@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

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    dct:description """
              This PhD thesis deals with some particular aspects of the algebraic systems resolution. Firstly, we introduce a way of minimizing the number of additive variables appearing in an algebraic system. For this, we make use of two invariants of variety introduced by Hironaka: the ridge and the directrix. Then, we propose fast arithmetic routines, the so-called relaxed routines, for p-adic integers. These routines allow us, then, to solve efficiently an algebraic system with rational coefficients locally, i.e. over the p-adic integers. In a fourth part, we are interested in the factorization of a bivariate polynomial, which is at the root of the decomposition of hypersurfaces into irreducible components. We propose an algorithm reducing the factorization of the input polynomial to that of a polynomial whose dense size is essentially equivalent to the convex-dense size of the input polynomial. In the last part, we consider real algebraic systems solving in average. We design a probabilistic algorithm computing an approximate complex zero of the real algebraic system given as input.
            """ ;
    dct:identifier "NNT: 2011EPXX0075" ;
    dct:issued "2026-05-27T21:51:54.199724"^^xsd:dateTime ;
    dct:language "fr" ;
    dct:modified "2026-05-27T21:51:54.199729"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Contributions to algebraic system solving: reduction, localization, singularities handling; implementations" ;
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    dcat:keyword "algebraic-systems-solving",
        "algorithmes",
        "algorithms",
        "factorisation-de-polynomes",
        "infoeu-reposemanticsdoctoralthesis",
        "infoinfo-cccomputer-science-cscomputational-complexity-cscc",
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        "mathmath-agmathematics-mathalgebraic-geometry-mathag",
        "nombres-p-adiques",
        "p-adic-numbers",
        "polynomial-factorization",
        "resolution-des-systemes-algebriques",
        "theses" ;
    dcat:landingPage <https://theses.hal.science/tel-00666435> .

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    dct:issued "2026-05-27T21:51:54.214077"^^xsd:dateTime ;
    dct:modified "2026-05-27T21:51:54.151269"^^xsd:dateTime ;
    dct:title "Contributions to algebraic system solving: reduction, localization, singularities handling; implementations" ;
    dcat:accessURL <https://theses.hal.science/tel-00666435> .

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