Thanks a lot Simon. All solved now.
On Mon, 3 Feb, 2020, 1:54 PM Simon King, wrote:
> Hi Samanta,
>
> On 2020-02-03, Samanta wrote:
> > I have defined the input variables in characteristic 2.
>
> No, you haven't, see below.
>
> > 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. = GF(2)[]
>
> Here, you define P as multivariate polynomial ring over the field
> GF(2), the four generators being x0, x1, x2, x3.
>
> > : x3=0
> > : x2=1
> > : x1=0
> > : x0=1
>
> Here, you override the previous definition and assign to x0,...,x3 some
> integers. The ring P still knows how its variables are called, but after
> the re-definition x0 does not belong to P any more.
>
> > Can anyone guide me how to get the output values in characteristic 2 if
> I
> > assign a value to the input?
>
> It is not totally clear to me what you want to do, so, I'm giving two
> different answers.
>
> 1. If you want four variables x0, x1, x2, x3 with values in GF(2),
> then you should simply define them as such:
> sage: x0 = GF(2)(1)
> sage: x1 = GF(2)(0)
> sage: x2 = GF(2)(1)
> sage: x3 = GF(2)(0)
> There is no need at all to define P in the first place.
>
> 2. If you want to symbolically work with polynomial expressions over
> GF(2) in indeterminates x0,...,x3, and want to eventually insert
> special values into the expressions, you could do the following:
> sage: P. = GF(2)[]
> sage: f = ((x0+x1)^2+(x2+x3)^2)^2
> sage: f
> x0^4 + x1^4 + x2^4 + x3^4
> sage: f(x0=1, x1=0, x2=1, x3=0)
> 0
>
> Best regards,
> Simon
>
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