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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<head>
<title>/Volumes/unix-files/u/ntl-new/ntl-9.9.0dev/doc/lzz_pE.cpp.html</title>
<meta name="Generator" content="Vim/7.1">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
</head>
<body bgcolor="#ffffff" text="#000000"><font face="monospace">
<br>
<br>
<font color="#0000ed"><i>/*</i></font><font color="#0000ed"><i>*************************************************************************\</i></font><br>
<br>
<font color="#0000ed"><i>MODULE: zz_pE</i></font><br>
<br>
<font color="#0000ed"><i>SUMMARY:</i></font><br>
<br>
<font color="#0000ed"><i>The class zz_pE is used to represent polynomials in Z_p[X] modulo a</i></font><br>
<font color="#0000ed"><i>polynomial P.&nbsp;&nbsp;The modulus P may be any polynomial with deg(P) &gt; 0,</i></font><br>
<font color="#0000ed"><i>not necessarily irreducible.&nbsp;&nbsp;The modulus p defining Z_p need</i></font><br>
<font color="#0000ed"><i>not be prime either.</i></font><br>
<br>
<font color="#0000ed"><i>Objects of the class zz_pE are represented as a zz_pX of degree &lt; deg(P).</i></font><br>
<br>
<font color="#0000ed"><i>An executing program maintains a &quot;current modulus&quot;, which is set to P</i></font><br>
<font color="#0000ed"><i>using zz_pE::init(P).&nbsp;&nbsp;The current modulus for zz_pE (as well as for zz_p)</i></font><br>
<font color="#0000ed"><i>*must* be initialized before an operations on zz_pE's are performed.</i></font><br>
<br>
<font color="#0000ed"><i>The modulus may be changed, and a mechanism is provided for saving and</i></font><br>
<font color="#0000ed"><i>restoring a modulus (see classes zz_pEPush and zz_pEContext below).</i></font><br>
<br>
<font color="#0000ed"><i>\*************************************************************************</i></font><font color="#0000ed"><i>*/</i></font><br>
<br>
<font color="#1773cc">#include </font><font color="#4a6f8b">&lt;NTL/lzz_pX.h&gt;</font><br>
<br>
<font color="#008b00"><b>class</b></font>&nbsp;zz_pE {<br>
<font color="#b02f60"><b>public</b></font>:<br>
&nbsp;&nbsp; <br>
&nbsp;&nbsp; zz_pE(); <font color="#0000ed"><i>// initial value 0</i></font><br>
<br>
&nbsp;&nbsp; zz_pE(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a); <font color="#0000ed"><i>// copy constructor</i></font><br>
&nbsp;&nbsp; <font color="#008b00"><b>explicit</b></font>&nbsp;zz_pE(<font color="#008b00"><b>const</b></font>&nbsp;zz_p&amp; a); <font color="#0000ed"><i>// promotion </i></font><br>
&nbsp;&nbsp; <font color="#008b00"><b>explicit</b></font>&nbsp;zz_pE(<font color="#008b00"><b>long</b></font>&nbsp;a); <font color="#0000ed"><i>// promotion </i></font><br>
&nbsp;&nbsp; <br>
&nbsp;&nbsp; zz_pE&amp; <font color="#b02f60"><b>operator</b></font>=(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a); <font color="#0000ed"><i>// assignment</i></font><br>
&nbsp;&nbsp; zz_pE&amp; <font color="#b02f60"><b>operator</b></font>=(<font color="#008b00"><b>const</b></font>&nbsp;zz_p&amp; a); <font color="#0000ed"><i>// assignment</i></font><br>
&nbsp;&nbsp; zz_pE&amp; <font color="#b02f60"><b>operator</b></font>=(<font color="#008b00"><b>long</b></font>&nbsp;a); <font color="#0000ed"><i>// assignment</i></font><br>
&nbsp;&nbsp; <br>
&nbsp;&nbsp; ~zz_pE(); <font color="#0000ed"><i>// destructor</i></font><br>
<br>
&nbsp;&nbsp; <font color="#008b00"><b>void</b></font>&nbsp;init(<font color="#008b00"><b>const</b></font>&nbsp;zz_pX&amp; P);<br>
&nbsp;&nbsp; <font color="#0000ed"><i>// zz_pE::init(P) initializes the current modulus to P;</i></font><br>
&nbsp;&nbsp; <font color="#0000ed"><i>// required: deg(P) &gt;= 1.</i></font><br>
&nbsp;&nbsp; <br>
&nbsp;&nbsp; <font color="#008b00"><b>static</b></font>&nbsp;<font color="#008b00"><b>const</b></font>&nbsp;zz_pXModulus&amp; modulus();<br>
&nbsp;&nbsp; <font color="#0000ed"><i>// zz_pE::modulus() yields read-only reference to the current modulus </i></font><br>
<br>
&nbsp;&nbsp; <font color="#008b00"><b>static</b></font>&nbsp;<font color="#008b00"><b>long</b></font>&nbsp;degree();<br>
&nbsp;&nbsp; <font color="#0000ed"><i>// zz_pE::degree() returns deg(P)</i></font><br>
<br>
&nbsp;&nbsp; <font color="#0000ed"><i>// typedefs to aid generic programming</i></font><br>
&nbsp;&nbsp; <font color="#008b00"><b>typedef</b></font>&nbsp;zz_pX rep_type;<br>
&nbsp;&nbsp; <font color="#008b00"><b>typedef</b></font>&nbsp;zz_pEContext context_type;<br>
&nbsp;&nbsp; <font color="#008b00"><b>typedef</b></font>&nbsp;zz_pEBak bak_type;<br>
&nbsp;&nbsp; <font color="#008b00"><b>typedef</b></font>&nbsp;zz_pEPush push_type;<br>
