SimplicialComplexes : Table of Contents

• SimplicialComplexes -- simplicial complexes
• boundary -- boundary operator
• boundary(SimplicialComplex) -- the boundary simplicial complex of D
• boundary(ZZ,SimplicialComplex) -- the boundary map from i-faces to (i-1)-faces
• buchbergerComplex -- Buchberger complex of a monomial ideal
• chainComplex(SimplicialComplex) -- The chain complex of boundary maps.
• coefficientRing(SimplicialComplex) -- get the coefficient ring
• dim(Face) -- The dimension of a face.
• dim(SimplicialComplex) -- dimension of a simplicial complex
• dual(SimplicialComplex) -- the Alexander dual of a simplicial complex
• Face -- The class of faces of simplicial complexes.
• face -- Generate a face.
• Face == Face -- Compare two faces.
• faceIdeal -- Key to simplicial complex.
• faces -- the i-faces of a simplicial complex
• faces(SimplicialComplex) -- Compute all faces of a simplicial complex.
• facets -- the facets of a simplicial complex
• fVector -- the f-vector of a simplicial complex
• 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(SimplicialComplex,Ring) -- Compute the homology of a simplicial complex.
• ideal(SimplicialComplex) -- the ideal of minimal nonfaces (the Stanley-Reisner ideal)
• isFaceOf -- Substitute a face to a different ring.
• isPure -- whether the facets are equidimensional
• isSubface -- Test whether a face is a subface of another face.
• label -- labels with monomials the faces of simplicial complex
• link -- link of a face in a simplicial complex
• lyubeznikComplex -- Simplicial complex supporting the Lyubeznik resolution of a monomial ideal
• monomialIdeal(SimplicialComplex) -- the monomial ideal of minimal nonfaces (the Stanley-Reisner ideal)
• net(Face) -- Printing a face.
• net(SimplicialComplex) -- Printing a simplicial complex.
• ring(Face) -- Ring of a face.
• ring(SimplicialComplex) -- get the associated ring of an object
• SimplicialComplex
• simplicialComplex -- create a simplicial complex
• SimplicialComplex == SimplicialComplex -- Compare two simplicial complexes.
• substitute(Face,PolynomialRing) -- Substitute a face to a different ring.
• substitute(SimplicialComplex,PolynomialRing) -- Substitute a simplicial complex to a different ring.
• superficialComplex -- Simplicial complex supporting a superficial resolution of a monomial ideal
• useFaceClass -- Option to return faces in the class Face
• vertices -- The vertices of a face of a simplicial complex.