  
  [1X1 [33X[0;0YIntroduction[133X[101X
  
  [33X[0;0YIn  1950  S.  MacLane  and  J.H.C. Whitehead, [Whi49] suggested that crossed
  modules modeled homotopy [22X2[122X-types. Later crossed modules have been considered
  as  [22X2[122X[13X-dimensional  groups[113X, [Bro82], [Bro87]. The commutative algebra version
  of  this  construction  has been adapted by T. Porter, [AP96], [Por87]. This
  algebraic  version  is  called  [13Xcombinatorial algebra theory[113X, which contains
  potentially important new ideas (see [AP96], [AP98], [AE03]).[133X
  
  [33X[0;0YA  share  package  [5XXMod[105X,  [AOUW15],  [AW00], was prepared by M. Alp and C.D.
  Wensley  for the [5XGAP[105X computational group theory language, initially for [5XGAP[105X3
  then  revised  for  [5XGAP[105X4.  The [22X2[122X-dimensional part of this programme contains
  functions for computing crossed modules and cat[22X^1[122X-groups and their morphisms
  [AOUW15].[133X
  
  [33X[0;0YThis  package  includes functions for computing crossed modules of algebras,
  cat[22X^1[122X-algebras  and  their  morphisms  by  analogy  with [13Xcomputational group
  theory[113X.  We  will  concentrate  on  group  rings over of abelian groups over
  finite  fields  because  these algebras are conveniently implemented in [5XGAP[105X.
  The  tools  needed are the group algebras in which the group algebra functor
  [22XmathcalK(.):Gr→   Alg[122X   is   left   adjoint   to   the  unit  group  functor
  [22XmathcalU(.):Alg→ Gr[122X.[133X
  
  [33X[0;0YThe   categories   [10XXModAlg[110X   (crossed   modules  of  algebras)  and  [10XCat1Alg[110X
  (cat[22X^1[122X-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 [AO15].[133X
  
  [33X[0;0YThere  are  aspects  of  commutative algebras for which no [5XGAP[105X functions yet
  exist,  for example semidirect products. We have included here functions for
  all homomorphisms of algebras.[133X
  
