Gourt > Science > Math > Number Theory > Software (2)
Computer software (or simply software) is the programs and procedures that enable a computer to perform a specific task, as opposed to the physical components of the system (hardware). This includes application software such as a word processor, which enables a user to perform a task, and system software such as an operating system, which enables other software to run properly, by interfacing with hardware and with other software.
The term "software" was first used in this sense by John W. Tukey in 1957. In computer science and software engineering, computer software is all information processed by computer systems, programs and data. The concept of reading different sequences of instructions into the memory of a device to control computations was invented by Charles Babbage as part of his difference engine. The theory that is the basis for most modern software was first proposed by Alan Turing in his 1935 essay Computable numbers with an application to the Entscheidungsproblem. Hally, Mike (2005:79). Electronic brains/Stories from the dawn of the computer age. British Broadcasting Corporation and Granta Books, London. ISBN 1-86-207663-4.
Relationship to hardware
Computer software is so called in contrast to computer hardware, which encompasses the physical interconnections and devices required to store and execute (or run) the software. In computers, software is loaded into RAM and executed in the central processing unit. At the lowest level, software consists of a machine language specific to an individual processor. A machine language consists of groups of binary values signifying processor instructions (object code), which change the state of the computer from its preceding state. Software is an ordered sequence of instructions for changing the state of the computer hardware in a particular sequence. It is generally written in high-level programming languages that are easier and more efficient for humans to use (closer to natural language) than machine language. High-level languages are compiled or interpreted into machine language object code. Software may also be written in an assembly language, essentially, a mnemonic representation of a machine language using a natural language alphabet. Assembly language must be assembled into object code via an assembler. More on [ Computer software ]
Computational Algebra :: Algorithms
Software :: Algebra
Software :: Math
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leftynews (Mark Mirro) Sun, 20 Dec 2009 00:15:36 -0000
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Aliquot - A DOS tool to compute aliquot chains with small starting numbers, by Ivo Düntsch.
apfloat - High-performance arbitrary precision arithmetic package for C++ and Java.
ARIBAS - An interactive interpreter for big integer and multi-precision floating point arithmetic with a Pascal/Modula like syntax. It has several builtin functions for algorithmic number theory.
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BIG_INT - A library of functions to handle arbitrary length integers, written on ANSI C99.
CALC - A calculator program for doing arbitrary precision integer arithmetic, written in ANSI C and Yacc, with a number of built-in functions for number theory, by Keith Matthews.
CLN - Class Library for Numbers - C++ library by Bruno Haible.
ECMNET - Elliptic curve factoring software.
Encyclopedia of Integer Sequences Seeker - EIS-Seeker is a libguile-based scheme interpreter devoted to the study of the Encyclopedia of Integer Sequences database. It is intended to help find new relations between sequences. C/Scheme, Posix.
Meta Description: [ The world's largest development and download repository of Open Source code and applications ]
Factorizer - A Windows program to find all factors of any positive integer less than 2^31 - 1; decompose numbers into their prime constituents; find prime numbersand pairs of primes; and to plot Erdos-Kac and Palmen Color histograms. Down load free demo, order full version online.
Meta Description: [ A Windows program to find all factors of any positive integer less than 2^31 - 2, to decompose numbers into their prime constituents, to find prime numbers and pairs of primes, and to plot Erdos-Kac and Palmen Color histograms. ]
FTP Sites, Calculator Programs and Archives - In the Number Theory Web.
Galois - An algebra/number theory package by R. Lidl, R. W. Matthews and R. Wells.
giantint - Library of routines for large integer arithmetic and number theory.
GIMPS FAQ list - About the Mersenne Prime Freeware.
Meta Description: [ Frequently asked questions about GIMPS ]
GNU MP Home Page - Free library for arbitrary precision arithmetic.
GNUBC - Supports arbitrary precision integer arithmetic calculations with interactive execution: it is a superior version of the basic bc program which comes with the UNIX operating system. Keith Matthews has written several number-theoretic programs.
