On a Java computer algebra system, its performance and applications

Kredel, Heinz

doi:10.1016/j.scico.2007.07.010

Cited by 14 publications

(7 citation statements)

References 15 publications

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“…This concludes the introduction to JAS, further details can be found, as already mentioned, in [11,5,7,9,8].…”

Section: Introduction To the Jas Librarymentioning

confidence: 53%

“…Due to space restrictions, we must assume some knowledge of Java, object oriented programming and JAS [9,7,11] in the following. The overall layout of the implemented classes is shown in figure 3.…”

Section: Class Layoutmentioning

confidence: 99%

“…In this paper we present an implementation of the algorithms for computing comprehensive Gröbner bases [23,25,14,20] in a Java computer algebra system (JAS) [5,9,6,7].…”

Section: Introductionmentioning

confidence: 99%

“…For an introduction to the JAS type system see [9,11]. To get an idea of the interplay of the types, classes and object construction consider the following type List<GenPolynomial<Product<Residue<BigRational>>>> of a list of polynomials with coefficients from a direct product of residue class rings modulo some polynomial ideal over the rational numbers.…”

Section: Introduction To the Jas Librarymentioning

confidence: 99%

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Comprehensive Gröbner Bases in a Java Computer Algebra System

Kredel

2014

Computer Mathematics

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We present an implementation of the algorithms for computing comprehensive Gröbner bases in a Java computer algebra system (JAS). Contrary to approaches to implement comprehensive Gröbner bases with minimal requirements to the computer algebra system, we aim to provide and utilize all necessary algebraic structures occurring in the algorithm. In the implementation of a condition we aim at the maximal semantic exploitation of the occurring algebraic structures: the set of equations equal zero are implemented as an ideal (with Gröbner base computation) and the set of inequalities are implemented as a multiplicative set which is simplified to polynomials of minimal degrees using, for example, square-free decomposition. With our approach we can also make the transition of a comprehensive Gröbner system to a polynomial ring over a (commutative, finite, von Neuman) regular coefficient ring and test or compute Gröbner bases in such polynomial rings.

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“…This concludes the introduction to JAS, further details can be found, as already mentioned, in [11,5,7,9,8].…”

Section: Introduction To the Jas Librarymentioning

confidence: 53%

Section: Class Layoutmentioning

confidence: 99%

“…In this paper we present an implementation of the algorithms for computing comprehensive Gröbner bases [23,25,14,20] in a Java computer algebra system (JAS) [5,9,6,7].…”

Section: Introductionmentioning

confidence: 99%

Section: Introduction To the Jas Librarymentioning

confidence: 99%

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Comprehensive Gröbner Bases in a Java Computer Algebra System

Kredel

2014

Computer Mathematics

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“…Computer algebra in Java has many advantages over implementations in more rustic languages such as Lisp or C, and was shown to be reasonably fast compared to them [11,12,13]. However it lacks good user interfaces.…”

Section: Introductionmentioning

confidence: 99%

Symbolic Script Programming for Java

Jolly,

Kredel

2009

Preprint

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Computer algebra in Java is a promising field of development. It has not yet reached an industrial strength, in part because of a lack of good user interfaces. Using a general purpose scripting language can bring a natural mathematical notation, akin to the one of specialized interfaces included in most computer algebra systems. We present such an interface for Java computer algebra libraries, using scripts available in the JSR 223 framework. We introduce the concept of 'symbolic programming' and show its usefulness by prototypes of symbolic polynomials and polynomial rings.

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Categories as Type Classes in the Scala Algebra System

Jolly

2013

Computer Algebra in Scientific Computing

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On a Java computer algebra system, its performance and applications

Cited by 14 publications

References 15 publications

Comprehensive Gröbner Bases in a Java Computer Algebra System

Comprehensive Gröbner Bases in a Java Computer Algebra System

Symbolic Script Programming for Java

Categories as Type Classes in the Scala Algebra System

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