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<!-- doxytag: class="LinBox::LidiaGfq" --><!-- doxytag: inherits="LinBox::FieldInterface" -->
<p>defines the Galois Field GF(p<sup>k</sup>).
<a href="class_lin_box_1_1_lidia_gfq.html#details">More...</a></p>
<p><code>#include <lidia-gfq.h></code></p>
<div id="dynsection-0" onclick="return toggleVisibility(this)" class="dynheader closed" style="cursor:pointer;">
<img id="dynsection-0-trigger" src="closed.png"/> Inheritance diagram for LidiaGfq:</div>
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<img src="class_lin_box_1_1_lidia_gfq.png" usemap="#LidiaGfq_map" alt=""/>
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<area href="class_lin_box_1_1_field_interface.html" title="This field base class exists solely to aid documentation organization." alt="FieldInterface" shape="rect" coords="0,0,90,24"/>
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<table class="memberdecls">
<tr><td colspan="2"><h2><a name="pub-types"></a>
Public Types</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">typedef LiDIA::gf_element </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Element type. <a href="#ade9f4af95ff70d278a9a7b0967586159"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ae785cc15d91b623ae90d44625cc53a3b"></a><!-- doxytag: member="LinBox::LidiaGfq::RandIter" ref="ae785cc15d91b623ae90d44625cc53a3b" args="" -->
typedef LidiaGfqRandIter<br class="typebreak"/>
< <a class="el" href="class_lin_box_1_1_lidia_gfq.html">LidiaGfq</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ae785cc15d91b623ae90d44625cc53a3b">RandIter</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Random element generator which is define in the wrapper LIDIA_randiter. <br/></td></tr>
<tr><td colspan="2"><h2><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a91917bb42f6b6446d056c44e36d27985"></a><!-- doxytag: member="LinBox::LidiaGfq::LidiaGfq" ref="a91917bb42f6b6446d056c44e36d27985" args="()" -->
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a91917bb42f6b6446d056c44e36d27985">LidiaGfq</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default constructor of the field. <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ac71c8f2f9206c49329a53d71088325ee">LidiaGfq</a> (const <a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> &p, const <a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> &k=1)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Constructor of GF(p^k). <a href="#ac71c8f2f9206c49329a53d71088325ee"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a508b58a10c2a590db2d7f8ae324de8d8"></a><!-- doxytag: member="LinBox::LidiaGfq::LidiaGfq" ref="a508b58a10c2a590db2d7f8ae324de8d8" args="(const LidiaGfq &F)" -->
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a508b58a10c2a590db2d7f8ae324de8d8">LidiaGfq</a> (const <a class="el" href="class_lin_box_1_1_lidia_gfq.html">LidiaGfq</a> &F)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Copy constructor. <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a72360c0948cf618508d806476578ccf2"></a><!-- doxytag: member="LinBox::LidiaGfq::~LidiaGfq" ref="a72360c0948cf618508d806476578ccf2" args="()" -->
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a72360c0948cf618508d806476578ccf2">~LidiaGfq</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Destructor. <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html">LidiaGfq</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a44da942e1eea93f6c806970257606602">operator=</a> (const <a class="el" href="class_lin_box_1_1_lidia_gfq.html">LidiaGfq</a> &F)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Assignment operator. <a href="#a44da942e1eea93f6c806970257606602"></a><br/></td></tr>
<tr><td colspan="2"><div class="groupHeader">Object management</div></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a59892db11d283587e8b9e3656f0c6f7f">init</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x, const <a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> &y=0) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Initialization of field Element from an integer. <a href="#a59892db11d283587e8b9e3656f0c6f7f"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ac4bb2576b5123c8fde1fab6165264ec3">convert</a> (<a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> &x, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &y) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Conversion of field base Element to an integer. <a href="#ac4bb2576b5123c8fde1fab6165264ec3"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a7ed3d5d8b4d9f1ab407365c020b18c58">assign</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &y) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Assignment of one field Element to another. <a href="#a7ed3d5d8b4d9f1ab407365c020b18c58"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade46ce0a344fcc718625a2296a8104ab">cardinality</a> (<a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> &c) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Cardinality. <a href="#ade46ce0a344fcc718625a2296a8104ab"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#aea4d4c3f059080408c3a6344cf9fff10">characteristic</a> (<a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> &c) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Characteristic. <a href="#aea4d4c3f059080408c3a6344cf9fff10"></a><br/></td></tr>
<tr><td colspan="2"><div class="groupHeader">Arithmetic Operations</div></td></tr>
<tr><td colspan="2"><div class="groupText"><p>x <- y op z; x <- op y These operations require all Elements, including x, to be initialized before the operation is called.</p>
<p>Uninitialized field Elements will give undefined results. </p>
