Section 5.2: Analysis

Congruence Class Arithmetic

This section is remarkably similar to Section 2.2. It deals with the developments of rings in F[x] and arithmetic of congruence classes in F[x] . The notation for these types of rings is different from what has previously been encountered: F[x](p(x)) where F is a field and p(x) a non constant polynomial in F[x] .

The ideas behind this section are relatively straightforward given that rings in \mathbb{Z} have already been studied. However arithmetic in this form may be more difficult. At least right now I fail to see how the ring \mathbb{Z}_2 [x] / (x^2+x+1) is composed of the elements \{ 0,\ 1,\ [x],\ [x+1]\} .

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