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Computer Algebra course, Spring 2007

Content

  • Algorithms for long integer multiplication and GCD computation.
  • Mathematical properties of Euclidean rings and polynomial rings.
  • Representing and simplifying mathematical formulae on a computer.
  • Symbolic differentiation of a formula.
  • Data structures for multivariate polynomials.
  • Pseudo division and polynomial GCD computation.
  • A modular algorithm for polynomial GCD computation.
  • The Fast Fourier Transform (FFT) and fast polynomial multiplication.
  • The P-adic Newton iteration and Hensel lifting.
  • Polynomial factorization over finite fields and over the integers.
  • Algorithms for rational function integration.
  • 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. Please read through this even if you have used Maple before.

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

Course Project ( .pdf format )

 

Assignments (  .pdf format  )

Solutions (  .mws format  )

 

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