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randomAbstractSimplicialComplex -- Create a random simplicial set

Description

Create a random abstract simplicial complex with vertices supported on a subset of [n] = {1,...,n}.

i1 : setRandomSeed(currentTime());
 
i2 : K = randomAbstractSimplicialComplex(4)

o2 = AbstractSimplicialComplex{-1 => {{}}     }
                               0 => {{1}, {4}}
                               1 => {{1, 4}}

o2 : AbstractSimplicialComplex

Create a random simplicial complex on [n] with dimension at most equal to r.

i3 : setRandomSeed(currentTime());
 
i4 : L = randomAbstractSimplicialComplex(6,3)

o4 = AbstractSimplicialComplex{-1 => {{}}                   }
                               0 => {{1}, {5}, {6}}
                               1 => {{1, 5}, {1, 6}, {5, 6}}
                               2 => {{1, 5, 6}}

o4 : AbstractSimplicialComplex

Create the random complex Y_d(n,m) which has vertex set [n] and complete (d − 1)-skeleton, and has exactly m d-dimensional faces, chosen at random from all binomial(binomial(n,d+1),m) possibilities.

i5 : setRandomSeed(currentTime());
 
i6 : M = randomAbstractSimplicialComplex(6,3,2)

o6 = AbstractSimplicialComplex{-1 => {{}}                                                   }
                               0 => {{1}, {2}, {4}, {5}, {6}}
                               1 => {{1, 2}, {1, 4}, {1, 5}, {1, 6}, {2, 5}, {4, 6}, {5, 6}}
                               2 => {{1, 2, 5}, {1, 4, 6}, {1, 5, 6}}

o6 : AbstractSimplicialComplex

See also

Ways to use randomAbstractSimplicialComplex:

For the programmer

The object randomAbstractSimplicialComplex is a method function.