</div></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a0763bd76c2ed93bc54973d632b98ec90">areEqual</a> (const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &y) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Equality of two Elements. <a href="#a0763bd76c2ed93bc54973d632b98ec90"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#aadf4e83f1ac414b0caa1bef2154dabdb">add</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &y, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &z) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Addition. <a href="#aadf4e83f1ac414b0caa1bef2154dabdb"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a2f2a41d18bd65f48cb5fb894fcd3b51b">sub</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &y, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &z) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Subtraction. <a href="#a2f2a41d18bd65f48cb5fb894fcd3b51b"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#adf251fca0ae6bc767b0e9c5f2d6081f7">mul</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &y, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &z) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Multiplication. <a href="#adf251fca0ae6bc767b0e9c5f2d6081f7"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a4d8f0ac0be4b8a5a074f441d74bf4276">div</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &y, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &z) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Division. <a href="#a4d8f0ac0be4b8a5a074f441d74bf4276"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a608fc0675ac7788b016f686fa3a6ec7e">neg</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &y) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Additive <a class="el" href="class_lin_box_1_1_inverse.html" title="A Blackbox for the inverse.">Inverse</a> (Negation). <a href="#a608fc0675ac7788b016f686fa3a6ec7e"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a9b2e67d87131ae67539834cd9cd3fa7a">inv</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &y) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Multiplicative <a class="el" href="class_lin_box_1_1_inverse.html" title="A Blackbox for the inverse.">Inverse</a>. <a href="#a9b2e67d87131ae67539834cd9cd3fa7a"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a09806701a7acb018cd70b179635720da">axpy</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &r, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &a, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &y) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Natural AXPY. <a href="#a09806701a7acb018cd70b179635720da"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a0865272ef30f366f2a7a06323ee7cc22">isZero</a> (const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Zero equality. <a href="#a0865272ef30f366f2a7a06323ee7cc22"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ab37695d9e0fb5b0064c85e8449ed596b">isOne</a> (const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">One equality. <a href="#ab37695d9e0fb5b0064c85e8449ed596b"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a25ec1b0d3d2d8da69636a121ef781a55">addin</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &y) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Inplace Addition. <a href="#a25ec1b0d3d2d8da69636a121ef781a55"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#aa14037ab7a2e80c0e663a760acbaff15">subin</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &y) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Inplace Subtraction. <a href="#aa14037ab7a2e80c0e663a760acbaff15"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a6e17c2a1321787d89a51b9f0eee0f408">mulin</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &y) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Inplace Multiplication. <a href="#a6e17c2a1321787d89a51b9f0eee0f408"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ac5966c66651795d1636a032e8bcd28ef">divin</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &y) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Inplace Division. <a href="#ac5966c66651795d1636a032e8bcd28ef"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a540bdfc0ce896b62d1a13247a2acfce2">negin</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Inplace Additive <a class="el" href="class_lin_box_1_1_inverse.html" title="A Blackbox for the inverse.">Inverse</a> (Inplace Negation). <a href="#a540bdfc0ce896b62d1a13247a2acfce2"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#acf833d5877bb610fef71aac14074d5ce">invin</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Inplace Multiplicative <a class="el" href="class_lin_box_1_1_inverse.html" title="A Blackbox for the inverse.">Inverse</a>. <a href="#acf833d5877bb610fef71aac14074d5ce"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a2a6378ec17b22af66cfa5e6901461cd1">axpyin</a> (<a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &r, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &a, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &x) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Inplace AXPY. <a href="#a2a6378ec17b22af66cfa5e6901461cd1"></a><br/></td></tr>
