scholarly journals Comparing Implementations of a Calculator for Exact Real Number Computation

2009 ◽  
Author(s):  
J. Raymundo Marcial-Romero ◽  
J. A. Hernández ◽  
Héctor A. Montes-Venegas
Keyword(s):  
Real Number ◽  
Exact Real Number Computation

scholarly journals A Scientific Calculator for Exact Real Number Computation Based on LRT, GMP and FC++

2012 ◽  
Vol 22 ◽  
pp. 35-41
Author(s):  
Alejandra Lucatero ◽  
J. Raymundo Marcial-Romero ◽  
J. A. Hernández
Keyword(s):  
Real Number ◽  
Programming Language ◽  
Functional Programming ◽  
Operational Semantics ◽  
Trigonometric Functions ◽  
Lazy Evaluation ◽  
Evaluation Mechanism ◽  
The One ◽  
Exact Real Number Computation ◽  
Scientific Calculator

Language for Redundant Test (LRT) is a programming language for exact real number computation. Its lazy evaluation mechanism (also called call-by-need) and its infinite list requirement, make the language appropriate to be implemented in a functional programming language such as Haskell. However, a direction translation of the operational semantics of LRT into Haskell as well as the algorithms to implement basic operations (addition subtraction, multiplication, division) and trigonometric functions (sin, cosine, tangent, etc.) makes the resulting scientific calculator time consuming and so inefficient. In this paper, we present an alternative implementation of the scientific calculator using FC++ and GMP. FC++ is a functional C++ library while GMP is a GNU multiple presicion library. We show that a direct translation of LRT in FC++ results in a faster scientific calculator than the one presented in Haskell.

scholarly journals Coinduction for Exact Real Number Computation

2007 ◽  
Vol 43 (3-4) ◽  
pp. 394-409 ◽  
Author(s):  
Ulrich Berger ◽  
Tie Hou
Keyword(s):  
Real Number ◽  
Exact Real Number Computation

scholarly journals Semantics of a sequential language for exact real-number computation

2007 ◽  
Vol 379 (1-2) ◽  
pp. 120-141 ◽  
Author(s):  
J. Raymundo Marcial-Romero ◽  
Martín H. Escardó
Keyword(s):  
Real Number ◽  
Exact Real Number Computation

Real number arithmetic for mixed behavioural and structural descriptions

1990 ◽  
Vol 137 (6) ◽  
pp. 446
Author(s):  
M.G. Hill ◽  
N.E. Peeling ◽  
I.F. Currie ◽  
J.D. Morison ◽  
E.V. Whiting ◽  
...  
Keyword(s):  
Real Number ◽  
Structural Descriptions

scholarly journals Mathematical Properties of Variable Topological Indices

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 43
Author(s):  
José M. Sigarreta
Keyword(s):  
Real Number ◽  
Large Class ◽  
Symmetric Functions ◽  
Topological Indices ◽  
Current Interest ◽  
Zagreb Indices ◽  
Mathematical Properties ◽  
Connectivity Indices ◽  
Optimal Bounds ◽  
New Framework

A topic of current interest in the study of topological indices is to find relations between some index and one or several relevant parameters and/or other indices. In this paper we study two general topological indices Aα and Bα, defined for each graph H=(V(H),E(H)) by Aα(H)=∑ij∈E(H)f(di,dj)α and Bα(H)=∑i∈V(H)h(di)α, where di denotes the degree of the vertex i and α is any real number. Many important topological indices can be obtained from Aα and Bα by choosing appropriate symmetric functions and values of α. This new framework provides new tools that allow to obtain in a unified way inequalities involving many different topological indices. In particular, we obtain new optimal bounds on the variable Zagreb indices, the variable sum-connectivity index, the variable geometric-arithmetic index and the variable inverse sum indeg index. Thus, our approach provides both new tools for the study of topological indices and new bounds for a large class of topological indices. We obtain several optimal bounds of Aα (respectively, Bα) involving Aβ (respectively, Bβ). Moreover, we provide several bounds of the variable geometric-arithmetic index in terms of the variable inverse sum indeg index, and two bounds of the variable inverse sum indeg index in terms of the variable second Zagreb and the variable sum-connectivity indices.

scholarly journals Fixed Point of Interpolative Rus–Reich–Ćirić Contraction Mapping on Rectangular Quasi-Partial b-Metric Space

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 32
Author(s):  
Pragati Gautam ◽  
Luis Manuel Sánchez Ruiz ◽  
Swapnil Verma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Real Number ◽  
Metric Space ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Rectangular Metric Space ◽  
New Type ◽  
Symmetry Requirement ◽  
Definition Of

The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the rectangular metric space defined by Branciari. Here, we obtain a fixed point theorem for interpolative Rus–Reich–Ćirić contraction mappings in the realm of rectangular quasi-partial b-metric spaces. Furthermore, an example is also illustrated to present the applicability of our result.

Sign in / Sign up

Export Citation Format

Share Document