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Introduction

**Marc Moreno Maza****
University of Western Ontario
AM 475 / AM 563 and CS424 / CS556 - Winter 2007
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**Date:** January 7, 2008

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- Computer Algebra

- A First Session with AXIOM

- A First Session with MAPLE
- A Second Session with AXIOM
- 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?

- Asymptotically fast algorithms

- Acknowledgments
- Bibliography
- About this document ...

2008-01-07