@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#> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00802698v2> a dcat:Dataset ;
    dct:description """
              We address the problem of solving systems of two bivariate polynomials of total degree at most $d$ with integer coefficients of maximum bitsize $\\tau$. It is known that a linear separating form, that is a linear combination of the variables that takes different values at distinct solutions of the system, can be computed in $\\sOB(d^{8}+d^7\\tau)$ bit operations (where $O_B$ refers to bit complexities and $\\sO$ to complexities where polylogarithmic factors are omitted) and we focus here on the computation of a Rational Univariate Representation (RUR) given a linear separating form. We present an algorithm for computing a RUR with worst-case bit complexity in $\\sOB(d^7+d^6\\tau)$ and bound the bitsize of its coefficients by $\\sO(d^2+d\\tau)$. We show in addition that isolating boxes of the solutions of the system can be computed from the RUR with $\\sOB(d^{8}+d^7\\tau)$ bit operations. Finally, we show how a RUR can be used to evaluate the sign of a bivariate polynomial (of degree at most $d$ and bitsize at most $\\tau$) at one real solution of the system in $\\sOB(d^{8}+d^7\\tau)$ bit operations and at all the $\\Theta(d^2)$ {real} solutions in only $O(d)$ times that for one solution.
            """ ;
    dct:identifier "Report N°: RR-8262" ;
    dct:issued "2026-05-08T03:03:35.797989"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-08T03:03:35.797993"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Rational Univariate Representations of Bivariate Systems and Applications" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00802698v2/resource/e4697476-fa4b-43de-a0b6-6087038d9d52> ;
    dcat:keyword "computer-algebra",
        "infoeu-reposemanticsreport",
        "infoinfo-cgcomputer-science-cscomputational-geometry-cscg",
        "polynomial-system-solving",
        "rational-univariate-representations",
        "reports" ;
    dcat:landingPage <https://inria.hal.science/hal-00802698> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00802698v2/resource/e4697476-fa4b-43de-a0b6-6087038d9d52> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-08T03:03:35.799893"^^xsd:dateTime ;
    dct:modified "2026-05-08T03:03:35.790147"^^xsd:dateTime ;
    dct:title "Rational Univariate Representations of Bivariate Systems and Applications" ;
    dcat:accessURL <https://inria.hal.science/hal-00802698> .

<https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> a foaf:Agent ;
    foaf:name "test_moissonnage_selune" .

<https://inria.hal.science/hal-00802698> a foaf:Document .