<tr><td colspan="2"><div class="groupHeader">Input/Output Operations</div></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">std::ostream & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#acd22def76f55c19076bb6c86104beaf0">write</a> (std::ostream &os) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Print field. <a href="#acd22def76f55c19076bb6c86104beaf0"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">std::istream & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#afed7ab1451380411e8e013b34a8adeee">read</a> (std::istream &is) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Read field. <a href="#afed7ab1451380411e8e013b34a8adeee"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">std::ostream & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a6ede1db1119b00f6cb2c78de8e971376">write</a> (std::ostream &os, const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &e) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Print field Element like a polynom. <a href="#a6ede1db1119b00f6cb2c78de8e971376"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">std::istream & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#a3c2869f376d743bcf539cd3cf46852bb">read</a> (std::istream &is, <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> &e) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Read field Element. <a href="#a3c2869f376d743bcf539cd3cf46852bb"></a><br/></td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>defines the Galois Field GF(p<sup>k</sup>). </p>
<p>Inherits from <code>galois_field</code> of <a class="el" href="group___li_d_i_a.html">LiDIA</a>. </p>
<dl class="pre"><dt><b>Precondition:</b></dt><dd><code>p</code> must be prime. </dd></dl>
</div><hr/><h2>Member Typedef Documentation</h2>
<a class="anchor" id="ade9f4af95ff70d278a9a7b0967586159"></a><!-- doxytag: member="LinBox::LidiaGfq::Element" ref="ade9f4af95ff70d278a9a7b0967586159" args="" -->
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<td class="memname">typedef LiDIA::gf_element <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a></td>
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<p>Element type. </p>
<p>This type is inherited from the LiDIA class LiDIA::gf_element </p>
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<hr/><h2>Constructor & Destructor Documentation</h2>
<a class="anchor" id="ac71c8f2f9206c49329a53d71088325ee"></a><!-- doxytag: member="LinBox::LidiaGfq::LidiaGfq" ref="ac71c8f2f9206c49329a53d71088325ee" args="(const integer &p, const integer &k=1)" -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html">LidiaGfq</a> </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td>
<td class="paramname"><em>p</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td>
<td class="paramname"><em>k</em> = <code>1</code> </td>
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<td>)</td>
<td></td><td><code> [inline]</code></td>
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<p>Constructor of GF(p^k). </p>
<p>A GF(p^k) field is constructed through the constructor of LiDIA LiDIA::galois_field We need a double cast to pass integer arguments to the LiDIA constructor </p>
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<hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="a44da942e1eea93f6c806970257606602"></a><!-- doxytag: member="LinBox::LidiaGfq::operator=" ref="a44da942e1eea93f6c806970257606602" args="(const LidiaGfq &F)" -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html">LidiaGfq</a>& operator= </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html">LidiaGfq</a> & </td>
<td class="paramname"><em>F</em></td><td>)</td>
<td><code> [inline]</code></td>
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<p>Assignment operator. </p>
<p>Assigns unparam_field object F to field. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">F</td><td>unparam_field object. </td></tr>
</table>
</dd>
</dl>
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</div>
<a class="anchor" id="a59892db11d283587e8b9e3656f0c6f7f"></a><!-- doxytag: member="LinBox::LidiaGfq::init" ref="a59892db11d283587e8b9e3656f0c6f7f" args="(Element &x, const integer &y=0) const " -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a>& init </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td>
<td class="paramname"><em>y</em> = <code>0</code> </td>
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<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
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<p>Initialization of field Element from an integer. </p>
<p>Behaves like C++ allocator construct. This function assumes the output field Element x has already been constructed, but that it is not already initialized. We also need to define the Element over the field. So what we always initialize the Element with the zero field value. If an integer different from zero is passed to the function the Element is initialized to a constant polynom of Z/pZ </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to field Element. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element to contain output (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>integer. </td></tr>
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</dd>
</dl>
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<a class="anchor" id="ac4bb2576b5123c8fde1fab6165264ec3"></a><!-- doxytag: member="LinBox::LidiaGfq::convert" ref="ac4bb2576b5123c8fde1fab6165264ec3" args="(integer &x, const Element &y) const " -->
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<td class="memname"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a>& convert </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td>
<td class="paramname"><em>x</em>, </td>
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<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>y</em> </td>
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<td>)</td>
<td></td><td> const<code> [inline]</code></td>
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<p>Conversion of field base Element to an integer. </p>
<p>This function assumes the output field base Element x has already been constructed, but that it is not already initialized. As Elements are represented by polynom the convert function return the valuation of polynom in characteristic by the Horner <a class="el" href="struct_lin_box_1_1_method.html" title="Method specifiers for controlling algorithm choice.">Method</a>. That keeps unicity of each Element. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to an integer. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>integer to contain output (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>constant field base Element. </td></tr>
