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87 lines
3.8 KiB
HTML
87 lines
3.8 KiB
HTML
4 years ago
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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<html>
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<!-- This manual describes how to install and use the GNU multiple precision
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arithmetic library, version 6.1.0.
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Copyright 1991, 1993-2015 Free Software Foundation, Inc.
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Permission is granted to copy, distribute and/or modify this document under
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the terms of the GNU Free Documentation License, Version 1.3 or any later
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version published by the Free Software Foundation; with no Invariant Sections,
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with the Front-Cover Texts being "A GNU Manual", and with the Back-Cover
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Texts being "You have freedom to copy and modify this GNU Manual, like GNU
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software". A copy of the license is included in
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GNU Free Documentation License. -->
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<!-- Created by GNU Texinfo 6.4, http://www.gnu.org/software/texinfo/ -->
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<head>
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<title>Perfect Power Algorithm (GNU MP 6.1.0)</title>
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<meta name="description" content="How to install and use the GNU multiple precision arithmetic library, version 6.1.0.">
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<meta name="keywords" content="Perfect Power Algorithm (GNU MP 6.1.0)">
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<meta name="resource-type" content="document">
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<meta name="distribution" content="global">
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<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
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<link href="index.html#Top" rel="start" title="Top">
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<link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
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<link href="Root-Extraction-Algorithms.html#Root-Extraction-Algorithms" rel="up" title="Root Extraction Algorithms">
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<link href="Radix-Conversion-Algorithms.html#Radix-Conversion-Algorithms" rel="next" title="Radix Conversion Algorithms">
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<link href="Perfect-Square-Algorithm.html#Perfect-Square-Algorithm" rel="prev" title="Perfect Square Algorithm">
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-->
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</style>
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</head>
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<body lang="en">
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<a name="Perfect-Power-Algorithm"></a>
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<div class="header">
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<p>
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Previous: <a href="Perfect-Square-Algorithm.html#Perfect-Square-Algorithm" accesskey="p" rel="prev">Perfect Square Algorithm</a>, Up: <a href="Root-Extraction-Algorithms.html#Root-Extraction-Algorithms" accesskey="u" rel="up">Root Extraction Algorithms</a> [<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<a name="Perfect-Power"></a>
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<h4 class="subsection">15.5.4 Perfect Power</h4>
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<a name="index-Perfect-power-algorithm"></a>
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<p>Detecting perfect powers is required by some factorization algorithms.
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Currently <code>mpz_perfect_power_p</code> is implemented using repeated Nth root
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extractions, though naturally only prime roots need to be considered.
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(See <a href="Nth-Root-Algorithm.html#Nth-Root-Algorithm">Nth Root Algorithm</a>.)
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</p>
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<p>If a prime divisor <em>p</em> with multiplicity <em>e</em> can be found, then only
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roots which are divisors of <em>e</em> need to be considered, much reducing the
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work necessary. To this end divisibility by a set of small primes is checked.
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</p>
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</body>
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</html>
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