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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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<Verb>BettiNumber(K,n):: SimplicialComplex, Int --> Int</Verb> 

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<Verb>BettiNumber(K,n):: PureCubicalComplex, Int --> Int</Verb> 

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<Verb>BettiNumber(K,n):: CubicalComplex, Int --> Int</Verb>

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<Verb>BettiNumber(K,n):: PurePermComplex, Int --> Int</Verb>

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<Verb>BettiNumber(K,n):: RegCWComplex, Int --> Int</Verb>

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<Verb>BettiNumber(K,n):: ChainComplex, Int --> Int</Verb>

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<Verb>BettiNumber(K,n):: SparseChainComplex, Int --> Int</Verb>

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<Verb>BettiNumber(K,n,p):: SimplicialComplex, Int, Int --> Int</Verb>

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<Verb>BettiNumber(K,n,p):: PureCubicalComplex, Int, Int --> Int</Verb>

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<Verb>BettiNumber(K,n,p):: CubicalComplex, Int, Int --> Int</Verb>

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<Verb>BettiNumber(K,n,p):: PurePermComplex, Int, Int --> Int</Verb>

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<Verb>BettiNumber(K,n,p):: RegCWComplex, Int, Int --> Int</Verb>

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<P/>Inputs a simplicial, cubical, pure cubical, pure permutahedral, 

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regular CW, chain or sparse chain complex  

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<M>K</M> together with an integer <M>n \ge 0</M> and returns the <M>n</M>th 

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Betti number of <M>K</M>.

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<P/>Inputs a simplicial, cubical, pure cubical,  pure permutahedral or

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 regular CW-complex 

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<M>K</M> together with an integer <M>n \ge 0</M> and a prime <M>p \ge 0</M> or 

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<M>p=0</M>. In this case  the <M>n</M>th

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Betti number of <M>K</M> over a field of characteristic <M>p</M> is returned.

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