gepo

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These are questions asked by gepo

Hi, all, I have a question about how to evaluate result of expression containing ROOTOF. for example: >alias(x = RootOf(Z^3+Z+1)) >A := a[2]*x^2+a[1]*x+1 >B := b[2]*x^2+b[1]*x+1 >M1 := A*B; >expand(M1); a[2]*x^4*b[2]+a[2]*x^3*b[1]+a[2]*x^2+a[1]*x^3*b[2]+a[1]*x^2*b[1]+a[1]*x+b[2]*x^2+b[1]*x+1 >evala(expand(M1)); x^2*(1+b[2]-b[1]+a[2]*b[1]*x+a[2]*b[2]*x^2+a[1]*b[2]*x+a[1]*b[1]+a[2]-a[1]-a[1]*x^2-x^2*b[1]-x+x^2) I have questions about expand(M1) and evala(expand(M1)). >expand(M1); a[2]*x^4*b[2]+a[2]*x^3*b[1]+a[2]*x^2+a[1]*x^3*b[2]+a[1]*x^2*b[1]+a[1]*x+b[2]*x^2+b[1]*x+1
Hi, all, I have a question, how to expand a multivariate polynomial, like this: F := [1-(x[1]-1)^2]*[1-(x[3]-1)^2]+[1-(x[1]-1)^2]*[1-(x[2]-2)^2]+(2*[1-(x[1]-1)^2])*[1-(x[2]-2)^2]*[1-(x[3]-1)^2] when I used expand(F); the result is the same as F itself, nothing changed. Whether there is some way to expand the multivariate polynomial into a completely expanded form, like: 2*x*y^2*z^2+2*x*y^2*z+x*y*z^2+x*y*z+x^2*z^2+x^2*z+x*z^2+x*z+x^2*y^2+2*x^2*y+x*y^2+2*x*y thanks.

For a given galois field, suppose there is such a polynomial function mapping from GF(q) to GF(q):
x^(q+m)+x^(q+m-1)+x^(q+m-2)+...+x^(1).
I can use x^q-x=0 to "reduce" it to such the following form:
x^(q-1)+x^(q-2)+x^(q-3)+...+x^(1)

now, the problem is whether this is the only method (x^q-x=0) to reduce a polynomial function mapping from GF(q) to GF(q)?

Thanks a lot.

Hi, all, I know there is a polynomial function from GF(2^m) to itself, but whether there is a mapping from GF(2^m) to GF(2^n)? thank you

When implementing the Groebner Basis over Galois Field(2^m), I found an interesting thing: to represent and compute over GF, you have to map first.

 for example

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