Introduction

**Marc Moreno Maza
University of Western Ontario
CS874b - Winter 2002**

*Date:* 6 June 2003

- Outline

- 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

- Implementing Computer Algebra: basic ideas
- Which mathematical types do we need to implement?
- How to encode the elements of these types?
- What are our requirements for the language?

- An introduction to the ALDOR language
- Motivations
- Characteristics of the ALDOR language
- First examples
- Names
- Abstraction and Application
- Variables and Constants
- Sequencing
- Dependent Types
- Domains
- Categories

- Implementing Computer Algebra with ALDOR

- Asymptotically fast algorithms

- Acknowledgments
- Bibliography
- About this document ...

2003-06-06