In 1950 S. MacLane and J.H.C. Whitehead, [Whi49] suggested that crossed modules modeled homotopy \(2\)-types. Later crossed modules have been considered as \(2\)*-dimensional groups*, [Bro82], [Bro87]. The commutative algebra version of this construction has been adapted by T. Porter, [AP96], [Por87]. This algebraic version is called *combinatorial algebra theory*, which contains potentially important new ideas (see [AP96], [AP98], [AE03]).

A share package **XMod**, [AOUW17], [AW00], was prepared by M. Alp and C.D. Wensley for the **GAP** computational group theory language, initially for **GAP**3 then revised for **GAP**4. The \(2\)-dimensional part of this programme contains functions for computing crossed modules and cat\(^{1}\)-groups and their morphisms [AOUW17].

This package includes functions for computing crossed modules of algebras, cat\(^{1}\)-algebras and their morphisms by analogy with *computational group theory*. We will concentrate on group rings over of abelian groups over finite fields because these algebras are conveniently implemented in **GAP**. The tools needed are the group algebras in which the group algebra functor \(\mathcal{K}(.):Gr\rightarrow Alg\) is left adjoint to the unit group functor \(\mathcal{U}(.):Alg\rightarrow Gr\).

The categories `XModAlg`

(crossed modules of algebras) and `Cat1Alg`

(cat\(^{1}\)-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].

There are aspects of commutative algebras for which no **GAP** functions yet exist, for example semidirect products. We have included here functions for all homomorphisms of algebras.

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