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Advanced Computer Algebra:
Introduction
Marc Moreno Maza
University of Western Ontario
CS874b - Winter 2002
Date:
6 June 2003
Outline
Course Description
Course Content
Class Schedule
Lecture Notes and Textbook
Student Evaluation
An introduction to Computer Algebra
Operations on rational numbers
Operations on real numbers
Operations on matrices
Operations on univariate polynomials
Algebraic systems
Conclusions
A review of complexity notions
Orders of magnitude
The complexity of divide-and-conquer algorithms
Implementing Computer Algebra: basic ideas
Which mathematical types do we need to implement?
How to encode the elements of these types?
Integers.
Rational numbers.
Modular Integers.
Real algebraic numbers.
Univariate polynomials.
Multivariate polynomials.
What are our requirements for the language?
Bounded genericity with dependent types
Inheritance
Post-facto extensions
Efficiency
An introduction to the A
LDOR
language
Motivations
Characteristics of the A
LDOR
language
First examples
Names
Abstraction and Application
Variables and Constants
Sequencing
Dependent Types
Domains
Categories
Implementing Computer Algebra with A
LDOR
Fundamental types
Algebraic types
Algebraic categories
Numbers
Univariate polynomials
Asymptotically fast algorithms
The Karatsuba trick
Experimentation
Acknowledgments
Bibliography
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Marc Moreno Maza
2003-06-06
