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arXiv · 1301.6104

The Qth-power algorithm in characteristic 0

Douglas A. Leonard
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Abstract

The Qth-power algorithm produces a useful canonical P-module presentation for the integral closures of certain integral extensions of $P:=\mathbf{F}[x_n,...,x_1]$, a polyonomial ring over the finite field $\mathbf{F}:=\mathbf{Z}_q$ of $q$ elements. Here it is shown how to use this for several small primes $q$ to reconstruct similar integral closures over the rationals $\mathbf{Q}$ using the Chinese remainder theorem to piece together presentations in different positive characteristics, and the extended Euclidean algorithm to reconstruct rational fractions to lift these to presentations over $\mathbf{Q}$.

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Douglas A. Leonard. 2013-01-25. The Qth-power algorithm in characteristic 0. https://arxiv.org/abs/1301.6104

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