<Verb>ChainComplex(K):: CubicalComplex --> ChainComplex</Verb>
<Verb>ChainComplex(K):: PureCubicalComplex --> ChainComplex</Verb>
<Verb>ChainComplex(K):: PurePermComplex --> ChainComplex</Verb>
<Verb>ChainComplex(Y):: RegCWComplex --> ChainComplex</Verb>
<Verb>ChainComplex(K):: SimplicialComplex --> ChainComplex</Verb><P/>
<P/> Inputs a cubical, or pure cubical, or pure permutahedral or simplicial
complex <M>K</M>
and returns its chain complex of free abelian groups. In degree <M>n</M> this chain 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 chain complex <M>C</M>
which is
chain homotopy equivalent
to the cellular chain complex of <M>Y</M>. In degree <M>n</M> the free abelian chain 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>.
