This chapter discusses computation with real numbers. The rational number methods of computation can be adapted to the solution of all computational problems with irrational numbers in a manner that is satisfactory for practical purposes. For any irrational number, there can be found a rational ...
Modern computing has adopted the floating point type as a default way to describe computations with real numbers. Thanks to dedicated hardware support, such computations are efficient on modern architectures, even in double precision. However, rigorous reasoning about the resulting programs remains diffic...
Efficient Computation of Class Numbers of Real Abelian Number Fields Let Km be a parametrized family of real abelian number fields of known regulators, e.g. the simplest cubic fields associated with the Q-irreducible cubic polynomials Pm(x) = x3 − mx2 − (m + 3)x − 1. W St茅pha...
int---整数。 float---实数(real numbers)。 bool---Boolean values True and False. NoneType---special and has one value, None can usetype ()to see the type of an object. can convert object of one type to another float (3) converts integer 3 to float 3.0. int (3.9) truncates float...
Several issues arising in the Blum/Shub/Smale theory of computation for rings and fields are addressed.The original exposition (Blum/Shub/Smale, (BSS), 1989) asks how generally output and halting sets coincide in subrings and subfields of real numbers. Aspects of this question were subsequently...
problem solving that involves numbers or quantities computation词组 parallel computation平行计算;并行运算 analog computation模拟计算 manual computation笔算 computation module计算模型;计算组件 performance computation性能(特性)计算 check computation核算;校验计算 ...
In this paper we describe a new package for dealing with single-valued interval computation on real numbers. The package, developed by the authors in free ware program Maxima, version 5.23.2, allows the user to manipulate single-valued real and extended intervals and carry out the most typical...
Most mathematical formulae are defined in terms of operations on real numbers, but computers can only operate on numeric values with finite precision and range. Using floating-point values as real numbers does not clearly identify the precision with which each value must be represented. Too little...
A model of computation with access to ℝ is suggested that is more restricted than, say fapC(ℝ) in [10]. In particular ℝ is treated as an accessory to the computer rather than an internal component. This has the desirable properties of a definabi
Harrison, J.: Theorem proving with the real numbers. CPHC/BCS distinguished dissertations, Springer (1998) 21. Harrison, J.: HOL Light: An overview. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) Theorem Proving in Higher Order Logics. Lecture Notes in Com- puter ...