SimplicialComplex

Functions and methods returning a simplicial complex :

• simplicialComplex -- create a simplicial complex
• "simplicialComplex(List)" -- see simplicialComplex -- create a simplicial complex

Methods that use a simplicial complex :

• "algebraicShifting(SimplicialComplex)" -- see algebraicShifting -- the algebraic shifting of a simplicial complex
• boundary(SimplicialComplex) -- the boundary simplicial complex of D
• boundary(ZZ,SimplicialComplex) -- the boundary map from i-faces to (i-1)-faces
• chainComplex(SimplicialComplex) -- The chain complex of boundary maps.
• "simplicialChainComplex(List,SimplicialComplex)" -- see chainComplex(SimplicialComplex) -- The chain complex of boundary maps.
• coefficientRing(SimplicialComplex)
• dim(SimplicialComplex) -- dimension of a simplicial complex
• dual(SimplicialComplex) -- the Alexander dual of a simplicial complex
• "faces(ZZ,SimplicialComplex)" -- see faces -- the i-faces of a simplicial complex
• faces(SimplicialComplex) -- Compute all faces of a simplicial complex.
• "facets(SimplicialComplex)" -- see facets -- the facets of a simplicial complex
• "fVector(SimplicialComplex)" -- see fVector -- the f-vector of a simplicial complex
• HH SimplicialComplex -- Compute the homology of a simplicial complex.
• "homology(Nothing,SimplicialComplex)" -- see HH SimplicialComplex -- Compute the homology of a simplicial complex.
• HH_ZZ SimplicialComplex -- Compute the homology of a simplicial complex.
• HH_ZZ(SimplicialComplex,Ring) -- Compute the homology of a simplicial complex.
• "homology(Nothing,SimplicialComplex,Ring)" -- see homology(SimplicialComplex,Ring) -- Compute the homology of a simplicial complex.
• homology(SimplicialComplex,Ring) -- Compute the homology of a simplicial complex.
• ideal(SimplicialComplex) -- the ideal of minimal nonfaces (the Stanley-Reisner ideal)
• "isFaceOf(Face,SimplicialComplex)" -- see isFaceOf -- Substitute a face to a different ring.
• "isPure(SimplicialComplex)" -- see isPure -- whether the facets are equidimensional
• "joinSimplicial(SimplicialComplex,SimplicialComplex)" -- see joinSimplicial -- the join of two simplicial complexes
• "label(SimplicialComplex,List)" -- see label -- labels with monomials the faces of simplicial complex
• "link(SimplicialComplex,RingElement)" -- see link -- link of a face in a simplicial complex
• monomialIdeal(SimplicialComplex) -- the monomial ideal of minimal nonfaces (the Stanley-Reisner ideal)
• net(SimplicialComplex) -- Printing a simplicial complex.
• ring(SimplicialComplex)
• SimplicialComplex * SimplicialComplex -- the join of two simplicial complexes
• SimplicialComplex == SimplicialComplex -- Compare two simplicial complexes.
• "skeleton(ZZ,SimplicialComplex)" -- see skeleton -- the n-skeleton of the simplicial complex D
• "star(SimplicialComplex,RingElement)" -- see star -- star of a face in a simplicial complex
• substitute(SimplicialComplex,PolynomialRing) -- Substitute a simplicial complex to a different ring.

For the programmer

The object SimplicialComplex is a type, with ancestor classes HashTable < Thing.