A true understanding of LDA requires an understanding of the "division algorithm" (DA) which is not to be confused with the LDA itself. A good discussion of the DA is given on page 35 of the book ...

Additionally, deterministic algorithms for root finding, based on adaptations of Graeffe transforms, have been refined to overcome previous limitations, ensuring reliable extraction of polynomial ...

Polynomial Long Division for the iPad is available in the iTunes store for $2.99. It's fantastic for helping kids (and grown-ups) practice polynomial manipulation and division.

The graph below shows the total number of publications each year in Algorithms for Polynomial Computation Over Finite Fields. References [1] Fast multivariate multi-point evaluation revisited .