Characteristic polynomials of p-adic matrices

Abstract : We analyze the precision of the characteristic polynomial of an n×n p-adic matrix A using differential precision methods developed previously. When A is integral with precision O(p^N), we give a criterion (checkable in time O˜(n^omega)) for χ(A) to have precision exactly O(p^N). We also give a O˜(n^3) algorithm for determining the optimal precision when the criterion is not satisfied, and give examples when the precision is larger than O(p^N).
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  • HAL Id : hal-01458027, version 1
  • ARXIV : 1702.01653

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Xavier Caruso, David Roe, Tristan Vaccon. Characteristic polynomials of p-adic matrices. The International Symposium on Symbolic and Algebraic Computation (ISSAC), University of Kaisersiautern, Jul 2017, Kaiserslautern, Germany. pp.389-396. ⟨hal-01458027⟩

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