&nbsp;&nbsp; <font color="#008b00"><b>typedef</b></font>&nbsp;zz_pEX poly_type;<br>
<br>
};<br>
<br>
<br>
<font color="#008b00"><b>const</b></font>&nbsp;zz_pX&amp; rep(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a); <font color="#0000ed"><i>// read-only access to representation of a</i></font><br>
<br>
<br>
<br>
<font color="#0000ed"><i>/*</i></font><font color="#0000ed"><i>*************************************************************************\</i></font><br>
<br>
<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Comparison</i></font><br>
<br>
<font color="#0000ed"><i>\*************************************************************************</i></font><font color="#0000ed"><i>*/</i></font><br>
<br>
<font color="#008b00"><b>long</b></font>&nbsp;<font color="#b02f60"><b>operator</b></font>==(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; b);<br>
<font color="#008b00"><b>long</b></font>&nbsp;<font color="#b02f60"><b>operator</b></font>!=(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; b);<br>
<br>
<font color="#008b00"><b>long</b></font>&nbsp;IsZero(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a);&nbsp;&nbsp;<font color="#0000ed"><i>// test for 0</i></font><br>
<font color="#008b00"><b>long</b></font>&nbsp;IsOne(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a);&nbsp;&nbsp;<font color="#0000ed"><i>// test for 1</i></font><br>
<br>
<font color="#0000ed"><i>// PROMOTIONS: ==, != promote {long, zz_p} to zz_pE on (a, b).</i></font><br>
<br>
<br>
<font color="#0000ed"><i>/*</i></font><font color="#0000ed"><i>*************************************************************************\</i></font><br>
<br>
<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Addition </i></font><br>
<br>
<font color="#0000ed"><i>\*************************************************************************</i></font><font color="#0000ed"><i>*/</i></font><br>
<br>
<font color="#0000ed"><i>// operator notation:</i></font><br>
<br>
zz_pE <font color="#b02f60"><b>operator</b></font>+(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; b);<br>
<br>
zz_pE <font color="#b02f60"><b>operator</b></font>-(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; b);<br>
zz_pE <font color="#b02f60"><b>operator</b></font>-(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a);<br>
<br>
zz_pE&amp; <font color="#b02f60"><b>operator</b></font>+=(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a);<br>
zz_pE&amp; <font color="#b02f60"><b>operator</b></font>+=(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_p&amp; a);<br>
zz_pE&amp; <font color="#b02f60"><b>operator</b></font>+=(zz_pE&amp; x, <font color="#008b00"><b>long</b></font>&nbsp;a);<br>
<br>
zz_pE&amp; <font color="#b02f60"><b>operator</b></font>++(zz_pE&amp; x); <font color="#0000ed"><i>// prefix</i></font><br>
<font color="#008b00"><b>void</b></font>&nbsp;<font color="#b02f60"><b>operator</b></font>++(zz_pE&amp; x, <font color="#008b00"><b>int</b></font>); <font color="#0000ed"><i>// postfix</i></font><br>
<br>
zz_pE&amp; <font color="#b02f60"><b>operator</b></font>-=(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a);<br>
zz_pE&amp; <font color="#b02f60"><b>operator</b></font>-=(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_p&amp; a);<br>
zz_pE&amp; <font color="#b02f60"><b>operator</b></font>-=(zz_pE&amp; x, <font color="#008b00"><b>long</b></font>&nbsp;a);<br>
<br>
zz_pE&amp; <font color="#b02f60"><b>operator</b></font>--(zz_pE&amp; x); <font color="#0000ed"><i>// prefix</i></font><br>
<font color="#008b00"><b>void</b></font>&nbsp;<font color="#b02f60"><b>operator</b></font>--(zz_pE&amp; x, <font color="#008b00"><b>int</b></font>); <font color="#0000ed"><i>// postfix</i></font><br>
<br>
<font color="#0000ed"><i>// procedural versions:</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;add(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; b); <font color="#0000ed"><i>// x = a + b</i></font><br>
<font color="#008b00"><b>void</b></font>&nbsp;sub(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; b); <font color="#0000ed"><i>// x = a - b </i></font><br>
<font color="#008b00"><b>void</b></font>&nbsp;negate(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a); <font color="#0000ed"><i>// x = - a </i></font><br>
<br>
<font color="#0000ed"><i>// PROMOTIONS: +, -, add, sub promote {long, zz_p} to zz_pE on (a, b).</i></font><br>
<br>
<br>
<font color="#0000ed"><i>/*</i></font><font color="#0000ed"><i>*************************************************************************\</i></font><br>
<br>
<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Multiplication </i></font><br>
<br>
