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# 9 Matrix Representations

This chapter describes functions which compute matrix representations for pcp-groups. So far the routines in this package are only able to compute matrix representations for torsion-free nilpotent groups.

- `UnitriangularMatrixRepresentation( G )`

  computes a faithful representation of a torsion-free nilpotent group G as unipotent lowertriangular matrices over the integers. The pc-presentation for G must not contain any power relations. The algorithm is described in dGN02.

- `IsMatrixRepresentation(` G`,` matrices`)`

  checks if the map defined by maping the i-th generator of the pcp-group G to the i-th matrix of matrices defines a homomorphism.

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