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You are not logged in. #301 20130724 20:54:29#302 20130724 20:57:33
Re: Define the intersection points of polynomialsYou could spend your life looking at it and never break the surface. 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. #303 20130724 21:03:26
Re: Define the intersection points of polynomialsNo, a0 a1 a2 are the newton coef. the formula tha associates the newton coef. with polynomial's coef is: But I dont think that you need the above formula. The only thing is to solve the set of the 4 a2's. Last edited by Herc11 (20130724 21:23:32) #304 20130724 21:23:36
Re: Define the intersection points of polynomialsOkay, running off the calculation now. 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. #305 20130724 21:49:55#306 20130724 21:51:30#307 20130724 21:52:20
Re: Define the intersection points of polynomialsWhy should the points of intersection of 4 quadratics be integers just because the coefficients are? 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. #308 20130724 22:00:08
Re: Define the intersection points of polynomialsBec ause all operations are executed on a Galois Field. Operations defined on GF return results of GF. This means that will return an element of GF. Last edited by Herc11 (20130724 22:00:59) #309 20130724 22:07:44
Re: Define the intersection points of polynomialsThe coefficients have to be numbers do they not? A GF is just a subset of N as far as we can compute them. remember they must be coefficients and x y coordinates. It is true that all simple operations like +  / * might be closed in the GF but intersections of quadratics is not a simple operation. It is easy to find 4 quadratics with coefficients like you want and a point on each like you want that do not have 2 points of intersection whose x y coordinates are even integers, let alone Gf(p). This proves that the GF is not closed under the intersection of the 4 quadratics. 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. #310 20130724 22:15:24
Re: Define the intersection points of polynomialsCoefficients must be GF elements. The set is defined on a GF, there is nothing else than GF. Only GF elements do exist for our problem. #311 20130724 22:19:48
Re: Define the intersection points of polynomialsI see no reason that the points of intersection have to be GF elements or any other type of elements.
What polynomials? Please produce your four polynomials and show that they have 2 points of intersection with the x's and y coordinates being GF elements. 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. #312 20130724 22:32:09
Re: Define the intersection points of polynomialsIn post #295 I wrote 4 sets of coef. a0 a1 a2. Each set of Newton coef. define a polynomial. #313 20130724 22:36:20#314 20130724 22:41:08
Re: Define the intersection points of polynomialsThat is what I was asking before. 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. #315 20130724 22:45:13#316 20130725 01:26:01
Re: Define the intersection points of polynomialsFor the first of the 4 quadratics: b0 = 3532013428986237192873119375732903841826161800807175630263233579248271193664082785199313240683451908515944502746 b1=410850838489261385759305566804597381684932406009429767177788799531275112939 b2 =11513183104216305498486345940371433157 b0 and b1 are obviously not members of GF(p). What do you want to do? 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. #317 20130725 02:07:11
Re: Define the intersection points of polynomialsOk. Now it is sure that the operations are not well defined. The elements that I gave you are in polynomial basis. Addition and Substraction on GF2^128 are the same operation and it is acomplished by xoring the elements. e.g. 0x78(XOR)0x5=0x7d. There is no way the result to be negative. Last edited by Herc11 (20130725 02:11:48) #318 20130725 02:16:07
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. #319 20130725 02:36:46#320 20130725 02:43:56
Re: Define the intersection points of polynomialsYes, they can solved over Reals. 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. #321 20130725 02:52:40#322 20130725 03:23:37
Re: Define the intersection points of polynomialsMay I ask what you plan to do with it? 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. #323 20130725 03:26:34#324 20130725 03:32:15
Re: Define the intersection points of polynomialsI have destroyed the code already and I am sorry but I am unable to recreate it. 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. #325 20130725 03:40:14 