Enlarging the REDUCE domain of computation

ABSTRACT

We describe the methods available in the current REDUCE system for introducing new mathematical domains, and illustrate these by discussing several new domains that significantly increase the power of the overall system.

REFERENCES

• Abbott, 1986: J. A. Abbott , R. J. Bradford , J. H. Davenport, The Bath algebraic number package, Proceedings of the fifth ACM symposium on Symbolic and algebraic computation, p.250-253, July 21-23, 1986, Waterloo, Ontario, Canada [doi>10.1145/32439.32490]
• Davenport, 1981: Davenport,J.H., On the Integration of Algebraic Functions, Lecture Notes in Computer Science 102, Springer, 1981.
• Feldmar, 1986: Feldmar,E., & K51big,K.S., REDUCE Procedures for the Manipulation of Generalized Power Series, Comp. Phys. Comm 39 (I 986) pp 267-284.
• Foderaro, 1983: John Keith Foderaro, The design of a language for algebraic computation systems, 1983
• Gebauer, 1986: Gebauer, R., & MSller,H.M., A Fast Variant of Buchberger's Algorithm, submitted to Joum. Symb. Comp.
• Griss, 1976: Martin L. Griss, The definition and use of data structures in REDUCE, Proceedings of the third ACM symposium on Symbolic and algebraic computation, p.53-59, August 10-12, 1976, Yorktown Heights, New York, United States [doi>10.1145/800205.806323]
• Harrington, 1978: Harrington,S., Infinite Power Series, Uuiversity of Utah, Dept. of Computer Science, Report UCP-62.
• Hearn, 1974: Hearn,A.C., A Mode Analyzing Algebraic Manipulation Program, Proe. ACM '74, ACM, New York, 1974, pp 722-724.
• Hearn, 1977: Hearn,A.C., The Structure of Algebraic Computations, Proc. Fourth Coll. on Adv. Comp. Meth. in Theor. Physics, St. Maximin, France, 1977, pp 1-15.
• Jenks, 1984: Richard D. Jenks, A Primer: 11 Keys to New Scratchpad, Proceedings of the International Symposium on Symbolic and Algebraic Computation, p.123-147, July 09-11, 1984
• Matula & Kornerup, 1985: Matula,D.W., & Komerup,P., Finite Precision Rational Arithmetic: Slash Number Systems, IEEE Transactions on Computers C-34, Vol. i, No. 1, January, 1985, pp 3-18.
• Norman, 1975: A. C. Norman, Computing with Formal Power Series, ACM Transactions on Mathematical Software (TOMS), v.1 n.4, p.346-356, Dec. 1975 [doi>10.1145/355656.355660]
• Sasaki, 1979: Tateaki Sasaki, An arbitrary precision real arithmetic package in REDUCE, Proceedings of the International Symposiumon on Symbolic and Algebraic Computation, p.358-368, June 01, 1979
• Trager, 1976: Barry M. Trager, Algebraic factoring and rational function integration, Proceedings of the third ACM symposium on Symbolic and algebraic computation, p.219-226, August 10-12, 1976, Yorktown Heights, New York, United States [doi>10.1145/800205.806338]
• Zippel, 1976: Richard E. Zippel, Univariate power series expansions in algebraic manipulation, Proceedings of the third ACM symposium on Symbolic and algebraic computation, p.198-208, August 10-12, 1976, Yorktown Heights, New York, United States [doi>10.1145/800205.806335]

INDEX TERMS

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

          Nouns: REDUCE

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Computations on discrete structures

  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms
          Subjects: Algebraic algorithms

General Terms:
Algorithms, Languages, Theory