The SAC-1 system: An introduction and survey

  • Authors:

  • George E. Collins

  • Affiliations:

  • -

  • Venue:
  • SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
  • Year:
  • 1971

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Abstract

SAC-1 is a program system for performing operations on multivariate polynomials and rational functions with infinite-precision coefficients. It is programmed, with the exception of a few simple primitives, in ASA Fortran. As a result the system is extremely accessible, portable, easy to learn, and indeed has been implemented at more than 20 institutions. The SAC-1 system's range of programmed capabilities is exceptionally broad, including, besides the usual operations, polynomial greatest common divisor and resultant calculation, polynomial factorization, exact polynomial real zero calculation, partial fraction decomposition, rational function integration, and solution of systems of linear equations with polynomial coefficients. SAC-1 is also outstanding in its computing time efficiency, which is achieved partially through the use of appropriate data structures, but primarily through the use of mathematically sophisticated and analyzed algorithms, which are briefly surveyed. The efficiency gains, frequently orders of magnitude, are such that many new applications are rendered feasible.