<p>In 1950 S. MacLane and J.H.C. Whitehead, <a href="chapBib_mj.html#biBwhitehead">[Whi49]</a> suggested that crossed modules modeled homotopy <span class="SimpleMath">\(2\)</span>-types. Later crossed modules have been considered as <span class="SimpleMath">\(2\)</span><em>-dimensional groups</em>, <a href="chapBib_mj.html#biBbrown1">[Bro82]</a>, <a href="chapBib_mj.html#biBbrown2">[Bro87]</a>. The commutative algebra version of this construction has been adapted by T. Porter, <a href="chapBib_mj.html#biBarvasi2">[AP96]</a>, <a href="chapBib_mj.html#biBporter1">[Por87]</a>. This algebraic version is called <em>combinatorial algebra theory</em>, which contains potentially important new ideas (see <a href="chapBib_mj.html#biBshammu1">[Sha92]</a>, <a href="chapBib_mj.html#biBarvasi2">[AP96]</a>, <a href="chapBib_mj.html#biBarvasi3">[AP98]</a>, <a href="chapBib_mj.html#biBarvasi4">[AE03]</a>).</p>
<p>A share package <strong class="pkg">XMod</strong>, <a href="chapBib_mj.html#biBalp3">[AOUW17]</a>, <a href="chapBib_mj.html#biBalp2">[AW00]</a>, was prepared by M. Alp and C.D. Wensley for the <strong class="pkg">GAP</strong> computational group theory language, initially for <strong class="pkg">GAP</strong>3 then revised for <strong class="pkg">GAP</strong>4. The <span class="SimpleMath">\(2\)</span>-dimensional part of this programme contains functions for computing crossed modules and cat<span class="SimpleMath">\(^{1}\)</span>-groups and their morphisms <a href="chapBib_mj.html#biBalp3">[AOUW17]</a>.</p>
<p>This package includes functions for computing crossed modules of algebras, cat<span class="SimpleMath">\(^{1}\)</span>-algebras and their morphisms by analogy with <em>computational group theory</em>. We will concentrate on group rings over of abelian groups over finite fields because these algebras are conveniently implemented in <strong class="pkg">GAP</strong>. The tools needed are the group algebras in which the group algebra functor <span class="SimpleMath">\(\mathcal{K}(.):Gr\rightarrow Alg\)</span> is left adjoint to the unit group functor <span class="SimpleMath">\(\mathcal{U}(.):Alg\rightarrow Gr\)</span>.</p>
<p>The categories <code class="code">XModAlg</code> (crossed modules of algebras) and <code class="code">Cat1Alg</code> (cat<span class="SimpleMath">\(^{1}\)</span>-algebras) are equivalent, and we include functions to convert objects and morphisms between them. The algorithms implemented in this package are analyzed in A. Odabas's Ph.D. thesis, [Oda09] and described in detail in the paper [AO16].
<p>There are aspects of commutative algebras for which no <strong class="pkg">GAP</strong> functions yet exist, for example semidirect products. We have included here functions for all homomorphisms of algebras.</p>
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