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 (http://www.lncc.br/) http://juaninf.blogspot.com ---------------------------------------------------------------------
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