Prime Numbers

9.6 Polynomial arithmetic 513
where it is understood that xj = 0 for all j > D − 1. We also define a
polynomial index function as
ind(x, d) =min{j : j ≥ d; xj = 0},
or ind(x, d) = 0 if the stated set of j is empty.
For example,
rev(1 + 3t 2 +6t 3 +9t 5 + t 6 , 3) = 6 + 3t + t 3 ,
ind(1 + 3t 2 +6t 3 , 1) = 2.
A remaindering algorithm can now be given:
Algorithm 9.6.4 (Fast polynomial mod). Let x(t),y(t) be given polynomials
with y(t) monic (high coefficient is 1). This algorithm returns the polynomial
remainder x(t) mody(t).
1. [Initialize]
if(deg(y) ==0) return 0;
d =deg(x) − deg(y);
if(d