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Computer Algebra course, Spring 2005

Content

  • Euclidean domains, the Euclidean algorithm and applications.
  • Integer multiplication: Karatsuba's algorithm, the Fast Fourier Transform.
  • Integer GCD computation: the binary GCD algorithm and Lehmer's algorithm.
  • Representing and simplifying mathematical formulae on a computer.
  • Symbolic differentiation of a formula.
  • Data structures for polynomials.
  • Polynomial GCD computation: Brown's algorithm.
  • The P-adic Newton iteration and Hensel lifting.
  • Polynomial factorization over finite fields.
  • Polynomial factorization over the integers.
  • Algorithms for rational function integrats.
  • The Risch decision procedure for elementary function integrals.

Textbook

Algorithms for Computer Algebra by Geddes, Czapor and Labahn

Software

We will use Maple extensively for calculations and programming in this course. The university has a site license. Maple is installed on the PCs and MACs in the assignment lab, the CECM lab, university open labs and the library. Maple is available from the microcomputer store for about $200.

The following Maple worksheet (in Maple worksheet format (.mws) and Adobe PDF format (.pdf) contains notes for how to use Maple.

MWS format (.mws)
PDF format (.pdf)

Please read through this even if you have used Maple before.

Assignments (  .pdf format  )

 

Assignment 1

 

Assignment 2

 

Assignment 3

 

Assignment 4

 

Assignment 5

 

Assignment 6

 

Course Project

 

p. (778) 782-4279 · f. (778) 782-4947 · Shrum Science K 10501 · Department of Mathematics · 8888 University Drive · Burnaby · BC · V5A 1S6 · Canada