Univariate power series expansions in REDUCE

ABSTRACT

We describe the development of a formal power series expansion package for Reduce which takes advantage of Reduce's domain mechanism to make for a seamless integration of series values with the rest of the Reduce system. Consequently, series values may be manipulated with the same algebraic operators as other algebraic objects. To create the illusion of infinite power series a simulated lazy-evaluation mechanism has been used. This paper reports our experience of using the Reduce domain mechanism and documents the algorithms and data structures that can be used to implement and to represent power series.

REFERENCES

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.3 Languages and Systems

          Nouns: REDUCE

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.3 Languages and Systems

          Nouns: MACSYMA

General Terms:
Algorithms, Languages