Bezannes « la Fosse à Carin » (51), une structure funéraire originale. Approche méthodologique

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Analysis and Depertubation of the C2^2Π and D2^2Σ+^+ states of CaF

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SymGrid: a Framework for Symbolic Computation on the Grid

Abstract. This paper introduces the design of SymGrid, a new Grid framework that will, for the first time, allow multiple invocations of symbolic computing applications to interact via the Grid. SymGrid is designed to support the specific needs of symbolic computation, including computational steering (greater interactivity), complex data structures, and domain-specific computational patterns (for irregular parallelism). A key issue is heterogeneity: SymGrid is designed to orchestrate components from different symbolic systems into a single coherent (possibly parallel) Grid application, building on the OpenMath standard for data exchange between mathematically-oriented applications. The work is being developed as part of a major EU infrastructure project.

Symmetrization based completion

We argue that most completion procedures for finitely presented algebras can be simulated by term completion procedures based on a generalized symmetrization process. Therefore we present three different constructive definitions of symmetrization procedures that can take the role of the orientation step in a symmetrization based completion procedure. We investigate confluence and compatibility properties of the symmetrized rules computed by the different symmetrization procedures. Based on semicompatibility properties we can present a generic version of the critical pair theorem that specializes to the critical pair theorems of Knuth-Bendix completion procedures and algebraic completion procedures like Buchberger's algorithm respectively. This critical pair theorem also applies to symmetrization based completion procedures using a normalized reduction relation if the result of the symmetrization is both semi-compatible and semi-stable. We conclude our paper showing how a generic Buchberger algorithm for polynomials over arbitrary finitely presented rings can be formulated as a symmetrization based completion procedure

Equational Prover of Theorema

The equational prover of the Theorema system is described. It is implemented on Mathematica and is designed for unit equalities in the first order or in the applicative higher order form. A (restricted) usage of sequence variables and Mathematica built-in functions is allowed