<font color="#0000ed"><i>\*************************************************************************</i></font><font color="#0000ed"><i>*/</i></font><br>
<br>
<br>
<font color="#0000ed"><i>// operator notation:</i></font><br>
<br>
zz_pE <font color="#b02f60"><b>operator</b></font>*(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; b);<br>
<br>
zz_pE&amp; <font color="#b02f60"><b>operator</b></font>*=(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a);<br>
zz_pE&amp; <font color="#b02f60"><b>operator</b></font>*=(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_p&amp; a);<br>
zz_pE&amp; <font color="#b02f60"><b>operator</b></font>*=(zz_pE&amp; x, <font color="#008b00"><b>long</b></font>&nbsp;a);<br>
<br>
<font color="#0000ed"><i>// procedural versions:</i></font><br>
<br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;mul(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; b); <font color="#0000ed"><i>// x = a * b</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;sqr(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a); <font color="#0000ed"><i>// x = a^2</i></font><br>
zz_pE sqr(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a); <br>
<br>
<font color="#0000ed"><i>// PROMOTIONS: *, mul promote {long, zz_p} to zz_pE on (a, b).</i></font><br>
<br>
<br>
<br>
<font color="#0000ed"><i>/*</i></font><font color="#0000ed"><i>*************************************************************************\</i></font><br>
<br>
<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Division</i></font><br>
<br>
<font color="#0000ed"><i>\*************************************************************************</i></font><font color="#0000ed"><i>*/</i></font><br>
<br>
<br>
<font color="#0000ed"><i>// operator notation:</i></font><br>
<br>
zz_pE <font color="#b02f60"><b>operator</b></font>/(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; b);<br>
<br>
zz_pE&amp; <font color="#b02f60"><b>operator</b></font>/=(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a);<br>
zz_pE&amp; <font color="#b02f60"><b>operator</b></font>/=(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_p&amp; a);<br>
zz_pE&amp; <font color="#b02f60"><b>operator</b></font>/=(zz_pE&amp; x, <font color="#008b00"><b>long</b></font>&nbsp;a);<br>
<br>
<br>
<font color="#0000ed"><i>// procedural versions:</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;div(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; b);<br>
<font color="#0000ed"><i>// x = a/b.&nbsp;&nbsp;If b is not invertible, an error is raised.</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;inv(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a);<br>
zz_pE inv(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a);<br>
<font color="#0000ed"><i>// x = 1/a</i></font><br>
<br>
<font color="#b02f60"><b>PROMOTIONS</b></font>:&nbsp;/, div promote {<font color="#008b00"><b>long</b></font>, zz_p} to zz_pE on (a, b).<br>
<br>
<br>
<font color="#0000ed"><i>/*</i></font><font color="#0000ed"><i>*************************************************************************\</i></font><br>
<br>
<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Exponentiation</i></font><br>
<br>
<font color="#0000ed"><i>\*************************************************************************</i></font><font color="#0000ed"><i>*/</i></font><br>
<br>
<br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;power(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;ZZ&amp; e); <br>
zz_pE power(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;ZZ&amp; e);<br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;power(zz_pE&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a, <font color="#008b00"><b>long</b></font>&nbsp;e); <br>
zz_pE power(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a, <font color="#008b00"><b>long</b></font>&nbsp;e);<br>
<br>
<font color="#0000ed"><i>// x = a^e (e may be negative)</i></font><br>
<br>
<br>
<br>
<font color="#0000ed"><i>/*</i></font><font color="#0000ed"><i>*************************************************************************\</i></font><br>
<br>
<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Random Elements</i></font><br>
<br>
<font color="#0000ed"><i>\*************************************************************************</i></font><font color="#0000ed"><i>*/</i></font><br>
<br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;random(zz_pE&amp; x);<br>
zz_pE random_zz_pE();<br>
<font color="#0000ed"><i>// x = random element in zz_pE.</i></font><br>
<br>
<font color="#0000ed"><i>/*</i></font><font color="#0000ed"><i>*************************************************************************\</i></font><br>
