Algebraic algorithms for computing the complex zeros of gaussian polynomials.
Algebraic algorithms for computing the complex zeros of gaussian polynomials.
The MACSYMA “big-floating-point” arithmetic system
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
LISP-based "big-float" system is not slow
ACM SIGSAM Bulletin
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With most FORTRAN implementations, each variable V in a user's program is characterized at compile time as V(B, M, N) to specify that V can store exactly only values of the form ±b1b2... bm x B±n, where the bj are B-digits, m ≤ M, and n ≤ N. One typical triple is (16, 6, 64). A system has been developed in which (108, 103, 108) is readily attainable, and M can be changed during execution. To achieve efficiency and portability, the implementation makes extensive use of the SAC-1 system developed by George Collins. This paper describes the routines comprising the system, and discusses a sample application, Theoretical and empirical computing times are also presented.