Generic, Type-Safe and Object Oriented Computer Algebra Software

Kredel, Heinz; Jolly, Raphael

doi:10.1007/978-3-642-15274-0_14

Cited by 4 publications

(2 citation statements)

References 14 publications

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“…It also enables us to automatically generate casting functions and we saw how their overhead can be reduced using rewriting rules. As for type-systems for a computer algebra system, there are several existing works [18,23]. However, these systems are not safe enough for discriminating variable arity at type-level and don't make use of rewriting rules.…”

Section: Discussionmentioning

confidence: 99%

“…In this section, we will see how the progressive type-level functionalities of GHC can be exploited to construct a safe, composable and flexible type-system for a computer algebra system. There are several existing works on type-systems for computer algebra, such as in Java and Scala [18,15], and DoCon. However, none of them achieves the same level of safety and composability as our approach, which utilises the power of dependent types and type-level functions.…”

Section: Type System For Safety and Composabilitymentioning

confidence: 99%

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A Purely Functional Computer Algebra System Embedded in Haskell

Ishii

2018

Developments in Language Theory

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We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-ofconcept, we present the computational-algebra package. It is a computer algebra system implemented as an embedded domain-specific language in Haskell, a purely functional programming language. Utilising methods in functional programming and prominent features of Haskell, this library achieves safety, composability, and correctness at the same time. To demonstrate the advantages of our approach, we have implemented advanced Gröbner basis algorithms, such as Faugère's F4 and F5, in a composable way.

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Section: Discussionmentioning

confidence: 99%

Section: Type System For Safety and Composabilitymentioning

confidence: 99%

A Purely Functional Computer Algebra System Embedded in Haskell

Ishii

2018

Developments in Language Theory

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Algebraic Structures as Typed Objects

Kredel

Jolly

2011

Computer Algebra in Scientific Computing

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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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Generic, Type-Safe and Object Oriented Computer Algebra Software

Cited by 4 publications

References 14 publications

A Purely Functional Computer Algebra System Embedded in Haskell

A Purely Functional Computer Algebra System Embedded in Haskell

Algebraic Structures as Typed Objects

Comprehensive Gröbner Bases in a Java Computer Algebra System

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