<br>
<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Norms and Traces</i></font><br>
<br>
<font color="#0000ed"><i>\*************************************************************************</i></font><font color="#0000ed"><i>*/</i></font><br>
<br>
<br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;trace(zz_p&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a);&nbsp;&nbsp;<font color="#0000ed"><i>// x = trace of a</i></font><br>
zz_p trace(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a);<br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;norm(zz_p&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a);&nbsp;&nbsp; <font color="#0000ed"><i>// x = norm of a</i></font><br>
zz_p norm(<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a);<br>
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<font color="#0000ed"><i>/*</i></font><font color="#0000ed"><i>*************************************************************************\</i></font><br>
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<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Input/Output</i></font><br>
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<font color="#0000ed"><i>\*************************************************************************</i></font><font color="#0000ed"><i>*/</i></font><br>
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ostream&amp; <font color="#b02f60"><b>operator</b></font>&lt;&lt;(ostream&amp; s, <font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; a);<br>
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istream&amp; <font color="#b02f60"><b>operator</b></font>&gt;&gt;(istream&amp; s, zz_pE&amp; x);<br>
<font color="#0000ed"><i>// a zz_pX is read and reduced mod p</i></font><br>
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<font color="#0000ed"><i>/*</i></font><font color="#0000ed"><i>*************************************************************************\</i></font><br>
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<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Modulus Switching </i></font><br>
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<font color="#0000ed"><i>A class zz_pEPush is provided for &quot;backing up&quot; the current modulus</i></font><br>
<font color="#0000ed"><i>and installing a new one.</i></font><br>
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<font color="#0000ed"><i>Here is what you do to save the current modulus, temporarily</i></font><br>
<font color="#0000ed"><i>set it to P, and automatically restore it:</i></font><br>
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<font color="#0000ed"><i>&nbsp;&nbsp; { </i></font><br>
<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;zz_pEPush push(P); </i></font><br>
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<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;...</i></font><br>
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<font color="#0000ed"><i>&nbsp;&nbsp; }</i></font><br>
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<font color="#0000ed"><i>The constructor for push will save the current modulus, and install P as the</i></font><br>
<font color="#0000ed"><i>current modulus.&nbsp;&nbsp;The destructor for push will restore the old modulus when the</i></font><br>
<font color="#0000ed"><i>scope enclosing it exits.&nbsp;&nbsp;This is the so-called RAII (resource acquisition is</i></font><br>
<font color="#0000ed"><i>initialization) paradigm.</i></font><br>
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<font color="#0000ed"><i>You could also do the following:</i></font><br>
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<font color="#0000ed"><i>&nbsp;&nbsp; {</i></font><br>
<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;zz_pEPush push; // just backup current modulus</i></font><br>
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<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;...</i></font><br>
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<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;zz_pE::init(P1); // install P1 </i></font><br>
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<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;...</i></font><br>
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<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;zz_pE::init(P2); // install P2</i></font><br>
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<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;// reinstall original modulus as close of scope</i></font><br>
