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<h1>cvec</h1>


<h2>Compact vectors over finite fields</h2>

<p>
    2.8.4</p>

<p>
    20 June 2025
  </p>

</div>
<p><b>
    Max Neunhöffer




  </b>
<br />Email: <span class="URL"><a href="mailto:max@9hoeffer.de">max@9hoeffer.de</a></span>
<br />Homepage: <span class="URL"><a href="http://www-groups.mcs.st-and.ac.uk/~neunhoef">http://www-groups.mcs.st-and.ac.uk/~neunhoef</a></span>
<br />Address: <br />Gustav-Freytag-Straße 40<br /> 50354 Hürth<br /> Germany<br />
</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2005-2014 by Max Neunhöffer</p>

<p><strong class="pkg">cvec</strong> is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.</p>

<p><strong class="pkg">cvec</strong> is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.</p>

<p>For a copy of the GNU General Public License, see the file <code class="file">LICENSE</code> included with this software, or see <span class="URL"><a href="https://www.gnu.org/licenses/gpl.html">https://www.gnu.org/licenses/gpl.html</a></span>.</p>

<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>

<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1_mj.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X873C99678745ABAF">1.1 <span class="Heading">Philosophy</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X786BACDB82918A65">1.2 <span class="Heading">Overview over this manual</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X80D704CC7EBFDF7A">1.3 <span class="Heading">Feedback</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2_mj.html#X81D63A85782CD477">2 <span class="Heading">Installation of the <strong class="pkg">cvec</strong>-Package</span></a>
</div>
<div class="ContChap"><a href="chap3_mj.html#X81F8AEBD87002F6F">3 <span class="Heading">The Data Structures</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7B9DCCCC83400B47">3.1 <span class="Heading">Finite field elements</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7ED5B368830755AF">3.2 <span class="Heading">Compressed Vectors in Memory</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X87968B277C5DF090">3.2-1 <span class="Heading">Packing of prime field elements</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7C195F41802266B7">3.2-2 <span class="Heading">Extension Fields</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X819040FD7BCBABB2">3.2-3 <span class="Heading">How is information about the base field stored?</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7DF0FE978626CE59">3.2-4 <span class="Heading">Limits that follow from the Data Format</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X78694256795D3A28">3.3 <span class="Heading">Compressed Matrices</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X783395FC81A451F3">3.4 <span class="Heading">External Representation of Matrices on Storage</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7B82906C7FFF36F5">3.4-1 <span class="Heading">Byte ordering and word length</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7ACD96C483D7DA8A">3.4-2 <span class="Heading">The header of a <code class="code">cmat</code> file</span></a>
</span>
</div></div>
</div>
<div class="ContChap"><a href="chap4_mj.html#X7D12102B824C97B4">4 <span class="Heading">Vectors</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X788B78DE82579F3D">4.1 <span class="Heading">Creation</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X83BF7BBC84478E77">4.1-1 CVec</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X83E8D01B82498337">4.1-2 CVec</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X826347BB7B81A06D">4.1-3 CVec</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X83E046D17AB12FF0">4.1-4 CVec</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X86642DDE797387E7">4.1-5 CVec</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7CC92B9E8286B025">4.1-6 CVec</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7B9566C1867C5EA6">4.1-7 CVecClass</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X78E5FA4881DE6D1A">4.1-8 CVecClass</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X871E42B97E3664EB">4.1-9 CVecClass</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X81C506327D635947">4.1-10 CVecClass</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X79F5D11E830B9768">4.1-11 CVecClass</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X87D5ABC1835C4A31">4.1-12 CVecClass</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X876613FC7A9A276C">4.1-13 ZeroSameMutability</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7BA2BD517C058720">4.1-14 ShallowCopy</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X84EBC4427913251F">4.1-15 Randomize</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X79862FF37B75BF48">4.2 <span class="Heading">Arithmetic</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X788A3D6482290F7D">4.2-1 <span class="Heading">Handling of scalars in arithmetic operations</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7C2F565480B1A4A1"><code>4.2-2 \+</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7CFEB1507E279EF2"><code>4.2-3 \-</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7DD3036C847E12DC">4.2-4 AdditiveInverseSameMutability</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7A34F9AA8330EBB9">4.2-5 AdditiveInverseMutable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8191F74E797B4A3D"><code>4.2-6 \*</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X820D829E87A82A80">4.2-7 AddRowVector</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X846D1EDA7B5B1B39">4.2-8 MultVector</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7F4B8B747E88C59B">4.2-9 ScalarProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X86115BE97842EC3B">4.2-10 ZeroMutable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7FB1A37D7F8603B9">4.2-11 ZeroVector</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7C68FFEC84A86786">4.3 <span class="Heading">Element access and slicing</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7A6A222E87452C27">4.3-1 ELM_LIST</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X78F1C2AE7A8DD868">4.3-2 