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</dd>
</dl>
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<a class="anchor" id="a7ed3d5d8b4d9f1ab407365c020b18c58"></a><!-- doxytag: member="LinBox::LidiaGfq::assign" ref="a7ed3d5d8b4d9f1ab407365c020b18c58" args="(Element &x, const Element &y) const " -->
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<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
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<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>y</em> </td>
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<td>)</td>
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<p>Assignment of one field Element to another. </p>
<p>This function assumes both field Elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>field Element. </td></tr>
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</dd>
</dl>
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<a class="anchor" id="ade46ce0a344fcc718625a2296a8104ab"></a><!-- doxytag: member="LinBox::LidiaGfq::cardinality" ref="ade46ce0a344fcc718625a2296a8104ab" args="(integer &c) const " -->
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<p>Cardinality. </p>
<p>Return integer representing cardinality of the field. Returns p^k. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>constant reference to integer representing cardinality of the field. </dd></dl>
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<a class="anchor" id="aea4d4c3f059080408c3a6344cf9fff10"></a><!-- doxytag: member="LinBox::LidiaGfq::characteristic" ref="aea4d4c3f059080408c3a6344cf9fff10" args="(integer &c) const " -->
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<td> const<code> [inline]</code></td>
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<p>Characteristic. </p>
<p>Return integer representing characteristic of the field. Returns p. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>constant reference to integer representing characteristic of the field. </dd></dl>
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<a class="anchor" id="a0763bd76c2ed93bc54973d632b98ec90"></a><!-- doxytag: member="LinBox::LidiaGfq::areEqual" ref="a0763bd76c2ed93bc54973d632b98ec90" args="(const Element &x, const Element &y) const " -->
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<td class="paramname"><em>x</em>, </td>
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<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>y</em> </td>
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<td>)</td>
<td></td><td> const<code> [inline]</code></td>
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<p>Equality of two Elements. </p>
<p>This function assumes both field Elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>boolean true if equal, false if not. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element </td></tr>
<tr><td class="paramname">y</td><td>field Element </td></tr>
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</dd>
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<a class="anchor" id="aadf4e83f1ac414b0caa1bef2154dabdb"></a><!-- doxytag: member="LinBox::LidiaGfq::add" ref="aadf4e83f1ac414b0caa1bef2154dabdb" args="(Element &x, const Element &y, const Element &z) const " -->
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<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>y</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>z</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Addition. </p>
<p>x = y + z This function assumes all the field Elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>field Element. </td></tr>
<tr><td class="paramname">z</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a2f2a41d18bd65f48cb5fb894fcd3b51b"></a><!-- doxytag: member="LinBox::LidiaGfq::sub" ref="a2f2a41d18bd65f48cb5fb894fcd3b51b" args="(Element &x, const Element &y, const Element &z) const " -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a>& sub </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>y</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>z</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Subtraction. </p>
<p>x = y - z This function assumes all the field Elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>field Element. </td></tr>
<tr><td class="paramname">z</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="adf251fca0ae6bc767b0e9c5f2d6081f7"></a><!-- doxytag: member="LinBox::LidiaGfq::mul" ref="adf251fca0ae6bc767b0e9c5f2d6081f7" args="(Element &x, const Element &y, const Element &z) const " -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a>& mul </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>y</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>z</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Multiplication. </p>
<p>x = y * z This function assumes all the field Elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>field Element. </td></tr>
<tr><td class="paramname">z</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a4d8f0ac0be4b8a5a074f441d74bf4276"></a><!-- doxytag: member="LinBox::LidiaGfq::div" ref="a4d8f0ac0be4b8a5a074f441d74bf4276" args="(Element &x, const Element &y, const Element &z) const " -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a>& div </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>y</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>z</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Division. </p>
