I found the solution. Many thanks for tonio
We are working in GF(2). Consider following polynomial:
Now multiply it by all monomials, that mean to get:
I know that but from where we have ? We should multiply by and then by . From this two new equations we have but how we could get it?
This is the second time you ask this question and this is the second time I don't understand what you mean: you call "A polynomial", which it is not since it is equalled to zero. It would then be an equality.
Next, you want this equality to be multiplied "by the monomials "....so you're working in the ring of polynomials in 4 indeterminates ?!
Anyway, you get 4 weird expressions that you call ...and I don't have the faintest idea from where did you get these expressions!. For example , multiplying the forementioned equality by the monomial we get:
....so ?? Of course , if you already know that no matter what VALUE in we choose for then you can EVALUATE and get ...both AS POLYNOMIALS this is not so!
I think you must first understand well what you want, then decide how to ask it in a clear way and then post again.
I agree with tonio.
These are equations not polynomials.
I think that this is some part of Yours previous post http://www.mathhelpforum.com/math-he...imination.html - 4 variables over GF(2).
So You consider equation and then You multiplied it by 4 monomials:
Am I right?
In last part You used word 'equations' - good!
PS. I knew that this problem/example I saw before. This is a toy example from http://math.uc.edu/~aac/pqcrypto2008...008mohamed.pdf