A preview of the next IBM-PC version of muMATH
Rational arithmetic can be either exact or automatically rounded to any precision, thus providing a unified alternative to the usual combination of exact rational plus arbitrary-precision floating-point arithmetic.
There is function plot graphics.
Two-dimensional output of expressions is provided, including raised exponents and built-up fractions.
The algebraic capabilities are substantially improved:
Simplification is more automatic and thorough, with options that are easier to use.
The default normal form tends to preserve factors at all levels while automatically achieving significant simplification of rational expressions, radicals and elementary transcendental expressions.
There are polynomial expansion, gcd and factoring algorithms with speeds that compare favorably with those of systems running on mainframes or Lisp machines.
KeywordsPartial Factorization Greatest Common Divisor Rational Arithmetic Implicit Operator Infinite Precision
Unable to display preview. Download preview PDF.
- Barton, D. and Fitch, J.P. : "Application of Algebraic Manipulation Programs in Physics", Reports on Progress in Physics 35, pp. 235ff.Google Scholar
- Bourne, S.R. : ACM SIGSAM Bulletin 24, pp. 8–11.Google Scholar
- Brown, W.S. : "On Computing with Factored Rational Expressions", ACM SIGSAM Bulletin 31, August, pp. 26–34.Google Scholar
- Campbell, J.A. : "Problem 2 — The Y2n Functions, ACM SIGSAM Bulletin 22, pp. 8–9.Google Scholar
- Fateman, R.J. : "The MACSYMA ‘Big-Floating-Point’ Arithmetic System", Proceedings of the 1976 ACM Symposium on Symbolic and Algebraic Computation, editor R.D. Jenks, pp. 209–213.Google Scholar
- Hall, A.D. : "Factored Rational Expressions in ALTRAN", ACM SIGSAM Bulletion 31, August, pp. 35–45.Google Scholar
- Matula, D.W. and Kornerup, P. : "Finite Precision Rational Arithmetic: Slash Number Systems", IEEE Transactions on Computers C-34, No. 1, January 1985, pp. 3–18.Google Scholar
- Muir, S.T. : A Treatise on the Theory of Determinants, Dover Press, N.Y.Google Scholar
- Sasaki, T. : "An Arbitrary Precision Real Arithmetic Package in REDUCE", in Symbolic & Algebraic Computation, Lecture Notes in Computer Science # 72, editor E.W. Ng, Springer Verlag, Berlin. pp. 358–368.Google Scholar
- Stoutemyer, D.R. [1984a]: "Which Polynomial Representation is Best?", Proceedings of the 1984 MACSYMA Users' Conference, editor E. Golden, General Electric, Schenectady, N.Y. USA, pp. 221–243.Google Scholar
- Stoutemyer, D.R. [1984b]: "Polynomial Remainder Sequence Greatest Common Divisors Revisited", proceedings of RSYMSAC, The Second International Symposium on Symbolic and Algebraic Computation by Computers, RIKEN Institute of Physical and Chemical Research, Wako-shi, Saitama, 351–01 Japan, pp. 1–1 through 1–12.Google Scholar
- Wang, P.S. : "An Improved Multivariable Polynomial Factorising Algorithm", Math. Comp. 32, pp. 1215–1231.Google Scholar
- Wang, P.S. : "Matrix Computations in MACSYMA", Proceedings of the 1977 MACSYMA User's Conference, NASA CP 2012, pp. 435–446.Google Scholar
- Zippel, R. : "Probabilistic Algorithms for Sparse Polynomials", Symbolic & Algebraic Computation, editor E.W. Ng, Lecture Notes in Computer Science 72, Springer-Verlag, pp. 227–239.Google Scholar