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You are not logged in. #276 20130723 20:17:59
Re: Define the intersection points of polynomialsNo, I chose the points later. I can find different points on the parabolas. It will just mean reprogramming it.
That is a good question and I do not know how the simultaneous set will react when the same x's are chosen for all the points. Remember, I only solved 2 problems before this one over the Reals. That is not a lot. I do know that on those problems I chose different x's. 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. #277 20130723 20:23:11#278 20130723 20:28:52
Re: Define the intersection points of polynomialsI am sure they intersect at 2 points. Here is a plot of them. 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. #279 20130723 20:31:39#280 20130723 20:38:51
Re: Define the intersection points of polynomialsThe coefficients of the parabolas are negative integers. For instance one of them is y = 10  14 x + 5 x^2. Only the leading coefficient needs to be an element of GF(113). 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. #281 20130723 20:41:48#282 20130723 20:44:03
Re: Define the intersection points of polynomialsThat I did not know. You say that all the coefficients of the four parabolas must be over GF(113) not just the first one? 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. #283 20130723 20:47:44
Re: Define the intersection points of polynomialsI thought that it was clear...All the parameteres of the problem are GF elemets . The set of equations is defined on GF you can not mix GF elements with integers. The problem will have no sense. The points are GF elements too. Last edited by Herc11 (20130723 20:48:38) #284 20130723 20:49:17
Re: Define the intersection points of polynomialsOkay, I will setup up the problem to be like that. I will post when I have it done. 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. #285 20130723 20:55:01
Re: Define the intersection points of polynomialsI think that you will find it difficult to find 4 quadraticks with 2 intersection points over GF{113}. I can construct polynomials over the GF{2^128}. I might be able to do it over 2^32. In 2^32 can you solve the set?i.e. has the Mathematica the appropriate equations? #286 20130723 20:55:58
Re: Define the intersection points of polynomialsI think it will be impossible to find 4 quadratics over GF(113). You want to go larger? 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. #287 20130723 20:57:49#288 20130723 21:00:37
Re: Define the intersection points of polynomials2^128 is not a prime. 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. #289 20130723 21:02:06#290 20130723 21:10:19
Re: Define the intersection points of polynomialsOne more thing. 2^128 is a 40 digit number. That means coefficients will be very large and graphing because of scaling will be difficult. 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. #291 20130723 21:15:38
Re: Define the intersection points of polynomialsYes. this is true that why I told you that there will be problems with 2^128. #292 20130723 21:19:01
Re: Define the intersection points of polynomialsI do not think solving is a problem at all. Forming a set of problems to solve has been troublesome. I will try with 2^128. 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. #293 20130723 21:22:10
Re: Define the intersection points of polynomialsThen I can provide you with the points and lead . coef etc... I mean that It might be a problem because you have to perform all the operations based on the irreducible problem. Last edited by Herc11 (20130723 21:22:55) #294 20130723 21:29:09
Re: Define the intersection points of polynomialsOkay, provide me with what you have. 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. #295 20130723 22:15:42
Re: Define the intersection points of polynomialsHere is what I have. I hope that I didnt make any mistake while copying the numbers. Note tha they are in Hex. Last edited by Herc11 (20130724 21:58:01) #296 20130723 22:45:35
Re: Define the intersection points of polynomialsHi; 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. #297 20130724 20:15:18#298 20130724 20:28:53
Re: Define the intersection points of polynomialsHi; 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. #299 20130724 20:47:17#300 20130724 20:52:06
Re: Define the intersection points of polynomialsNothing is easy with Mathematica. It is a real bear. Its strengths are also its weaknesses. Thousands of commands makes everyone go wow but it is difficult to remember them all. 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. 