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Intro to Computer Algebra, Spring 2013

MACM 401/701 and CMPT 881/MATH 819, Spring 2013

Office hours: Tuesdays and Wednesdays 10-11am

Content

  • (2) Algorithms for long integer multiplication and GCD computation.
  • (3) Unique factorization, Euclidean rings and polynomial rings.
  • (1) Pseudo division and polynomial GCD computation.
  • (1) Data structures for multivariate polynomials.
  • (1) Ring morphisms and the Chinese remainder theorem.
  • (2) Polynomial interpolation and the Fast Fourier Transform.
  • (2) A modular algorithm for polynomial GCD computation.
  • (3) The P-adic Newton iteration, Hensel's lemma and Hensel lifting.
  • (3) Polynomial factorization over finite fields and the integers.
  • (2) Resultants and algorithms for rational function integration.
  • (1) Representation and differentiation of formulae on a computer.
  • (3) The Risch decision procedure for elementary function integrals.

Textbook

Algorithms for Computer Algebra by Geddes, Czapor and Labahn

Maple

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.

MapleNotes.mws     MapleNotes.pdf

Handouts

January 7th: Course Information Sheet (.txt)


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