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Implementing the Round Four maximal order algorithm. (English) Zbl 0817.11064

Let \(p\) be a prime and let \(f\) be a monic separable polynomial with integral \(p\)-adic coefficients. The authors describe in detail the so- called “round four algorithm” to compute the maximal order of the algebras \(\mathbb{Q}_ p [X]/ (f)\). The method combines the usual Dedekind criterion with decompositions of the algebra by means of orthogonal idempotents. The algorithm can be used as an efficient factorization algorithm of the polynomial \(f\). The authors give several examples and explicit programs.
Reviewer: R.Schoof (Roma)

MSC:

11Y40 Algebraic number theory computations
11Y16 Number-theoretic algorithms; complexity
11S05 Polynomials

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References:

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