The command sage: P.<x0,x1,x2,x3> = GF(2)[]
is *not* declaring variables x0, x1, etc to be elements in GF(2) but rather *assigns* x0, x1, etc to be generators of a poynomial algebra. sage: P.<x0,x1,x2,x3> = GF(2)[] sage: (x0 * x1 + x3 + 1)^2 x0^2*x1^2 + x3^2 + 1 If you want to use elements of GF(2) simply do sage: K = GF(2) sage: x3 = K(0) sage: x2 = K(1) sage: x1 = K(0) sage: x0 = K(1) Then sage: s1= x0*x2*x3 + x0*x2 + x0 + x1*x2 + x2 sage: s0= x0*x1*x3 + x0*x2 + x0*x3 + x1 + 1 sage: print(s1,s0) 1 0 Vincent PS: the command sage: x3 = 0 assigns x3 the number 0 (which is an integer). There is no such thing as "typing a variable" in Python. You can do sage: x3 = 0 # defines x3 as an integer sage: x3 = [0, 1, 3] # redefines x3 as a list sage: x3 = "hello" # redefines x3 as a string Le 03/02/2020 à 08:31, Samanta a écrit :
I have defined the input variables in characteristic 2. But when I assign a particular value to the input, output gives the result in simple algebra not in characteristic 2. Here is my code: sage: P.<x0,x1,x2,x3> = GF(2)[] ....: x3=0 ....: x2=1 ....: x1=0 ....: x0=1 ....: s1= x0*x2*x3 + x0*x2 + x0 + x1*x2 + x2 ....: s0= x0*x1*x3 + x0*x2 + x0*x3 + x1 + 1 ....: print s1,s0 ....: 3 2 Here I want s1, s0 as 1,0. If I don't assign any value to the input, the output will gives value in charateristic 2 like sage: P.<x0,x1,x2,x3> = GF(2)[] ....: print x0+x1+x0 ....: x1 Can anyone guide me how to get the output values in characteristic 2 if I assign a value to the input? Thanks in advance
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