Computer Algebra Algorithms*

INTRODUCTION ...................................................................................................................... 1 ARITHMETIC ........................................................................................................................... 2 Integer and Polynomial Addition, Multiplication, and Division with Remainder ............. 2 Integer and Polynomial Greatest Common Divisor ........................................................... 3 Floating Point Numbers and Power Series ........................................................................ 5 Matrix Arithmetic ............................................................................................................... 6 Arithmetic with Concisely Represented Expressions ......................................................... 7 SEMINAL PROBLEMS ............................................................................................................. 9 Factorization ...................................................................................................................... 9 Computing with Groups ..................................................................................................... 11 Integration in Closed Form ................................................................................................ 12 Solving Systems of Polynomial Equations ......................................................................... 14 Decision Methods for Elementary Algebra and Geometry ................................................ 16 LINKAGES ................................................................................................................................ 17 Parallel Algorithms ............................................................................................................ 17 Logic Programming and Simplification ............................................................................. 18 Language and System Design ............................................................................................ 18 Activities Outside Computer Algebra ................................................................................ 19 CONCLUSION .......................................................................................................................... 19 LITERATURE CITED ............................................................................................................... 21