On Wednesday, October 1, 2014 3:30:16 PM UTC-7, Kim Schoener wrote:
>
> Hi Peter, hi Martin,
>
> somehow both approaches I think don't work for me. For example, the square 
> (m1^2) is carried in both approaches, even though it can be simplified to 
> m1 in GF(2). I would like sage to account for the GF(2) in order to 
> simplify terms. For example I would expect that x * (x + 1) is simplified 
> to 0 if x is a variable in GF(2).
>

It means that you want to work modulo the ideal 
(m1^2-m1,m2^2-m2,m3^2-m3,m4^2-m4). You can use

sage: P.<m1,m2,m3,m4>=BooleanPolynomialRing()
sage: m1^2+m1
0
sage: q=matrix(2,2,[m1,m2,m3,m4])
sage: q^2
[   m1 + m2*m3 m1*m2 + m2*m4]
[m1*m3 + m3*m4    m2*m3 + m4]

 

> Is there a way to do this or does sage lack that funcitonality?
>
> Thank you,
> Kim
>

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