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Computer Algebra course, Spring 2009

Content

  • (2) Algorithms for long integer multiplication and GCD computation.
  • (2) Mathematical properties of Euclidean rings and polynomial rings.
  • (2) Pseudo division and polynomial GCD computation.
  • (1) Representing and simplifying mathematical formulae on a computer.
  • (1) Data structures for multivariate polynomials.
  • (2) Ring morphisms and the Chinese remainder theorem.
  • (1) The Fast Fourier Transform (FFT).
  • (2) A modular algorithm for polynomial GCD computation.
  • (2) The P-adic Newton iteration.
  • (1) Hensel's lemma and linear Hensel lifting.
  • (2) Polynomial factorization over finite fields and the integers.
  • (2) Algorithms for rational function integration.
  • (3) 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. Much of the course is about how Maple works. SFU has a site license for Maple. 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. Please read through this even if you have used Maple before.

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

Assignments (  .pdf format  )

 

 

 

 

 

 

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