can not give you clear answers because I also do not understand many things. #341 20130725 18:50:25
Re: Define the intersection points of polynomialsYou did not offend me. The people on that site that made such an assertion without providing any worked example did. In computation we want numbers not concepts and jargon. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #342 20130725 18:52:37
Re: Define the intersection points of polynomialsThe first a_1 and the second a_1. Last edited by Herc11 (20130725 18:52:55) #343 20130725 19:01:40
Re: Define the intersection points of polynomials
That is what they teach in school and it is the biggest myth in the entire world. There are many cases where theory does not match the numbers. Theoreticians can not get numbers! Computational people can! Math is split into pure and applied and they do not even speak the same language. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #344 20130725 19:37:39#345 20130725 19:56:07
Re: Define the intersection points of polynomialsOkay, but isn't that just the slope? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #346 20130725 20:00:55#347 20130725 20:07:11
Re: Define the intersection points of polynomialsThose are the equations for the slope of of the line between (x0,y0) (x1,y1) and (x0,y0)(x2,y2). In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #348 20130725 20:14:39#349 20130725 20:28:05
Re: Define the intersection points of polynomialsYou are right about that. We have x0,x1,x2 and y0,y1,y2 so what is there to solve for? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #350 20130725 20:38:15
Re: Define the intersection points of polynomialsIn order to be sure that the system has a solution I construt the system of equations to have a common point the x0 y0. i.e. I define the intersection point x0y0 and then I pretend that I do not know it.. 