Thanks you to reply. The paper does not show the equations. --------------------------------------------------------------------- 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 ---------------------------------------------------------------------
El lun, 8 feb 2021 a las 15:26, Emmanuel Charpentier (< emanuel.charpent...@gmail.com>) escribió: > 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. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-support/6e9c9a52-00a4-4c82-8e2f-2866a4ff9dean%40googlegroups.com > <https://groups.google.com/d/msgid/sage-support/6e9c9a52-00a4-4c82-8e2f-2866a4ff9dean%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "sage-support" group. 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