<p>x = y / z This function assumes all the field Elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>field Element. </td></tr>
<tr><td class="paramname">z</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a608fc0675ac7788b016f686fa3a6ec7e"></a><!-- doxytag: member="LinBox::LidiaGfq::neg" ref="a608fc0675ac7788b016f686fa3a6ec7e" args="(Element &x, const Element &y) const " -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a>& neg </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>y</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Additive <a class="el" href="class_lin_box_1_1_inverse.html" title="A Blackbox for the inverse.">Inverse</a> (Negation). </p>
<p>x = - y This function assumes both field Elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a9b2e67d87131ae67539834cd9cd3fa7a"></a><!-- doxytag: member="LinBox::LidiaGfq::inv" ref="a9b2e67d87131ae67539834cd9cd3fa7a" args="(Element &x, const Element &y) const " -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a>& inv </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>y</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Multiplicative <a class="el" href="class_lin_box_1_1_inverse.html" title="A Blackbox for the inverse.">Inverse</a>. </p>
<p>x = 1 / y This function assumes both field Elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a09806701a7acb018cd70b179635720da"></a><!-- doxytag: member="LinBox::LidiaGfq::axpy" ref="a09806701a7acb018cd70b179635720da" args="(Element &r, const Element &a, const Element &x, const Element &y) const " -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a>& axpy </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>r</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>y</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
</tr>
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</div>
<div class="memdoc">
<p>Natural AXPY. </p>
<p>r = a * x + y This function assumes all field Elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to r. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">r</td><td>field Element (reference returned). </td></tr>
<tr><td class="paramname">a</td><td>field Element. </td></tr>
<tr><td class="paramname">x</td><td>field Element. </td></tr>
<tr><td class="paramname">y</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a0865272ef30f366f2a7a06323ee7cc22"></a><!-- doxytag: member="LinBox::LidiaGfq::isZero" ref="a0865272ef30f366f2a7a06323ee7cc22" args="(const Element &x) const " -->
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<td class="memname">bool isZero </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em></td><td>)</td>
<td> const<code> [inline]</code></td>
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<div class="memdoc">
<p>Zero equality. </p>
<p>Test if field Element is equal to zero of field. This function assumes the field Element has already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>boolean true if equals zero of field, false if not. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="ab37695d9e0fb5b0064c85e8449ed596b"></a><!-- doxytag: member="LinBox::LidiaGfq::isOne" ref="ab37695d9e0fb5b0064c85e8449ed596b" args="(const Element &x) const " -->
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<td class="memname">bool isOne </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em></td><td>)</td>
<td> const<code> [inline]</code></td>
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<div class="memdoc">
<p>One equality. </p>
<p>Test if field Element is equal to one of field. This function assumes the field Element has already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>boolean true if equals one of field, false if not. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a25ec1b0d3d2d8da69636a121ef781a55"></a><!-- doxytag: member="LinBox::LidiaGfq::addin" ref="a25ec1b0d3d2d8da69636a121ef781a55" args="(Element &x, const Element &y) const " -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a>& addin </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>y</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
</tr>
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<div class="memdoc">
<p>Inplace Addition. </p>
<p>x += y This function assumes both field Elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="aa14037ab7a2e80c0e663a760acbaff15"></a><!-- doxytag: member="LinBox::LidiaGfq::subin" ref="aa14037ab7a2e80c0e663a760acbaff15" args="(Element &x, const Element &y) const " -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a>& subin </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>y</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
</tr>
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<div class="memdoc">
<p>Inplace Subtraction. </p>
<p>x -= y This function assumes both field Elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a6e17c2a1321787d89a51b9f0eee0f408"></a><!-- doxytag: member="LinBox::LidiaGfq::mulin" ref="a6e17c2a1321787d89a51b9f0eee0f408" args="(Element &x, const Element &y) const " -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a>& mulin </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>y</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
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<div class="memdoc">
<p>Inplace Multiplication. </p>
<p>x *= y This function assumes both field Elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="ac5966c66651795d1636a032e8bcd28ef"></a><!-- doxytag: member="LinBox::LidiaGfq::divin" ref="ac5966c66651795d1636a032e8bcd28ef" args="(Element &x, const Element &y) const " -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a>& divin </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>y</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Inplace Division. </p>