ASS_LIST</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7D12C17C873DE3B4">4.3-3 ELMS_LIST</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X78878E5E839265A6">4.3-4 CVEC_Slice</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X80EC354D78D7B5A6">4.3-5 CopySubVector</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X84347D8B7DFA790C">4.3-6 CVEC_Concatenation</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X81F3C9697E5636B6">4.4 <span class="Heading">Comparison of Vectors and other information</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8155313286F88093">4.4-1 =</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X790D69A88340E510">4.4-2 LT</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X78952A3C788B7DB3">4.4-3 IsZero</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7F42E5AD87EC9D5A">4.4-4 PositionNonZero</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8370979D7F451279">4.4-5 PositionLastNonZero</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X780769238600AFD1">4.4-6 Length</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X80A1A9C386FD0E1B">4.5 <span class="Heading">Changing representation, Unpacking</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7BD632E57E1EB300">4.5-1 Unpack</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X850FB74483F87453">4.5-2 IntegerRep</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7FDFEF7A7E850151">4.5-3 NumberFFVector</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7E055C467B1B54D8">4.5-4 CVecNumber</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X853A85AE878B0CBF">4.6 <span class="Heading">Access to the base field</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X854192428704857E">4.6-1 BaseDomain</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X842335E47DC49702">4.6-2 BaseField</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X81B99EEC7C134213">4.6-3 Characteristic</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X81E3BBBB80096DC2">4.6-4 DegreeFFE</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X823EFBDB7ED49554">4.7 <span class="Heading">Hashing techniques for <code class="code">cvec</code>s</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7F0228A18327F87D">4.7-1 CVEC_HashFunctionForCVecs</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X82C8DE4C78B80B1E">4.7-2 ChooseHashFunction</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap5_mj.html#X812CCAB278643A59">5 <span class="Heading">Matrices</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X788B78DE82579F3D">5.1 <span class="Heading">Creation</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X85E5342B7E2C0E83">5.1-1 CMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X83220C57790E002F">5.1-2 CMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7BAB2E0A7D00D552">5.1-3 CMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X815BE0D27A5110FD">5.1-4 CMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7CB106397A3F21BE">5.1-5 CVEC_ZeroMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8045240986D4EF22">5.1-6 CVEC_IdentityMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X849B5B9B7BD65AA2">5.1-7 CVEC_RandomMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X78BD0AD885D4C2FF">5.1-8 MutableCopyMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X879384D479EB1D82">5.1-9 Matrix</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7C9F7D327BAECA5E">5.2 <span class="Heading">Matrices as lists</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X795EC9D67E34DAB0">5.2-1 Add</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7E98B11B79BA9167">5.2-2 Remove</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X80ED7496817F0E16">5.2-3 ELM_LIST</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X80748BB47CB7FA59">5.2-4 ASS_LIST</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X83C78ABB810BBF5B">5.2-5 ELMS_LIST</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X79E164537CC34B14">5.2-6 ASSS_LIST</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7E22E27979A2DD7C">5.2-7 Length</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X846BC7107C352031">5.2-8 ShallowCopy</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7ECE9056792F28BA">5.2-9 Collected</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8727F2928467C2F9">5.2-10 DuplicateFreeList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X79E31DB27C82D6E1">5.2-11 Append</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7C86D7F7795125F0">5.2-12 Filtered</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X82AACD43853C24D1">5.2-13 Unbind</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X79862FF37B75BF48">5.3 <span class="Heading">Arithmetic</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X819B1A8A7DE1EE88"><code>5.3-1 \+</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X814AFD8E8377D4DB"><code>5.3-2 \-</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X82AFC3A987140922">5.3-3 AdditiveInverseSameMutability</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8548396F7D4CAC21">5.3-4 AdditiveInverseMutable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X848404F57FBFFE7A"><code>5.3-5 \*</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7DAFB0227C5529C6"><code>5.3-6 \*</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8255927C7923A294"><code>5.3-7 \^</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7F673C397A919D81"><code>5.3-8 \*</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X781AD339797C0625">5.3-9 ZeroSameMutability</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X796D9B2C83C0667B">5.3-10 ZeroMutable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7ED3BC7D8198EE2E">5.3-11 OneSameMutability</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7FBD3ABF80EB659C">5.3-12 OneMutable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X78F9A4028122E39B">5.3-13 InverseMutable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8593B0F886BBD8A7">5.3-14 InverseSameMutability</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X87F304F3826A7063">5.3-15 TransposedMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8634C79E7DB22934">5.3-16 KroneckerProduct</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X845009E07A011131">5.4 <span class="Heading">Comparison of matrices and other information</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7E2074A77AFF518A">5.4-1 =</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7AA30F9B7CA1A376">5.4-2 LT</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X86A0FAA57E4C26FC">5.4-3 IsZero</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X814D78347858EC13">5.4-4 IsOne</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7FF01BF686AD0623">5.4-5 IsDiagonalMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7ECFBD9F8664982B">5.4-6 IsUpperTriangularMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X81671CFD7CFE4819">5.4-7 IsLowerTriangularMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X875B076C8559CAF0">5.4-8 CVEC_HashFunctionForCMats</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7D5E6AF77B09AB35">5.4-9 ChooseHashFunction</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7B54DF167CFC6C0F">5.5 <span class="Heading">Slicing and submatrices</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X838B45F7790E9FDF">5.5-1 ExtractSubMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7ED9E5D4809E3B50">5.5-2 CopySubMatrix</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X805F24017D4348E2">5.6 <span class="Heading">Information about matrices</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7B5FF52186205C5E">5.6-1 BaseField</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7EC55E298313BCB1">5.6-2 Characteristic</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7E9F7B7E7BEDA69E">5.6-3 DegreeFFE</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7C6624AF7CEAA74D">5.6-4 DefaultField</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X78DA04477DDD0ACE">5.7 <span class="Heading">Input and output</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7DF1D51F7924429A">5.7-1 CVEC_WriteMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X794D936C7E99F805">5.7-2 CVEC_WriteMatToFile</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X78F898D17D9E522C">5.7-3 CVEC_WriteMatsToFile</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X79E47CB5831D48CC">5.7-4 CVEC_ReadMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X824FA01878D60EE1">5.7-5 CVEC_ReadMatFromFile</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X79397B1D78E0746A">5.7-6 CVEC_ReadMatsFromFile</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7DA0D38A7D5DBDFF">5.8 <span class="Heading">Grease</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7DF5A56F8747DD45">5.8-1 GreaseMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7E8A9C7E7E014FC7">5.8-2 UnGreaseMat</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7A0D26B180BEDE37">5.9 <span class="Heading">Everything else</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7B97048782F7EE43">5.9-1 Randomize</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8114198F7D6486CB">5.9-2 OverviewMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X84AAF220841589D9">5.9-3 Unpack</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap6_mj.html#X8571243581CAD780">6 <span class="Heading">Linear Algebra routines</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X79C4BA5B821BBE58">6.1 <span class="Heading">Semi echelonised bases and cleaning</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X87855EEA8779C855">6.1-1 EmptySemiEchelonBasis</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7D12102B824C97B4">6.1-2 Vectors</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X8464F2B87BCA3D34">6.1-3 Length</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7F4EA39D7D18D9B7">6.1-4 CleanRow</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X826541AA7FD12F9B">6.1-5 SemiEchelonBasisMutable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X82A37BC982B1D8CA">6.1-6 SemiEchelonBasisMutable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X839298477E3F7345">6.1-7 SemiEchelonBasisMutableX</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X8309FC85858FC96B">6.1-8 SemiEchelonBasisMutableT</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X845EFC3B87BED1BB">6.1-9 SemiEchelonBasisMutableTX</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X837F20C4831FA08E">6.1-10 SemiEchelonBasisMutableP</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X8218306B812EB85E">6.1-11 SemiEchelonBasisMutablePX</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7E5C2C297CAAE3FB">6.1-12 MutableNullspaceMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7A9596C98725862E">6.1-13 MutableNullspaceMatX</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7DA0D5887DB12DC4">6.1-14 NullspaceMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X87684B0F7AB7B7DB">6.1-15 NullspaceMatDestructive</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X825613828322BD22">6.2 <span class="Heading">Characteristic and minimal polynomial</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7BB7DCBF78177638">6.2-1 CharacteristicPolynomialOfMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7FE2A9D281A74FDD">6.2-2 FactorsOfCharacteristicPolynomial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7A110EA07A2EC59C">6.2-3 MinimalPolynomialOfMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X862C6AA0794E41C4">6.2-4 CharAndMinimalPolynomialOfMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X839407B37A85AAC8">6.2-5 MinimalPolynomialOfMatrixMC</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap7_mj.html#X854F8C5579845066">7 <span class="Heading">Performance</span></a>
</div>
<div class="ContChap"><a href="chap8_mj.html#X865BC7FE84250875">8 <span class="Heading">Cooperation with the <strong class="pkg">GAP</strong> library</span></a>
</div>
<div class="ContChap"><a href="chap9_mj.html#X7A489A5D79DA9E5C">9 <span class="Heading">Examples</span></a>
</div>
<div class="ContChap"><a href="chapInd_mj.html"><span class="Heading">Index</span></a></div>
<br />
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