Show that { a + bX + cX^2 | a,b,c in Z2 and X^3 = 1 + X } is a field and calculate inverses of X, X^2 and 1+X.

Simple.

i96 : describe(R) ZZ -- [X] 2 o96 = ---------- 3 X + X + 1 i97 : ( (X)_R )^-1 2 o97 = X + 1 o97 : R i98 : ( (X^2) )^-1 2 o98 = X + X + 1 o98 : R i99 : ( (1+X)_R )^-1 2 o99 = X + X o99 : R

It would be cool to be able to do something like asList(R) where Macaulay2 should reply with 0, 1, 1+X, 1+X^2, etc.

For now I'll do it like this.

i136 : i=0; while i < 7 list (R_0)^i do i = i+1 2 2 2 2 o137 = {1, X, X , X + 1, X + X, X + X + 1, X + 1} o137 : List

## No comments:

## Post a Comment