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You are not logged in. #251 20130723 03:33:22#252 20130723 03:41:50
Re: Define the intersection points of polynomialsHere is another one: We get x = 5, which corresponds to solving that equation over GF(19) 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. #253 20130723 03:43:10#254 20130723 03:43:59
Re: Define the intersection points of polynomialsI changed post #252, so please check again. 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. #255 20130723 03:47:31#256 20130723 03:57:35
Re: Define the intersection points of polynomialsOkay, then for the sake of argument because we have nothing else to go on let's assume Mathematica can solve your equations over the GF you want. This is a pragmatic decision, if we assume it can not we are done right here. Let's proceed with the assumption and see what the heck happens. 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. #257 20130723 03:58:14#258 20130723 04:00:18
Re: Define the intersection points of polynomialsNow, I can continue to ask the remaining questions. 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. #259 20130723 04:02:15#260 20130723 04:05:56
Re: Define the intersection points of polynomialsThis is what we agree on:
A Gf(113) will be used. 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. #261 20130723 04:09:23#262 20130723 04:11:13
Re: Define the intersection points of polynomialsI understand the problem well enough to work on it. I am currently a little busy with 4 other problems and will start modifying the cubic code that I used to solve the other problems. This will take some time. 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. #263 20130723 04:16:55#264 20130723 05:51:51
Re: Define the intersection points of polynomialsSo far I have found it very difficult to even construct 4 quadratics and 2 points of intersection all of them over Z let alone 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. #265 20130723 05:53:11#266 20130723 05:55:39
Re: Define the intersection points of polynomialsIt is a little early to say. But it does suggest they are rare. That means that getting an answer to them in the required form is very rare. 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. #267 20130723 05:57:25#268 20130723 06:03:07
Re: Define the intersection points of polynomialsYou can use Newton Interpolation i.e the formulas for a that I have posted eralier to compute the polynomials. #269 20130723 06:09:53
Re: Define the intersection points of polynomialsI can do all that. The trouble is the answers are not coming back as integers let alone 1  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. #270 20130723 06:14:08#271 20130723 06:24:11
Re: Define the intersection points of polynomialsI think I have a method now that is working to generate the problems. I will go back to work on the solutions. 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. #272 20130723 19:16:29
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. #273 20130723 20:01:24#274 20130723 20:10:52
Re: Define the intersection points of polynomialsThat will be a problem when I get to that. 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. #275 20130723 20:14:30
Re: Define the intersection points of polynomialsThe choice of same x's would a problem if wou were solving the problem over real numbers? Last edited by Herc11 (20130723 20:19:53) 