Section 4.2
The residue class ring
R is a field. Let d be a polynomial in R[X]. In this section we describe how to add and multiply residue classes in R[X]/(d). We use addition and multiplication for the operations of taking sum and product, respectively.
The sum and product of the residue classes a + dR[X] and b + dR[X] in R[X]/(d) are defined as follows.
The multiplication point is often omitted.
In computations modulo a polynomial d it is helpful to consider this polynomial as being zero. This is allowed since d + (d) = 0 + (d).