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**1 - 2**of**2**### Computing "Small" 1-Homological Models for Commutative Differential Graded Algebras

"... We use homological perturbation machinery specific for the algebra category [13] to give an algorithm for computing the differential structure of a small 1-homological model for commutative differential graded algebras (briefly, CDGAs). The complexity of the procedure is studied and a computer packa ..."

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We use homological perturbation machinery specific for the algebra category [13] to give an algorithm for computing the differential structure of a small 1-homological model for commutative differential graded algebras (briefly, CDGAs). The complexity of the procedure is studied and a computer package in Mathematica is described for determining such models.

### An Algorithm for Computing Cocyclic Matrices Developed Over Some Semidirect Products

"... An algorithm for calculating a set of generators of representative 2-cocycles on semidirect product of finite abelian groups is constructed, in light of the theory over cocyclic matrices developed by Horadam and de Launey in [7, 8]. The method involves some homological perturbation techniques [3, 1] ..."

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An algorithm for calculating a set of generators of representative 2-cocycles on semidirect product of finite abelian groups is constructed, in light of the theory over cocyclic matrices developed by Horadam and de Launey in [7, 8]. The method involves some homological perturbation techniques [3, 1], in the homological correspondent to the work which Grabmeier and Lambe described in [12] from the viewpoint of cohomology. Examples of explicit computations over all dihedral groups D4t are given, with aid of Mathematica. 1