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 :

• 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) -- get the coefficient ring
• 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
• 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) -- get the associated ring of an object
• SimplicialComplex == SimplicialComplex -- Compare two simplicial complexes.
• 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.