SIMATH  a computer algebra system for number theoretic applications  Horst G. Zimmer
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Название: 
SIMATH  a computer algebra system for number theoretic applications 
Автор: 
Horst G. Zimmer 
Категория: 
Информатика. Компьютеры

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Книга 
Дата: 
23.02.2009 11:16:21 
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The aim of this paper is to give a survey of the wide range of number theoretic applications of the computer algebra system SIMATH [42].' This system, focusing on algebraic number theory, enables the user to attack a broad spectrum of number theoretic problems. Special attention is paid to the arithmetic of elliptic curves and its applications in cryptography.
SIMATH is developed by the research group of the author at the Universitat des Saarlandes in Saarbriicken. It is written in the programming language С and will be soon extended to the programming language C++. A list system serves as a foundation for all SIMATH types such as integers, rationale, polynomials, algebraic numbers, algebraic functions, matrices and vectors. In addition to the libraries which contain all SIMATH functions, the system is equipped with a calculator called simcalc. In simcalc almost all SIMATH functions are available and can be handled in an interactive mode.
SIMATH is running on 32 bit Unix systems. An interface enables the user to apply other computer algebra systems such as MAPLE, KANT, LiDIA or PARI while working with SIMATH. This is accomplished by using a simple script language to extract numerical data from text files. A comparison of the performance of SIMATH with that of the other systems mentioned is not possible, since most of the algorithms under consideration in this survey are missing in the other systems.
Symbolic computation is one of the main ingredients of the system. The technical details are contained in the
'SIMATH was supported in part by the DFG within the research program "Algorithmic Number Theory and Algebra". However, the referees of the DFCi eventually suggested that we discontinue the development of SIMATH and instead incorporate some of our algorithms in other systems We hope that this survey, together with [48], illustrates why we prefer to ignore this suggestion.
Permission to make digital/hard copy of all or part of this work for personal or classroom use is granted without fee provided that copiesare not made or distributed for profit or commercial advantage, the copyright notice, the title of the publication and its date appear, ami notice is given that copying is by permission of ACM, Inc. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. ISSAC97, Maui, Hawaii, USA ©1ЯЯ7 ACM 0897918754/ 97/ 0007 $ З.Г>0 
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