<font color="#0000ed"><i>&nbsp;&nbsp; }</i></font><br>
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<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</i></font><br>
<font color="#0000ed"><i>The zz_pEPush interface is good for implementing simple stack-like</i></font><br>
<font color="#0000ed"><i>modulus &quot;context switching&quot;.&nbsp;&nbsp;For more general context switching,</i></font><br>
<font color="#0000ed"><i>see zz_pEContext below.&nbsp;&nbsp;There is also an older zz_pEBak class</i></font><br>
<font color="#0000ed"><i>that may also be useful.</i></font><br>
<br>
<font color="#0000ed"><i>..........................................................................</i></font><br>
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<font color="#0000ed"><i>It is critical that zz_pE objects created under one zz_pE modulus are not used in</i></font><br>
<font color="#0000ed"><i>any non-trivial way &quot;out of context&quot;, i.e., under a different (or undefined)</i></font><br>
<font color="#0000ed"><i>zz_pE modulus.&nbsp;&nbsp;However, for ease-of-use, some operations may be safely</i></font><br>
<font color="#0000ed"><i>performed out of context.&nbsp;&nbsp;These safe operations include: the default and copy</i></font><br>
<font color="#0000ed"><i>constructor, the destructor, and the assignment operator.&nbsp;&nbsp;In addition is is</i></font><br>
<font color="#0000ed"><i>generally safe to read any zz_pE object out of context (i.e., printing it out, or</i></font><br>
<font color="#0000ed"><i>fetching its underlying representive using the rep() function).</i></font><br>
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<font color="#0000ed"><i>Any unsafe uses out of context are not in general checked, and may </i></font><br>
<font color="#0000ed"><i>lead to unpredictable behavior.</i></font><br>
<br>
<br>
<font color="#0000ed"><i>\*************************************************************************</i></font><font color="#0000ed"><i>*/</i></font><br>
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<font color="#0000ed"><i>// A convenient interface for common cases</i></font><br>
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<font color="#008b00"><b>class</b></font>&nbsp;zz_pEPush {<br>
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<font color="#b02f60"><b>public</b></font>:<br>
zz_pEPush();&nbsp;&nbsp;<font color="#0000ed"><i>// backup current modulus</i></font><br>
<font color="#008b00"><b>explicit</b></font>&nbsp;zz_pEPush(<font color="#008b00"><b>const</b></font>&nbsp;zz_pX&amp; p); <br>
<font color="#008b00"><b>explicit</b></font>&nbsp;zz_pEPush(<font color="#008b00"><b>const</b></font>&nbsp;zz_pEContext&amp; context); <br>
&nbsp;&nbsp;<font color="#0000ed"><i>// backup current modulus and install the given one</i></font><br>
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<font color="#b02f60"><b>private</b></font>:<br>
zz_pEPush(<font color="#008b00"><b>const</b></font>&nbsp;zz_pEPush&amp;); <font color="#0000ed"><i>// disabled</i></font><br>
<font color="#008b00"><b>void</b></font>&nbsp;<font color="#b02f60"><b>operator</b></font>=(<font color="#008b00"><b>const</b></font>&nbsp;zz_pEPush&amp;); <font color="#0000ed"><i>// disabled</i></font><br>
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};<br>
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<font color="#0000ed"><i>// more general context switching:</i></font><br>
<font color="#0000ed"><i>// A zz_pEContext object has a modulus Q (possibly &quot;null&quot;),</i></font><br>
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<font color="#008b00"><b>class</b></font>&nbsp;zz_pEContext {<br>
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<font color="#b02f60"><b>public</b></font>:<br>
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zz_pEContext(); <font color="#0000ed"><i>// Q = &quot;null&quot;</i></font><br>
<font color="#008b00"><b>explicit</b></font>&nbsp;zz_pEContext(<font color="#008b00"><b>const</b></font>&nbsp;zz_pX&amp; P); <font color="#0000ed"><i>// Q = P</i></font><br>
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<font color="#008b00"><b>void</b></font>&nbsp;save(); <font color="#0000ed"><i>// Q = CurrentModulus</i></font><br>
<font color="#008b00"><b>void</b></font>&nbsp;restore() <font color="#008b00"><b>const</b></font>; <font color="#0000ed"><i>// CurrentModulus = Q</i></font><br>
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zz_pEContext(<font color="#008b00"><b>const</b></font>&nbsp;zz_pEContext&amp;);&nbsp;&nbsp;<font color="#0000ed"><i>// copy</i></font><br>
