منابع مشابه
Effective Hilbert Irreducibility
I Abstract n this paper we prove by entirely elementary means a very effective version of the Hilbert Irreducibility-n Theorem. We then apply our theorem to construct a probabilistic irreducibility test for sparse multivariate poly omials over arbitrary perfect fields. For the usual coefficient fields the test runs in polynomial time in the input K size.
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We discuss the Hilbert Irreducibility Theorem, presenting briefly a new approach which leads to novel conclusions, especially in the context of algebraic groups. After a short survey of the issues and of the known theory, we shall illustrate the main principles and mention some new results; in particular, we shall state a toric analogue of Bertini’s Theorem and a lifting theorem for rational po...
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Using recent absolute irreducibility testing algorithms, we derive new irreducibility forms. These are integer polynomials in variables which are the generic coefficients of a multivariate polynomial of a given degree. A (multivariate) polynomial over a specific field is said to be absolutely irreducible if it is irreducible over the algebraic closure of its coefficient field. A specific polyno...
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We address a problem that arises in cryptographic protocol analysis when the equational properties of the cryptosystem are taken into account: in many situations it is necessary to guarantee that certain terms generated during a state exploration are in normal form with respect to the equational theory. We give a tool-independent methodology for state exploration, based on unification and narro...
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We study the problem of constructing and enumerating, for any integers m,n > 1, number fields of degree n whose ideal class groups have “large” m-rank. Our technique relies fundamentally on Hilbert’s irreducibility theorem and results on integral points of bounded degree on curves.
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ژورنال
عنوان ژورنال: Information and Control
سال: 1985
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(85)80056-5