InforLorV4, PascalFrancis, Corpus, bibRecord, 000C66

Avoiding slack variables in the solving of linear diophantine equations and inequations

Identifieur interne : 000C66 ( PascalFrancis/Corpus ); précédent : 000C65; suivant : 000C67

Avoiding slack variables in the solving of linear diophantine equations and inequations

Auteurs : F. Ajili ; E. Contejean

Source :

Theoretical computer science [ 0304-3975 ] ; 1997.

RBID : Pascal:97-0270951

Descripteurs français

Pascal (Inist)
- Système inéquation, Système équation, Système linéaire, Equation diophantienne, Algorithme.

English descriptors

KwdEn :
- Algorithm, Diophantine equation, Equation system, Inequation system, Linear system.

Abstract

Copyright (c) 1996 Elsevier Science B.V. All rights reserved. In this paper, we present an algorithm for solving directly linear Diophantine systems of both equations and inequations. Here directly means without adding slack variables for encoding inequalities as equalities. This algorithm is an extension of the algorithm due to Contejean and Devie (1994) for solving linear Diophantine systems of equations, which is itself a generalization of the algorithm of Fortenbacher (Clausen and Fortenbacher, 1989) for solving a single linear Diophantine equation. All the nice properties of the algorithm of Contejean and Devie are still satisfied by the new algorithm: it is complete, i.e. provides a (finite) description of the set of solutions, it can be implemented with a bounded stack, and it admits an incremental version. All of these characteristics enable its easy integration in the CLP paradigm.

Notice en format standard (ISO 2709)

Pour connaître la documentation sur le format Inist Standard.

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A08	`01`	`1`	`ENG`	`@1 Avoiding slack variables in the solving of linear diophantine equations and inequations`
A11	`01`	`1`		`@1 AJILI (F.)`
A11	`02`	`1`		`@1 CONTEJEAN (E.)`
A14	`01`			`@1 INRIA Lorraine & CRIN, 615 rue du jardin botanique BP 101 @2 54602 Villers-lès-Nancy Cedex @3 FRA @Z 1 aut.`
A14	`02`			`@1 LRI, CNRS URA 410, Bât 490, Université Paris-Sud, Centre d’Orsay @2 91405 Orsay Cedex @3 FRA @Z 2 aut.`
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A23	`01`			`@0 ENG`
A24	`01`			`@0 eng`
A43	`01`			`@1 INIST @2 17243 @5 354000063259310014`
A44				`@0 9000 @1 © 1997 Elsevier Science B.V. All rights reserved.`
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A60				`@1 P`
A61				`@0 A`
A64	`01`	`1`		`@0 Theoretical computer science`
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C01	`01`		`ENG`	@0 Copyright (c) 1996 Elsevier Science B.V. All rights reserved. In this paper, we present an algorithm for solving directly linear Diophantine systems of both equations and inequations. Here directly means without adding slack variables for encoding inequalities as equalities. This algorithm is an extension of the algorithm due to Contejean and Devie (1994) for solving linear Diophantine systems of equations, which is itself a generalization of the algorithm of Fortenbacher (Clausen and Fortenbacher, 1989) for solving a single linear Diophantine equation. All the nice properties of the algorithm of Contejean and Devie are still satisfied by the new algorithm: it is complete, i.e. provides a (finite) description of the set of solutions, it can be implemented with a bounded stack, and it admits an incremental version. All of these characteristics enable its easy integration in the CLP paradigm.
C02	`01`	`X`		`@0 001D02A05`
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C03	`05`	`X`	`GER`	`@0 Algorithmus @5 05`
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Format Inist (serveur)

NO :	PASCAL 97-0270951 Elsevier
ET :	Avoiding slack variables in the solving of linear diophantine equations and inequations
AU :	AJILI (F.); CONTEJEAN (E.)
AF :	INRIA Lorraine & CRIN, 615 rue du jardin botanique BP 101/54602 Villers-lès-Nancy Cedex/France (1 aut.); LRI, CNRS URA 410, Bât 490, Université Paris-Sud, Centre d’Orsay/91405 Orsay Cedex/France (2 aut.)
DT :	Publication en série; Niveau analytique
SO :	Theoretical computer science; ISSN 0304-3975; Coden TCSCDI; Pays-Bas; Da. 1997; Vol. 173; No. 1; Pp. 183-208; Abs. anglais
LA :	Anglais
EA :	Copyright (c) 1996 Elsevier Science B.V. All rights reserved. In this paper, we present an algorithm for solving directly linear Diophantine systems of both equations and inequations. Here directly means without adding slack variables for encoding inequalities as equalities. This algorithm is an extension of the algorithm due to Contejean and Devie (1994) for solving linear Diophantine systems of equations, which is itself a generalization of the algorithm of Fortenbacher (Clausen and Fortenbacher, 1989) for solving a single linear Diophantine equation. All the nice properties of the algorithm of Contejean and Devie are still satisfied by the new algorithm: it is complete, i.e. provides a (finite) description of the set of solutions, it can be implemented with a bounded stack, and it admits an incremental version. All of these characteristics enable its easy integration in the CLP paradigm.
CC :	001D02A05
FD :	Système inéquation; Système équation; Système linéaire; Equation diophantienne; Algorithme
ED :	Inequation system; Equation system; Linear system; Diophantine equation; Algorithm
GD :	Algorithmus
SD :	Sistema inecuación; Sistema ecuación; Sistema lineal; Ecuación diofántica; Algoritmo
LO :	INIST-17243.354000063259310014
ID :	97-0270951

Links to Exploration step

Pascal:97-0270951

Le document en format XML

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Avoiding slack variables in the solving of linear diophantine equations and inequations

Avoiding slack variables in the solving of linear diophantine equations and inequations

Source :

Descripteurs français

English descriptors

Abstract

Notice en format standard (ISO 2709)

Format Inist (serveur)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri