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<div class="ChapSects"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
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<h3>1 <span class="Heading">Introduction</span></h3>
<p>The <strong class="pkg">HAPprime</strong> package is a <strong class="pkg">GAP</strong> package which supplements the <strong class="pkg">HAP</strong> package (<span class="URL"><a href="http://hamilton.nuigalway.ie/Hap/www/">http://hamilton.nuigalway.ie/Hap/www/</a></span>), providing new and improved functions for doing homological algebra over small prime-power groups. A detailed overview of the <strong class="pkg">HAPprime</strong> package, with examples and documentation of the high-level functions, is provided in the accompanying <strong class="pkg">HAPprime</strong> user guide.</p>
<p>This document, the datatypes reference manual, supplements the <strong class="pkg">HAPprime</strong> user guide. It describes the new <strong class="pkg">GAP</strong> datatypes defined by the <strong class="pkg">HAPprime</strong> package, and all of the associated functions for working with each of these datatypes. The datatypes are</p>
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<dt><strong class="Mark"><code class="keyw">FpGModuleGF</code></strong></dt>
<dd><p>(Chapter <a href="chap5.html#X820435E87D83DF34"><b>5</b></a>) a free FG-module compactly represented in terms of generating elements, with operations that do as much manipulation as possible within this form, thus minimizing memory use.</p>
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<dt><strong class="Mark"><code class="keyw">FpGModuleHomomorphismGF</code></strong></dt>
<dd><p>(Chapter <a href="chap6.html#X82F28552819A6542"><b>6</b></a>) a free linear homomorphism between two FG-modules, each represented as a <code class="keyw">FpGModuleGF</code>. this also uses the compact generator form to save memory in its operations.</p>
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<dt><strong class="Mark"><code class="keyw">HAPResolution</code></strong></dt>
<dd><p>(Chapter <a href="chap2.html#X7C0B125E7D5415B4"><b>2</b></a>) this datatype, defined in the <strong class="pkg">HAP</strong> package, represents a free FG-resolution of a FG-module. <strong class="pkg">HAPprime</strong> extends the definition of this datatype to save memory, and provides additional functions to operate on resolutions.</p>
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<dt><strong class="Mark"><code class="keyw">HAPDerivation</code></strong></dt>
<dd><p>(Chapter <a href="chap8.html#X80C0FB5A7B72B145"><b>8</b></a>) a derivation over a polynomial ring R. In particular, <strong class="pkg">HAPprime</strong> provides functions to calculate the kernel and homology of derivations for polynomials over prime fields.</p>
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<p>In addition, Chapter <a href="chap10.html#X7B65E0C37AAB6066"><b>10</b></a> provides documentation for some general functions defined in <strong class="pkg">HAPprime</strong> which extend some of the basic <strong class="pkg">GAP</strong> functionality in areas such as matrices and polynomials.</p>
<p>Each chapter of this reference manual begins with an overview of the datatype, and then implementation details of any interesting functions. The function reference of related functions then follows, subdivided into sections of related functions. Examples demonstrating the use of each function are given at the end of each section.</p>
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