Normal Forms and Algebraic Representations

  • K. O. Geddes
  • S. R. Czapor
  • G. Labahn


This chapter is concerned with the computer representation of the algebraic objects discussed in Chapter 2. The zero equivalence problem is introduced and the important concepts of normal form and canonical form are defined. Various normal forms are presented for polynomials, rational functions, and power series. Finally data structures are considered for the representation of multiprecision integers, rational numbers, polynomials, rational functions, and power series.


Normal Form Power Series Canonical Function Form Level Multivariate Polynomial 
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  1. 1.
    W.S. Brown, “On Computing with Factored Rational Expressions,” ACM S1GSAM Bull., 8 pp. 26–34 (1974).CrossRefGoogle Scholar
  2. 2.
    B.F. Caviness, “On Canonical Forms and Simplification,” J. ACM, 2 pp. 385–396 (1970).CrossRefMathSciNetGoogle Scholar
  3. 3.
    B.W. Char, K.O. Geddes, G.H. Gonnet, B.L. Leong, M.B. Monagan, and S.M. Watt, Maple V Language Reference Manual, Springer-Verlag (1991).Google Scholar
  4. 4.
    A.C. Hearn, “Polynomial and Rational Function Representations,” Tech. Report UCP-29, Univ. of Utah (1974).Google Scholar
  5. 5.
    E. Horowitz and S. Sahni, Fundamentals of Computer Algorithms, Computer Science Press, Maryland (1978).zbMATHGoogle Scholar
  6. 6.
    A.D. Hall Jr., “The Altran System for Rational Function Manipulation — A Survey,” Comm. ACM, 14 pp. 517–521 (1971).CrossRefGoogle Scholar
  7. 7.
    J. Moses, “Algebraic Simplification: A Guide for the Perplexed,” Comm. ACM, 14 pp. 527–537 (1971).zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    A.C. Norman, “Computing with Formal Power Series,” ACM TOMS, 1 pp. 346–356 (1975).zbMATHCrossRefGoogle Scholar
  9. 9.
    D. Richardson, “Some Unsolvable Problems Involving Elementary Functions of a Real Variable,” J. Symbolic Logic, 33 pp. 511–520 (1968).Google Scholar

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • K. O. Geddes
    • 1
  • S. R. Czapor
    • 2
  • G. Labahn
    • 1
  1. 1.University of WaterlooCanada
  2. 2.Laurentian UniversityCanada

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