zz_pEContext&amp; <font color="#b02f60"><b>operator</b></font>=(<font color="#008b00"><b>const</b></font>&nbsp;zz_pEContext&amp;); <font color="#0000ed"><i>// assignment</i></font><br>
~zz_pEContext(); <font color="#0000ed"><i>// destructor</i></font><br>
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};<br>
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<font color="#0000ed"><i>// An older interface:</i></font><br>
<font color="#0000ed"><i>// To describe this logic, think of a zz_pEBak object</i></font><br>
<font color="#0000ed"><i>// of having two components: a modulus Q (possibly &quot;null&quot;) and </i></font><br>
<font color="#0000ed"><i>// an &quot;auto-restore bit&quot; b.</i></font><br>
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<font color="#008b00"><b>class</b></font>&nbsp;zz_pEBak {<br>
<font color="#b02f60"><b>public</b></font>:<br>
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&nbsp;&nbsp; zz_pEBak();&nbsp;&nbsp;<font color="#0000ed"><i>// Q = &quot;null&quot;, b = 0</i></font><br>
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&nbsp;&nbsp; ~zz_pEBak();&nbsp;&nbsp;<font color="#0000ed"><i>// if (b) CurrentModulus = Q</i></font><br>
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&nbsp;&nbsp; <font color="#008b00"><b>void</b></font>&nbsp;save();&nbsp;&nbsp;<font color="#0000ed"><i>// Q = CurrentModulus, b = 1 </i></font><br>
&nbsp;&nbsp; <font color="#008b00"><b>void</b></font>&nbsp;restore();&nbsp;&nbsp;<font color="#0000ed"><i>// CurrentModulus = Q, b = 0</i></font><br>
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<font color="#b02f60"><b>private</b></font>:<br>
&nbsp;&nbsp; zz_pEBak(<font color="#008b00"><b>const</b></font>&nbsp;zz_pEBak&amp;);&nbsp;&nbsp;<font color="#0000ed"><i>// copy disabled</i></font><br>
&nbsp;&nbsp; <font color="#008b00"><b>void</b></font>&nbsp;<font color="#b02f60"><b>operator</b></font>=(<font color="#008b00"><b>const</b></font>&nbsp;zz_pEBak&amp;);&nbsp;&nbsp;<font color="#0000ed"><i>// assignment disabled</i></font><br>
};<br>
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<font color="#0000ed"><i>/*</i></font><font color="#0000ed"><i>*************************************************************************\</i></font><br>
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<font color="#0000ed"><i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Miscellany</i></font><br>
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<font color="#0000ed"><i>\*************************************************************************</i></font><font color="#0000ed"><i>*/</i></font><br>
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<font color="#008b00"><b>void</b></font>&nbsp;clear(zz_pE&amp; x); <font color="#0000ed"><i>// x = 0</i></font><br>
<font color="#008b00"><b>void</b></font>&nbsp;set(zz_pE&amp; x); <font color="#0000ed"><i>// x = 1</i></font><br>
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<font color="#008b00"><b>static</b></font>&nbsp;<font color="#008b00"><b>const</b></font>&nbsp;zz_pE&amp; zz_pE::zero();<br>
<font color="#0000ed"><i>// zz_pE::zero() yields a read-only reference to zero</i></font><br>
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<font color="#008b00"><b>void</b></font>&nbsp;zz_pE::swap(zz_pE&amp; x);<br>
<font color="#008b00"><b>void</b></font>&nbsp;swap(zz_pE&amp; x, zz_pE&amp; y);<br>
<font color="#0000ed"><i>// swap (done by &quot;pointer swapping&quot;, if possible).</i></font><br>
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<font color="#008b00"><b>static</b></font>&nbsp;ZZ&amp; zz_pE::cardinality();<br>
<font color="#0000ed"><i>// yields the cardinality, i.e., p^{zz_pE::degree()}</i></font><br>
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zz_pE::zz_pE(INIT_NO_ALLOC_TYPE);<br>
<font color="#0000ed"><i>// special constructor: invoke as zz_pE x(INIT_NO_ALLOC);</i></font><br>
<font color="#0000ed"><i>// initializes x to 0, but allocates no space (this is now the default)</i></font><br>
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zz_pE::zz_pE(INIT_ALLOC_TYPE);<br>
<font color="#0000ed"><i>// special constructor: invoke as zz_pE x(INIT_ALLOC);</i></font><br>
<font color="#0000ed"><i>// initializes x to 0, but allocates space</i></font><br>
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zz_pE::allocate();<br>
<font color="#0000ed"><i>// useful in conjunction with the INIT_NO_ALLLOC constructor:</i></font><br>
<font color="#0000ed"><i>// x.allocate() will pre-allocate space for x, using the</i></font><br>
<font color="#0000ed"><i>// current modulus</i></font><br>
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