<Verb>ResolutionBieberbachGroup(G):: MatrixGroup --> FreeResolution</Verb>
<Verb>ResolutionBieberbachGroup(G,v):: MatrixGroup, List --> FreeResolution</Verb><P/>


<P/> 
Inputs a torsion free crystallographic group <M>G</M>, also known as a 
Bieberbach group, represented using <B>AffineCrystGroupOnRight</B>
 as in the GAP package Cryst. It also optionally inputs 
a choice of vector 
<M>v</M> in the Euclidean space <M>\mathbb R^n</M> on which <M>G</M>
 acts freely. The function returns <M>n+1</M> terms of the free ZG-resolution 
of <M>\mathbb Z</M> arising as the cellular chain complex of the tessellation of <M>\mathbb R^n</M>
 by the Dirichlet-Voronoi fundamental domain determined by <M>v</M>.
No contracting homotopy is returned with the resolution.

<P/>
This function is part of the HAPcryst package written by Marc Roeder
 and thus requires the HAPcryst package to be loaded.

<P/>
The function requires the use of Polymake software.

