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MaplePrimes Activity

These are questions asked by gepo

Hi, all, After some computation, I got a huge polynomial: a00*x^123+a45*x^233+a02*x^123+a67*x^156+a47*x^67+.......(with more than 30,000 monomials). This generated polynomial has some features: 1: the degree of each monomial is not more than 256. 2:each monomial only has ONE coefficient. 3:There are two or more monomials have the same degree, so they can be combined together. Such as a00*x^123+a02*x^123=(a00+a02)*x^123. 4:for any coefficient a[ij], i is from 0 though 15, j is also from 0 through 15.
Hi,all, here is my question: alias(alpha=RootOf(x^32+x^26+x^19+x^15+x^13+x^11+x^9+x^8+x^4+x+1)); and then i want to compute: alpha^12345678987654321; But when I did it in maple, it failed. I think there should be some way to do it. Would you like to help me? Thanks Gepo
Hi, all, Is there a way to list some primitive polynomials for a given degree over galois field GF(2). For example, I want to get some primitive polynomials of GF(2^32), is there a way to do that? Thanks Gepo
Hi, all, Is there a way to extract all the variables in a list of polynomials? For example: L:=[2*a*b,x^2+y,d*y^2]; I want to get [a,b,x,y,d]. The order of variables does not matter. Thanks Gepo
Hi, all, I have known how to compute Groebner basis over galois field. For example, the following example is to compute Groebner basis over GF(2^3): alias(alpha=RootOf(Z^3+Z+1)); F := {alpha*x*y+alpha^2+1, alpha^2*x^2-1}; G := Groebner[Basis](F, plex(x,y), characteristic=2); But now I have a doubt. If I give one more "alias", is the Groebner basis still computed over GF(2^3)? For example: alias(alpha=RootOf(Z^3+Z+1)); alias(beta=RootOf(u^2+u+1)); F := {alpha*x*y+alpha^2+1, alpha^2*x^2-1,alpha^2*beta+x*y}; G := Groebner[Basis](F, plex(x,y), characteristic=2);
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