HiPiLib - High Performance Libraries - Home of PIOLOGIE, a library for arbitrary precision arithmetic, operating on natural, integer and rational numbers.
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Implementations of Extended LLL - By Wilberd van der Kallen.
Java PHASER Project - An application for numerically and graphically analyzing dynamical systems.
Meta Description: [ PHASER: A Universal Simulator for Dynamical Systems ]
Jim Howell Software - Large integer arithmetic.
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KANT / KASH - KANT is a software package for sophisticated computations in number fields and in global function fields. With KASH you are able to use the powerful KANT V4 functions within a shell.
Kaprekar Series Generator - A java application for determining the Kaprekar Constants and Series for numbers in various radixes.
Meta Description: [ Introduction to the Kaprekar Series Generator ]
L - A C++ class library, datasets and command line program for computing zeros and values of L-functions, by Michael Rubinstein.
Meta Description: [ The L function software and zeros/values database homepage ]
Large Number Arithmetic in BASIC - Library for large-integer arithmetic, plus some number theory modules.
Meta Description: [ BASIC library for large-integer arithmetic, plus some number theory modules ]
LiDIA - C++ Library For Computational Number Theory.
Meta Description: [ The LiDIA Group ]
Magma Computational Algebra System Home Page - A large, well-supported software package for computationally hard problems in algebra, number theory, geometry and combinatorics.
Meta Description: [ The Magma Computational Algebra system for alg
ebra, number theory and geometry. ]
MAGMA/PARI Calculator - Web interface for short programs in either language.
Maple Worksheets by John Cosgrave - A selection of Maple (V.5) worksheets for teaching purposes.
Math Archives Software - PC/Number Theory section.
Math Archives Software - Mac/Number Theory section.
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Mersenne Prime Freeware - Freeware to search for Mersenne Primes. Pointers to FreeLIP, GMP, HFloat, apfloat, CALC.
Meta Description: [ Freeware to search for Mersenne Primes. ]
MIRACL - Multiprecision Integer and Rational Arithmetic C/C++ Library.
Meta Description: [ Shamus Software, the developers of the MIRACL library, the fastest multiprecision library in the world! ]
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Multiprecision Software Directory - Fortran multiprecision software by David H. Bailey of Lawrence Berkeley Lab.
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NTL: A Library for doing Number Theory - A high-performance, portable C++ library providing data structures and algorithms for manipulating signed, arbitrary length integers, and for vectors, matrices, and polynomials over the integers and over finite fields.
Number Field Sieve NET - A client/server system for NFSNET by Henrik Olsen.
Number-Theoretic Hacks - Algorithms implemented by David Eppstein.
NZMATH - Python based number theory oriented calculation system, developed at Tokyo Metropolitan University. Downloads, mailing list.
p-adic Arithmetic - A Mathematica package by Stany De Smedt.
Meta Description: [ This package is meant to do p-adic calculations. It allows addition, subtraction, multiplication and division of p-adic numbers written in Hensel expansion. Also functions as log, exp, sin, cos, sinh and cosh are defined using their power series expansion. At the end, we included a part to calcul... ]
SAGE - System for Arithmetic Geometry Experimentation: a framework for number theory, algebra, and geometry, initially designed for computing with elliptic curves and modular forms, by William Stein. Open source under GPL.
Schulenberg and Associates - Factoring programs. Windows, free download.
Meta Description: [ software for stock market timing and QQQQ buy and sell signals ]
SIMATH - Computer algebra system for number theoretic applications.
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Software Packages of Interest to Number Theory - Links maintained by John Cremona.
ZEN - A toolbox for computation in finite rings, by Florent Chabaud and Reynald Lercier. ANSI-C source, free download, GPL.
Meta Description: [ Mathematical library for fast computation in finite extension over finite rings. ]
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