Are those 65 inequalities independent ? For example ``` x+y<5 x+y<3 ```
are distinct, but only the second defines the solution : the first is implied by the second... Could you check the independence of the 65 inequalities in the paper ? For example, you may try to solve the system of 65 inequalities of the paper, and see if (a newer version of) sage is able to reduce it. HTH, Le dimanche 7 février 2021 à 19:51:46 UTC+1, juaninf a écrit : > Yes, but according to that paper it will be 65, and not 37. The paper is > from 2016, maybe with an older SAGE version I get 65?. I tried version 7 > and also I obtained 37. > > --------------------------------------------------------------------- > D.Sc. Juan del Carmen Grados Vásquez > Laboratório Nacional de Computação Científica > Tel: +55 21 97633 3228 <+55%2021%2097633-3228> > (http://www.lncc.br/) > http://juaninf.blogspot.com > --------------------------------------------------------------------- > > El dom, 7 feb 2021 a las 22:43, Vincent Delecroix (<20100.d...@gmail.com>) > escribió: > >> Note that these are 37 inequalities and not 65. >> >> Le 07/02/2021 à 19:41, Vincent Delecroix a écrit : >> > Dear Juan, >> > >> > With sage 9.2 I obtain very quickly the output >> > >> > An inequality (-1, -1, -1, 0, 0, 0, 1) x + 2 >= 0 >> > An inequality (0, -1, 0, 0, 0, 0, 0) x + 1 >= 0 >> > An inequality (-1, 0, 0, 0, 0, 0, 0) x + 1 >= 0 >> > An inequality (0, 0, -1, 0, 0, 0, 0) x + 1 >= 0 >> > An inequality (-1, 1, 0, 0, 0, 0, -1) x + 1 >= 0 >> > An inequality (-1, 0, 1, 0, 0, 0, -1) x + 1 >= 0 >> > An inequality (0, -1, 1, 0, 0, 0, -1) x + 1 >= 0 >> > An inequality (0, 1, -1, 0, 0, 0, -1) x + 1 >= 0 >> > An inequality (1, -1, 0, 0, 0, 0, -1) x + 1 >= 0 >> > An inequality (1, 0, -1, 0, 0, 0, -1) x + 1 >= 0 >> > An inequality (1, 1, 1, -3, 0, 0, -2) x + 2 >= 0 >> > An inequality (0, 0, 1, -1, 0, 0, -1) x + 1 >= 0 >> > An inequality (1, 0, 0, -1, 0, 0, -1) x + 1 >= 0 >> > An inequality (0, 0, 0, -1, 0, 0, 0) x + 1 >= 0 >> > An inequality (0, 1, 0, -1, 0, 0, -1) x + 1 >= 0 >> > An inequality (0, 0, 0, 0, -1, 0, 0) x + 1 >= 0 >> > An inequality (0, 0, 0, 0, 0, -1, 0) x + 1 >= 0 >> > An inequality (0, 0, -1, 1, -1, 0, -1) x + 2 >= 0 >> > An inequality (-1, 0, 0, 1, -1, 0, -1) x + 2 >= 0 >> > An inequality (0, -1, 0, 1, -1, 0, -1) x + 2 >= 0 >> > An inequality (-1, -1, -1, 3, -3, 0, -2) x + 5 >= 0 >> > An inequality (1, 1, 1, 0, 0, 0, 1) x - 1 >= 0 >> > An inequality (0, 0, 1, 0, 0, 0, 0) x + 0 >= 0 >> > An inequality (0, 0, 0, 1, 0, 0, 0) x + 0 >= 0 >> > An inequality (0, 0, 1, 0, 1, -1, -1) x + 1 >= 0 >> > An inequality (0, 1, 0, 0, 1, -1, -1) x + 1 >= 0 >> > An inequality (1, 1, 1, 0, 3, -3, -2) x + 2 >= 0 >> > An inequality (-1, -1, -1, 3, 0, 3, -2) x + 2 >= 0 >> > An inequality (0, 1, 0, 0, 0, 0, 0) x + 0 >= 0 >> > An inequality (1, 0, 0, 0, 1, -1, -1) x + 1 >= 0 >> > An inequality (0, 0, 0, 0, 0, 0, 1) x + 0 >= 0 >> > An inequality (1, 0, 0, 0, 0, 0, 0) x + 0 >= 0 >> > An inequality (0, 0, 0, 0, 1, 0, 0) x + 0 >= 0 >> > An inequality (0, 0, 0, 0, 0, 1, 0) x + 0 >= 0 >> > An inequality (0, -1, 0, 1, 0, 1, -1) x + 1 >= 0 >> > An inequality (-1, 0, 0, 1, 0, 1, -1) x + 1 >= 0 >> > An inequality (0, 0, -1, 1, 0, 1, -1) x + 1 >= 0 >> > >> > You should describe more precisely what is the problem with your >> > version 9. What is not working with the code? >> > >> > Best regards, >> > Vincent >> > >> > Le 07/02/2021 à 19:34, Juan Grados a écrit : >> >> Dear members, >> >> I am trying to reproduce page 9 of >> >> https://eprint.iacr.org/2016/407.pdf but >> >> until now is not possible to find the 65 inequalities that paper says. >> >> I am >> >> thinking that maybe this is because the version of SAGE I am using >> >> (this is >> >> 9). Do you think that there is any chance to obtain 65 inequalities >> >> using P.Hrepresentation() in other version of SAGE? >> >> >> >> from sage.all import * >> >> vertices = [i for i in range(2**6)] >> >> vertices_to_drop = [] >> >> def eq(x, y, z): >> >> if (x == y and y == z): >> >> return 1 >> >> return 0 >> >> for j in range(2**6): >> >> if ((((j>>5)&1) == ((j>>4)&1) and ((j>>4)&1) == ((j>>3)&1)) and >> >> (((j>>3)&1) != (((j>>2)&1) ^ ((j>>1)&1) ^ ((j>>0)&1)))): >> >> vertices_to_drop.append(j); >> >> possible_patterns = list(set(vertices) - set(vertices_to_drop)) >> >> print(possible_patterns) >> >> possible_patterns_vector = [] >> >> for num in possible_patterns: >> >> possible_patterns_vector.append([int(n) for n in >> >> bin(num)[2:].zfill(6)] + [eq(((num>>5)&1), ((num>>4)&1), ((num>>3)&1)) >> >> ^ 1]) >> >> print(possible_patterns_vector[0]) >> >> print(possible_patterns_vector[1]) >> >> P = Polyhedron(vertices = possible_patterns_vector) >> >> for h in P.Hrepresentation(): >> >> print(h) >> >> >> >> >> >> >> >> >> >> --------------------------------------------------------------------- >> >> D.Sc. Juan del Carmen Grados Vásquez >> >> Laboratório Nacional de Computação Científica >> >> Tel: +55 21 97633 3228 <+55%2021%2097633-3228> >> >> (http://www.lncc.br/) >> >> http://juaninf.blogspot.com >> >> --------------------------------------------------------------------- >> >> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sage-support" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to sage-support...@googlegroups.com. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sage-support/a5e68912-24fb-b598-1311-04350e2251a6%40gmail.com >> . >> > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. 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