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A Hybrid Gröbner bases approach to computing power integral bases

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Abstract

Bettale, Faugère, and Perret [3] present and analyze a hybrid method for solving multivariate polynomial systems over finite fields that mixes Gröbner bases computations with an exhaustive search. Inspired by their method, we use a hybrid approach to characterize all power integral bases in the pth cyclotomic field \({\mathbb{Q}(\zeta_p)}\) for the regular primes p = 29, 31, 41. For each prime p this involves solving a system of (p−1)/2 multivariate polynomial equations of degree (p−1)/2 in (p−1)/2 variables over the finite field \({\mathbb{Z}/p\mathbb{Z}}\).

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  1. Mathematics Department, Seattle University, Seattle, WA, 98122, U.S.A

    L. Robertson & R. Russell

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  1. L. Robertson
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  2. R. Russell
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Correspondence to L. Robertson.

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Robertson, L., Russell, R. A Hybrid Gröbner bases approach to computing power integral bases. Acta Math. Hungar. 147, 427–437 (2015). https://doi.org/10.1007/s10474-015-0544-3

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