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 mathcalK(.):Gr→ Alg is left adjoint to the unit group functor mathcalU(.):Alg→ 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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