# Lecture 11: Polynomial and Integer Multiplication using the FFT

### Background Material

- The material on interpolation and a modular algorithm for
polynomial multiplication from Lecture 9
and Lecture 10 on the FFT.
- Elements of Algebra and Algebraic Computing, John D. Lipson,
Benjamin Cummings Publishing Co., 1981.

### Reading

- Chapter 9 (pp. 293-308) of Lipson (handout, see above for reference).

### Topics

- Review of evaluation, pointwise product, interpolation algorithm
for polynomial multiplication.
- The inverse DFT.
- Computation of the FFT in Z_p.
- The primitive element theorem.
- The prime number theorem and Fourier primes.

- The three primes algorithm.

### Lecture Slides

- fast.ppt - power point slides containing
lecture notes on FFT-based polynomial and integer (3 primes)
multiplication.

### Maple worksheets and programs

- interp.mws - Worksheet containing an
implementation of the evaluate, pointwise product, interpolate
algorithm for polynomial multiplication.
- fft.mw - Worksheet containing an implementation
of a recursive FFT.

### Assignment

Created: Nov. 15, 2005 by jjohnson@cs.drexel.edu