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• W2042803397 abstract "This paper deals with the problem of computing the degrees and multiplicities of the irreducible factors of a given multivariate polynomial. This includes the important question of testing for irreducibility. A probabilistic reduction from multivariate to bivariate polynomials is given, over an arbitrary (effectively computable) field. It uses an expected number of field operations (and certain random choices) that is polynomial in the length of a computation by which the input polynomial is presented, and the degree of the polynomial. Over algebraic number fields and over finite fields, we obtain polynomial-time probabilistic algorithms. They are based on an effective version of Hilbert's irreducibility theorem." @default.
• W2042803397 created "2016-06-24" @default.
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• W2042803397 date "1985-10-01" @default.
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• W2042803397 title "Irreducibility of multivariate polynomials" @default.
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• W2042803397 doi "https://doi.org/10.1016/0022-0000(85)90043-1" @default.
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