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137 lines
6.7 KiB
HTML
137 lines
6.7 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>Integer Roots (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="Integer Roots (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 name="Generator" content="makeinfo">
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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="Integer-Functions.html#Integer-Functions" rel="up" title="Integer Functions">
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<link href="Number-Theoretic-Functions.html#Number-Theoretic-Functions" rel="next" title="Number Theoretic Functions">
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<link href="Integer-Exponentiation.html#Integer-Exponentiation" rel="prev" title="Integer Exponentiation">
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<style type="text/css">
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ul.no-bullet {list-style: none}
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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="Integer-Roots"></a>
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<div class="header">
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<p>
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Next: <a href="Number-Theoretic-Functions.html#Number-Theoretic-Functions" accesskey="n" rel="next">Number Theoretic Functions</a>, Previous: <a href="Integer-Exponentiation.html#Integer-Exponentiation" accesskey="p" rel="prev">Integer Exponentiation</a>, Up: <a href="Integer-Functions.html#Integer-Functions" accesskey="u" rel="up">Integer Functions</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="Root-Extraction-Functions"></a>
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<h3 class="section">5.8 Root Extraction Functions</h3>
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<a name="index-Integer-root-functions"></a>
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<a name="index-Root-extraction-functions"></a>
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<dl>
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<dt><a name="index-mpz_005froot"></a>Function: <em>int</em> <strong>mpz_root</strong> <em>(mpz_t <var>rop</var>, const mpz_t <var>op</var>, unsigned long int <var>n</var>)</em></dt>
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<dd><p>Set <var>rop</var> to <em></em> the truncated integer
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part of the <var>n</var>th root of <var>op</var>. Return non-zero if the computation
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was exact, i.e., if <var>op</var> is <var>rop</var> to the <var>n</var>th power.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpz_005frootrem"></a>Function: <em>void</em> <strong>mpz_rootrem</strong> <em>(mpz_t <var>root</var>, mpz_t <var>rem</var>, const mpz_t <var>u</var>, unsigned long int <var>n</var>)</em></dt>
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<dd><p>Set <var>root</var> to <em></em> the truncated
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integer part of the <var>n</var>th root of <var>u</var>. Set <var>rem</var> to the
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remainder, <em><var>u</var>-<var>root</var>**<var>n</var></em>.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpz_005fsqrt"></a>Function: <em>void</em> <strong>mpz_sqrt</strong> <em>(mpz_t <var>rop</var>, const mpz_t <var>op</var>)</em></dt>
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<dd><p>Set <var>rop</var> to <em></em> the truncated
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integer part of the square root of <var>op</var>.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpz_005fsqrtrem"></a>Function: <em>void</em> <strong>mpz_sqrtrem</strong> <em>(mpz_t <var>rop1</var>, mpz_t <var>rop2</var>, const mpz_t <var>op</var>)</em></dt>
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<dd><p>Set <var>rop1</var> to <em>the truncated integer part
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of the square root of <var>op</var></em>, like <code>mpz_sqrt</code>. Set <var>rop2</var> to the
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remainder <em><var>op</var>-<var>rop1</var>*<var>rop1</var></em>, which will be zero if <var>op</var> is a
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perfect square.
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</p>
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<p>If <var>rop1</var> and <var>rop2</var> are the same variable, the results are
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undefined.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpz_005fperfect_005fpower_005fp"></a>Function: <em>int</em> <strong>mpz_perfect_power_p</strong> <em>(const mpz_t <var>op</var>)</em></dt>
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<dd><a name="index-Perfect-power-functions"></a>
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<a name="index-Root-testing-functions"></a>
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<p>Return non-zero if <var>op</var> is a perfect power, i.e., if there exist integers
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<em><var>a</var></em> and <em><var>b</var></em>, with <em><var>b</var>>1</em>, such that
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<em><var>op</var> equals <var>a</var> raised to the power <var>b</var></em>.
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</p>
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<p>Under this definition both 0 and 1 are considered to be perfect powers.
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Negative values of <var>op</var> are accepted, but of course can only be odd
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perfect powers.
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</p></dd></dl>
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<dl>
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<dt><a name="index-mpz_005fperfect_005fsquare_005fp"></a>Function: <em>int</em> <strong>mpz_perfect_square_p</strong> <em>(const mpz_t <var>op</var>)</em></dt>
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<dd><a name="index-Perfect-square-functions"></a>
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<a name="index-Root-testing-functions-1"></a>
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<p>Return non-zero if <var>op</var> is a perfect square, i.e., if the square root of
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<var>op</var> is an integer. Under this definition both 0 and 1 are considered to
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be perfect squares.
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</p></dd></dl>
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<hr>
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<div class="header">
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<p>
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Next: <a href="Number-Theoretic-Functions.html#Number-Theoretic-Functions" accesskey="n" rel="next">Number Theoretic Functions</a>, Previous: <a href="Integer-Exponentiation.html#Integer-Exponentiation" accesskey="p" rel="prev">Integer Exponentiation</a>, Up: <a href="Integer-Functions.html#Integer-Functions" accesskey="u" rel="up">Integer Functions</a> [<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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</div>
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</body>
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</html>
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