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- Eric Domenjoud, Francis Klay, Christophe Ringeissen
- CADE
- 1994

- Eric Domenjoud
- MFCS
- 1991

We describe through an algebraic and geometrical study, a new method for solving systems of linear diophantine equations. This approach yields an algorithm which is intrinsically parallel. In addition to the algorithm, we give a geometrical interpretation of the satissability of an homogeneous system, as well as upper bounds on height and length of all… (More)

- Eric Domenjoud
- Journal of Automated Reasoning
- 1992

We show in this note that the equation αx1 + #x22EF; +αxp≐ACβy1 + α +βyq where + is an AC operator and αx stands for x+...+x (α times), has exactly $$\left( { - 1} \right)^{p + q} \sum\limits_{i = 0}^p {\sum\limits_{j = 0}^q {\left( { - 1} \right)^{1 + 1} \left( {\begin{array}{*{20}c} p \\ i \\ \end{array} } \right)\left( {\begin{array}{*{20}c} q \\ j \\… (More)

- Eric Domenjoud, Damien Jamet, Jean-Luc Toutant
- DGCI
- 2009

While connected rational arithmetical discrete lines and connected rational arithmetical discrete planes are entirely characterized, only partial results exist for the irrational arithmetical discrete planes. In the present paper, we focus on the connectedness of irrational arithmetical discrete planes, namely the arithmetical discrete planes with a normal… (More)

- Eric Domenjoud, Ana Paula Tomás
- CP
- 1995

We describe a new algorithm for solving a conjunction of linear diophantine equations, inequations and disequations in natural numbers. We derive our algorithm from one proposed by Elliott in 1903 for solving a single homogeneous equation. This algorithm was then extended to solve homogeneous systems of equations by MacMahon. We show how it further extends… (More)

- Eric Domenjoud
- J. Symb. Comput.
- 1991

- Eric Domenjoud, Xavier Provençal, Laurent Vuillon
- DGCI
- 2014

We investigate connections between a well known multidimensional continued fraction algorithm, the so-called fully subtractive algorithm, the finiteness property for β-numeration, and the connectedness of arithmetic discrete hyperplanes. A discrete hyperplane is said to be critical if its thickness is equal to the infimum of the set of thicknesses for which… (More)

In the present paper, we propose a new definition of discrete parabolas, the so-called arithmetic discrete parabolas. We base our approach on a non-constant thickness function and characterized the 0connected and 1-connected parabolas in terms of thickness function. This results extend the well-known characterization of the κ-connectedness of arithmetic… (More)

- Eric Domenjoud, Claude Kirchner, Jianyang Zhou
- Electronic Notes in Discrete Mathematics
- 1998