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- W1972815444 abstract "We consider the problem of computing the monic gcd of two polynomials over a number field L = ℚ(α1,…,αn). Encarnacion, Langemyr and McCallum have already shown how Brown's modular GCD algorithm for polynomials over ℚ can be modified to work for ℚ(α).Our first contribution is an extension of Encarnacion's modular GCD algorithm to the case n > 1 without converting to a single field extension. Our second contribution is a proof that it is not necessary to test if p divides the discriminant. This simplifies the algorithm; it is correct without this test.Our third contribution is the design of a data structure for representing multivariate polynomials over number fields with multiple field extensions. We have a complete implementation of the modular GCD algorithm using it. We provide details of some practical improvements." @default.
- W1972815444 created "2016-06-24" @default.
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- W1972815444 date "2002-07-10" @default.
- W1972815444 modified "2023-09-26" @default.
- W1972815444 title "A modular GCD algorithm over number fields presented with multiple extensions" @default.
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- W1972815444 doi "https://doi.org/10.1145/780506.780520" @default.
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