<Verb>CochainComplex(K):: CubicalComplex --> CochainComplex</Verb>
<Verb>CochainComplex(K):: PureCubicalComplex --> CochainComplex</Verb>
<Verb>CochainComplex(K):: PurePermComplex --> CochainComplex</Verb>
<Verb>CochainComplex(Y):: RegCWComplex --> CochainComplex</Verb>
<Verb>CochainComplex(K):: SimplicialComplex --> CohainComplex</Verb><P/>

<P/> Inputs a cubical, or pure cubical, or pure permutahedral or simplicial 
 complex <M>K</M> 
and returns its cochain complex of free abelian groups. In degree <M>n</M> 
this cochain complex has one free generator for each <M>n</M>-dimensional 
cell of <M>K</M>.

<P/> Inputs a regular CW-complex <M>Y</M> and returns a cochain complex <M>C</M>
which is
chain homotopy equivalent 
to the cellular cochain complex of <M>Y</M>. In degree <M>n</M> the free 
abelian cochain group <M>C_n</M> has one free generator for each 
critical <M>n</M>-dimensional cell of <M>Y</M> with respect to some discrete 
vector field on <M>Y</M>. 


