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Intro to Computer Algebra, Spring 2015

MACM 401, MATH 701 and MATH 819

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.
  • (2) The Chinese remainder theorem and polynomial interpolation.
  • (2) The Fast Fourier Transform and fast multiplication.
  • (2) A modular algorithm for polynomial GCD computation.
  • (3) The P-adic Newton iteration, Hensel's lemma and Hensel lifting.
  • (2) 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.
  • (4) 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 Maplesoft for a very good price at Maple 18 for Canadian Students for $99

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 8th: Course Information Sheet (.txt)


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