### Irreducibility of multivariate polynomials

Joachim von zur Gathen
<span title="">1985</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6ovb2qpkfenhmb7mcksobrcxq" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
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
more &raquo; ... sented, 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. T
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0022-0000(85)90043-1">doi:10.1016/0022-0000(85)90043-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u6ip3d3tjbdb5jemmc4l4ng4lq">fatcat:u6ip3d3tjbdb5jemmc4l4ng4lq</a> </span>
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