Unique Factorization Domains in the Java Computer Algebra System
Unique Factorization Domains in the Java Computer Algebra System
复制标题
Java 计算机代数系统中独特的因式分解域
DOI：
10.1007/978-3-642-21046-4_5
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Heinz Kredel
中科院分区：
文献类型：
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作者：
Heinz Kredel
本文描述了在Java计算机代数库（JAS）中唯一分解域即多元多项式最大公约数（gcd）和分解为不可约部分的递归算法的实现。gcd、结果和因式分解的实现是代数几何中任何计算的基本组成部分，特别是几何中的自动演绎。这些算法在过程编程语言中有各种各样的实现。我们的目标是用现代面向对象的编程语言实现泛型数据类型，就像Java编程语言提供的那样。我们举例说明了JAS的类型设计和实现适用于几种最大公约数算法的实现和多元多项式的分解。由于这种设计，我们可以在其他计算机代数系统中不常见的非常一般的设置中使用这个包。例如，在系数算法中对于高级Grobner基的计算像在有理函数域上的多项式环或（有限的，交换的）正则环中。新包为非专家提供了从几种实现中选择一种的工厂方法。此外，我们还为gcd实现引入了一个并行代理，它可以同时运行不同的实现。
This paper describes the implementation of recursive algorithms in unique factorization domains, namely multivariate polynomial greatest common divisors (gcd) and factorization into irreducible parts in the Java computer algebra library (JAS). The implementation of gcds, resultants and factorization is part of the essential building blocks for any computation in algebraic geometry, in particular in automated deduction in geometry. There are various implementations of these algorithms in procedural programming languages. Our aim is an implementation in a modern object oriented programming language with generic data types, as it is provided by Java programming language. We exemplify that the type design and implementation of JAS is suitable for the implementation of several greatest common divisor algorithms and factorization of multivariate polynomials. Due to the design we can employ this package in very general settings not commonly seen in other computer algebra systems. As for example, in the coefficient arithmetic for advanced Grobner basis computations like in polynomial rings over rational function fields or (finite, commutative) regular rings. The new package provides factory methods for the selection of one of the several implementations for non experts. Further we introduce a parallel proxy for gcd implementations which runs different implementations concurrently.
DOI：
10.1145/143242.143362
发表时间：
1992-08
期刊：
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影响因子：
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作者：
M. Noro;T. Takeshima
通讯作者：
M. Noro;T. Takeshima