Homework 7

Due: Tuesday, November 11, 1997
 
Problem 1.  Compute by hand  gcd( g(x), h(x) )  over  GF(2)[x]  , where
                        g(x) = x12+x9+x8+x6+x4+x+1

and

                        h(x) = x11+x10+x6+x5+x4+x3+1.

Then compute with MAPLE  gcd( g(x), h(x) )  over  Q[x] , where  Q 
denotes the field of rational numbers.


Problem 2.  Compute the addition and multiplication tables for the ring

                                R3 = GF(2)[x]/(x3+1)

Also express each of the following ideals in the ring  R3 as a set of elements of R3 .

                        (0),  (1+x), (x2+x+1), (1), (x2+1), (x3+1), (x5+x+1).

For example,

                        (0) = { 0 }   and   ( x4 + x2 +1 ) = { 0, x2 + x+1 }

Last Modified: 6:22pm, November 6, 1997