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Division and Slope Factorization of p-Adic Polynomials

Abstract : We study two important operations on polynomials defined over complete discrete valuation fields: Euclidean division and factorization. In particular, we design a simple and efficient algorithm for computing slope factorizations, based on Newton iteration. One of its main features is that we avoid working with fractional exponents. We pay particular attention to stability, and analyze the behavior of the algorithm using several precision models.
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https://hal.archives-ouvertes.fr/hal-01266537
Contributor : Xavier Caruso <>
Submitted on : Tuesday, February 2, 2016 - 9:25:16 PM
Last modification on : Thursday, January 7, 2021 - 4:32:41 PM
Long-term archiving on: : Saturday, November 12, 2016 - 4:42:15 AM

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Xavier Caruso, David Roe, Tristan Vaccon. Division and Slope Factorization of p-Adic Polynomials. ISSAC 2016, Jul 2016, Waterloo, Canada. ⟨10.1145/1235⟩. ⟨hal-01266537⟩

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