<p>x /= y This function assumes both field Elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a540bdfc0ce896b62d1a13247a2acfce2"></a><!-- doxytag: member="LinBox::LidiaGfq::negin" ref="a540bdfc0ce896b62d1a13247a2acfce2" args="(Element &x) const " -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a>& negin </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em></td><td>)</td>
<td> const<code> [inline]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Inplace Additive <a class="el" href="class_lin_box_1_1_inverse.html" title="A Blackbox for the inverse.">Inverse</a> (Inplace Negation). </p>
<p>x = - x This function assumes the field Element has already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element (reference returned). </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="acf833d5877bb610fef71aac14074d5ce"></a><!-- doxytag: member="LinBox::LidiaGfq::invin" ref="acf833d5877bb610fef71aac14074d5ce" args="(Element &x) const " -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a>& invin </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em></td><td>)</td>
<td> const<code> [inline]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Inplace Multiplicative <a class="el" href="class_lin_box_1_1_inverse.html" title="A Blackbox for the inverse.">Inverse</a>. </p>
<p>x = 1 / x This function assumes the field Elementhas already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field Element (reference returned). </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a2a6378ec17b22af66cfa5e6901461cd1"></a><!-- doxytag: member="LinBox::LidiaGfq::axpyin" ref="a2a6378ec17b22af66cfa5e6901461cd1" args="(Element &r, const Element &a, const Element &x) const " -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a>& axpyin </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>r</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>x</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
</tr>
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<p>Inplace AXPY. </p>
<p>r += a * x This function assumes all field Elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to r. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">r</td><td>field Element (reference returned). </td></tr>
<tr><td class="paramname">a</td><td>field Element. </td></tr>
<tr><td class="paramname">x</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="acd22def76f55c19076bb6c86104beaf0"></a><!-- doxytag: member="LinBox::LidiaGfq::write" ref="acd22def76f55c19076bb6c86104beaf0" args="(std::ostream &os) const " -->
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<td class="memname">std::ostream& write </td>
<td>(</td>
<td class="paramtype">std::ostream & </td>
<td class="paramname"><em>os</em></td><td>)</td>
<td> const<code> [inline]</code></td>
</tr>
</table>
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<div class="memdoc">
<p>Print field. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>output stream to which field is written. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">os</td><td>output stream to which field is written. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="afed7ab1451380411e8e013b34a8adeee"></a><!-- doxytag: member="LinBox::LidiaGfq::read" ref="afed7ab1451380411e8e013b34a8adeee" args="(std::istream &is) const " -->
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<td class="memname">std::istream& read </td>
<td>(</td>
<td class="paramtype">std::istream & </td>
<td class="paramname"><em>is</em></td><td>)</td>
<td> const<code> [inline]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Read field. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>input stream from which field is read. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">is</td><td>input stream from which field is read. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a6ede1db1119b00f6cb2c78de8e971376"></a><!-- doxytag: member="LinBox::LidiaGfq::write" ref="a6ede1db1119b00f6cb2c78de8e971376" args="(std::ostream &os, const Element &e) const " -->
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<td class="memname">std::ostream& write </td>
<td>(</td>
<td class="paramtype">std::ostream & </td>
<td class="paramname"><em>os</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>e</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Print field Element like a polynom. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>output stream to which field Element is written. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">os</td><td>output stream to which field Element is written. </td></tr>
<tr><td class="paramname">e</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a3c2869f376d743bcf539cd3cf46852bb"></a><!-- doxytag: member="LinBox::LidiaGfq::read" ref="a3c2869f376d743bcf539cd3cf46852bb" args="(std::istream &is, Element &e) const " -->
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<td class="memname">std::istream& read </td>
<td>(</td>
<td class="paramtype">std::istream & </td>
<td class="paramname"><em>is</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_lidia_gfq.html#ade9f4af95ff70d278a9a7b0967586159">Element</a> & </td>
<td class="paramname"><em>e</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Read field Element. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>input stream from which field Element is read. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">is</td><td>input stream from which field Element is read. </td></tr>
<tr><td class="paramname">e</td><td>field Element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="field_2lidia-gfq_8h.html">field/lidia-gfq.h</a></li>
</ul>
</div>
<hr class="footer"/><address class="footer"><small>Generated on Tue Aug 30 2011 for linbox by 
<a href="http://www.doxygen.org/index.html">
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