2021-05-27 15:00:25 +0200 received badge ● Famous Question (source) 2019-01-26 03:32:54 +0200 received badge ● Notable Question (source) 2018-09-08 10:40:50 +0200 received badge ● Popular Question (source) 2018-09-02 19:11:39 +0200 received badge ● Nice Question (source) 2015-04-28 08:56:42 +0200 asked a question defining boolean variables in sage Hi Guys, By writing this: B. = BooleanPolynomialRing()  Not only a Boolean Polynomial Ring in 'a' and 'b' is defined, but 'a' and 'b' are also treated as boolean variables. However, if we write in this manner: B = BooleanPolynomialRing(names = ['a','b'])  We'll obtain a Boolean Polynomial Ring in 'a' and 'b', but we don't even get 'a' and 'b' as variables. Is there any way to resolve the issue in the second method, especially, if we have a boolean polynomial ring of >1000 variables? Thanks in advance! 2015-03-05 05:28:36 +0200 asked a question converting from direct representation to indirect representation for S-boxes Hi guys, let's we want to get the polynomial expression for a S-Box. sage: S = mq.SBox(7,6,0,4,2,5,1,3) sage: P = S.ring() We can get the indirect representation... sage: S.polynomials() [x0*x2 + x1 + y1 + 1, x0*x1 + x1 + x2 + y0 + y1 + y2 + 1, x0*y1 + x0 + x2 + y0 + y2, x0*y0 + x0*y2 + x1 + x2 + y0 + y1 + y2 + 1, x1*x2 + x0 + x1 + x2 + y2 + 1, x0*y0 + x1*y0 + x0 + x2 + y1 + y2, x0*y0 + x1*y1 + x1 + y1 + 1, x1*y2 + x1 + x2 + y0 + y1 + y2 + 1, x0*y0 + x2*y0 + x1 + x2 + y1 + 1, x2*y1 + x0 + y1 + y2, x2*y2 + x1 + y1 + 1, y0*y1 + x0 + x2 + y0 + y1 + y2, y0*y2 + x1 + x2 + y0 + y1 + 1, y1*y2 + x2 + y0]  or the direct representation sage: P. = PolynomialRing(GF(2),6,order='lex') sage: S.polynomials([x0,x1,x2],[y0,y1,y2], groebner=True) [y0 + x0*x1 + x0*x2 + x0 + x1*x2 + x1 + 1, y1 + x0*x2 + x1 + 1, y2 + x0 + x1*x2 + x1 + x2 + 1]  My question is, given the direct representation of the S-Box, can we retrieve the indirect representation for the S-Box? 2015-02-16 14:44:54 +0200 received badge ● Student (source) 2015-02-16 03:46:12 +0200 received badge ● Editor (source) 2015-02-16 03:45:32 +0200 asked a question simplifying expressions in GF(2) Hi guys, I know that for a variable $x$ in $GF(2)$, $x^2 = x$, and $2x=0$. How do I simplify a polynomial expression in $GF(2)$ in the Sage interface? For example, I should obtain $$(a+b+1)^2=a^2+b^2+1+2a+2b+2ab=a+b+1$$