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Article Dans Une Revue Mathematics of Computation Année : 2024

Power detection over number fields

Résumé

We describe an algorithm that, given an integral ideal A \mathfrak {A} in a number field K K , finds the largest integer k ⩾ 1 k\geqslant 1 such that A \mathfrak {A} is a k k -th power, and at the same time computes the ideal B \mathfrak {B} such that A = B k \mathfrak {A} = \mathfrak {B}^k . This algorithm does not require the complete factorization of A \mathfrak {A} into a product of prime ideals; given the maximal order Z K \mathbb {Z}_K , we prove that it has polynomial time complexity. We apply this algorithm to the reduction of elements of K ∗ K^* modulo k k -th powers.
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Dates et versions

hal-04561403 , version 1 (27-04-2024)

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Citer

Karim Belabas, Denis Simon. Power detection over number fields. Mathematics of Computation, 2024, 93 (348), pp.1953-1961. ⟨10.1090/mcom/3913⟩. ⟨hal-04561403⟩
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