Dear members of support, I think I managed to solve this question. That is after apply an algorithm I found the same quantity of inequalities the authors claims -- 13 inequalities. But now, I would like to know if any one of you see any relation between the autoher inequalities and sage inequalities
These are the sage inequalities An inequality (1, 0, -1, 0, 0, 0, 1) x + 0 >= 0 An inequality (0, -1, 1, 0, 0, 0, 1) x + 0 >= 0 An inequality (-1, 1, 0, 0, 0, 0, 1) x + 0 >= 0 An inequality (-1, -1, -1, 0, 0, 0, -1) x + 3 >= 0 An inequality (1, 1, 1, 0, 0, 0, -1) x + 0 >= 0 An inequality (1, 1, 1, -3, -3, -3, 2) x + 6 >= 0 An inequality (-1, -1, -1, 3, -3, -3, 2) x + 6 >= 0 An inequality (-1, -1, -1, -3, 3, -3, 2) x + 6 >= 0 An inequality (-1, -1, -1, -3, -3, 3, 2) x + 6 >= 0 An inequality (1, 1, 1, 3, 3, -3, 2) x + 0 >= 0 An inequality (1, 1, 1, 3, -3, 3, 2) x + 0 >= 0 An inequality (1, 1, 1, -3, 3, 3, 2) x + 0 >= 0 An inequality (0, 0, -1, 1, 1, 1, 1) x + 0 >= 0 And those are the authors inequalities β[i]−γ[i] + (¬eq(α[i],β[i], γ[i])) ≥ 0, α[i]−β[i] + (¬eq(α[i],β[i], γ[i])) ≥ 0, −α[i] +γ[i] + (¬eq(α[i],β[i], γ[i])) ≥ 0, −α[i]−β[i]−γ[i]−(¬eq(α[i],β[i], γ[i])) ≥ −3, α[i] +β[i] +γ[i]−(¬eq(α[i],β[i], γ[i])) ≥ 0, −β[i] +α[i+1] +β[i+1] +γ[i+1] + (¬eq(α[i],β[i], γ[i])) ≥ 0, β[i] +α[i+1]−β[i+1] +γ[i+1] + (¬eq(α[i],β[i], γ[i])) ≥ 0, β[i]−α[i+1] +β[i+1] +γ[i+1] + (¬eq(α[i],β[i], γ[i])) ≥ 0, α[i] +α[i+1] +β[i+1]−γ[i+1] + (¬eq(α[i],β[i], γ[i])) ≥ 0, γ[i]−α[i+1]−β[i+1]−γ[i+1] + (¬eq(α[i],β[i], γ[i])) ≥ −2, −β[i] +α[i+1]−β[i+1]−γ[i+1] + (¬eq(α[i],β[i], γ[i])) ≥ −2, −β[i]−α[i+1] +β[i+1]−γ[i+1] + (¬eq(α[i],β[i], γ[i])) ≥ −2, −β[i]−α[i+1]−β[i+1] +γ[i+1] + (¬eq(α[i],β[i], γ[i])) ≥ −2 The vertices has the following form (α[i], β[i], γ[i], α[i+1], β[i+1], γ[i+1], (¬eq(α[i],β[i], γ[i])) --------------------------------------------------------------------- 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 15:35, Juan Grados (<juan...@gmail.com>) escribió: > 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. 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/CABhJSpnmyLp%2B-NELfgQxXR9a0xjUOmY-kDPSPZvPu2kDFknVKw%40mail.gmail.com.
