A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials-中国期刊网

摘要 ThispaperpresentsanewalgorithmforcomputingtheextendedHenselconstruction(EHC)ofmultivariatepolynomialsinmainvariablexandsub-variablesu1,u2,···,umoveranumberfieldK.Thisalgorithmfirstconstructsasetbyusingtheresultantoftwoinitialcoprimefactorsw.r.t.x,andthenobtainstheHenselfactorsbycomparingthecoefficientsofxionbothsidesofanequation.SincetheHenselfactorsarepolynomialsofthemainvariablewithcoefficientsinfractionfieldK(u1,u2,···,um),thecomputationcostofhandlingrationalfunctionscanbehigh.Therefore,theauthorsuseamethodwhichmultipliesresultantandremovesthedenominatorsoftherationalfunctions.Unlikepreviously-developedalgorithmsthatuseinterpolationfunctionsorGrobnerbasis,thealgorithmrelieslittleonpolynomialdivision,andavoidsmultiplyingbydifferentfactorswhenremovingthedenominatorsofHenselfactors.AllalgorithmsareimplementedusingMagma,acomputationalalgebrasystemandexperimentsindicatethatouralgorithmismoreefficient.

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A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials

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A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials

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