<Verb>PersistentBettiNumbers(K,n):: FilteredSimplicialComplex, Int --> List</Verb>
<Verb>PersistentBettiNumbers(K,n):: FilteredPureCubicalComplex, Int --> List</Verb> 
<Verb>PersistentBettiNumbers(K,n):: FilteredRegCWComplex, Int --> List</Verb>
<Verb>PersistentBettiNumbers(K,n):: FilteredChainComplex, Int --> List</Verb>
<Verb>PersistentBettiNumbers(K,n):: FilteredSparseChainComplex, Int --> List</Verb>
<Verb>PersistentBettiNumbers(K,n,p):: FilteredSimplicialComplex, Int, Int --> List</Verb>
<Verb>PersistentBettiNumbers(K,n,p):: FilteredPureCubicalComplex, Int, Int --> List</Verb>
<Verb>PersistentBettiNumbers(K,n,p):: FilteredRegCWComplex, Int, Int --> List</Verb>
<Verb>PersistentBettiNumbers(K,n,p):: FilteredChainComplex, Int, Int --> List</Verb>
<Verb>PersistentBettiNumbers(K,n,p):: FilteredSparseChainComplex, Int, Int --> List</Verb>




<P/>Inputs a filtered simplicial, filtered pure cubical,  
filtered regular CW, filtered chain or filtered sparse chain complex  
<M>K</M> together with an integer <M>n \ge 0</M> and returns the <M>n</M>th 
PersistentBetti numbers of <M>K</M> as a list of lists of integers.



<P/>Inputs a filtered simplicial, filtered pure cubical,                    
filtered regular CW, filtered chain or filtered sparse chain complex
<M>K</M> together with an integer <M>n \ge 0</M>  and a prime <M>p \ge 0</M> or 
<M>p=0</M>. In this case  the <M>n</M>th
PersistentBetti numbers of <M>K</M> over a field of characteristic <M>p</M> are returned.



