Displaying similar documents to “Galois Lattice as a Framework to Specify Building Class Hierarchies Algorithms”

Évariste Galois and the social time of mathematics

Caroline Ehrhardt (2011)

Revue d'histoire des mathématiques

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The thrust of this article is to offer a new approach to the study of Galois’s . Drawing on methodology developed by social and cultural historians, it contextualizes Galois’s work by situating it in the parisian mathematical milieu of the 1820s and 1830s. By reconstructing the social process whereby a young man became an established mathematician at the time, this article shows that Galois’s trajectory was far from unusual, and most importantly, that he was not treated differently from...

Clausal relations and C-clones

Edith Vargas (2010)

Discussiones Mathematicae - General Algebra and Applications

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We introduce a special set of relations called clausal relations. We study a Galois connection Pol-CInv between the set of all finitary operations on a finite set D and the set of clausal relations, which is a restricted version of the Galois connection Pol-Inv. We define C-clones as the Galois closed sets of operations with respect to Pol-CInv and describe the lattice of all C-clones for the Boolean case D = {0,1}. Finally we prove certain results about C-clones over a larger set. ...

Self-portraits with Évariste Galois (and the shadow of Camille Jordan)

Frédéric Brechenmacher (2011)

Revue d'histoire des mathématiques

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This paper investigates the collections of 19th century texts in which Evariste Galois’s works were referred to in connection to those of Camille Jordan. Before the 1890s, when object-oriented disciplines developed, most of the papers referring to Galois have underlying them three main . These groups of texts were revolving around the works of individuals: Kronecker, Klein, and Dickson. Even though they were mainly active for short periods of no more than a decade, the three networks...

Differential equations and algebraic transcendents: french efforts at the creation of a Galois theory of differential equations 1880–1910

Tom Archibald (2011)

Revue d'histoire des mathématiques

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A “Galois theory” of differential equations was first proposed by Émile Picard in 1883. Picard, then a young mathematician in the course of making his name, sought an analogue to Galois’s theory of polynomial equations for linear differential equations with rational coefficients. His main results were limited by unnecessary hypotheses, as was shown in 1892 by his student Ernest Vessiot, who both improved Picard’s results and altered his approach, leading Picard to assert that his lay...

Invariants and differential Galois groups in degree four

Julia Hartmann (2002)

Banach Center Publications

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This note extends the algorithm of [hess] for computing unimodular Galois groups of irreducible differential equations of order four. The main tool is invariant theory.

Remarks on the intrinsic inverse problem

Daniel Bertrand (2002)

Banach Center Publications

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The intrinsic differential Galois group is a twisted form of the standard differential Galois group, defined over the base differential field. We exhibit several constraints for the inverse problem of differential Galois theory to have a solution in this intrinsic setting, and show by explicit computations that they are sufficient in a (very) special situation.