<Verb>SimplifiedComplex(K):: RegularCWComplex --> RegularCWComplex</Verb>
<Verb>SimplifiedComplex(K):: PurePermComplex --> PurePermComplex</Verb>
<Verb>SimplifiedComplex(R):: FreeResolution --> FreeResolution</Verb>
<Verb>SimplifiedComplex(C):: ChainComplex --> ChainComplex</Verb><P/>


<P/> Inputs a regular CW-complex or a pure permutahedral complex
<M>K</M> and returns a homeomorphic complex with  possibly fewer cells and certainly no more cells.

<P/> Inputs a free <M>\mathbb ZG</M>-resolution <M>R</M> of <M>\mathbb Z</M>
and returns  a
<M>\mathbb ZG</M>-resolution <M>S</M> with potentially fewer free generators.

<P/> Inputs a chain complex   <M>C</M> of free abelian groups  
and returns  a
chain homotopic chain complex  <M>D</M> with potentially fewer free generators. 

