SimplicialComplexes : Table of Contents

• SimplicialComplexes -- exploring abstract simplicial complexes within commutative algebra
• algebraicShifting -- the algebraic shifting of a simplicial complex
• bartnetteSphereComplex(PolynomialRing) -- make a non-polytopal 3-sphere with 8 vertices
• barycentricSubdivision(SimplicialComplex,Ring) -- create the barycentric subdivision of a simplicial complex
• barycentricSubdivision(SimplicialMap,Ring,Ring) -- create the map between barycentric subdivisions corresponding to a simplicial map
• bjornerComplex(PolynomialRing) -- make a shellable 2-polyhedron with 6 vertices
• boundaryMap(ZZ,SimplicialComplex) -- make a boundary map between the oriented faces of an abstract simplicial complex
• buchbergerResolution -- make a Buchberger resolution of a monomial ideal
• buchbergerSimplicialComplex -- make the Buchberger complex of a monomial ideal
• chainComplex(SimplicialComplex) -- create the chain complex associated to a simplicial complex.
• chainComplex(SimplicialMap) -- constructs the associated map between chain complexes
• coefficientRing(SimplicialComplex) -- get the coefficient ring of the underlying polynomial ring
• connectedComponents(SimplicialComplex) -- find the connected components of an abstract simplicial complex
• dim(SimplicialComplex) -- find the dimension of an abstract simplicial complex
• dual(SimplicialComplex) -- make the Alexander dual of an abstract simplicial complex
• dunceHatComplex(PolynomialRing) -- make a realization of the dunce hat with 8 vertices
• elementaryCollapse(SimplicialComplex,RingElement) -- construct the elementary collapse of a free face in a simplicial complex
• faces(SimplicialComplex) -- get the list of faces for an abstract simplicial complex
• faces(ZZ,SimplicialComplex) -- get the $i$-faces of an abstract simplicial complex
• facets(SimplicialComplex) -- get the list of maximal faces
• Finding attributes and properties -- information about accessing features of an abstract simplicial complex
• flagfVector(List,SimplicialComplex) -- compute a flag $f$-number of a colored simplicial complex
• flagfVector(SimplicialComplex) -- compute the flag $f$-vector of an colored simplicial complex
• fVector(SimplicialComplex) -- compute the f-vector of an abstract simplicial complex
• grunbaumBallComplex(PolynomialRing) -- make a nonshellable 3-ball with 14 vertices and 29 facets
• HH SimplicialMap -- Compute the induced map on homology of a simplicial map.
• HH^ZZ SimplicialMap -- Compute the induced map on cohomology of a simplicial map.
• HH^ZZ(SimplicialComplex,Ring) -- compute the reduced cohomology of an abstract simplicial complex
• HH^ZZ(SimplicialComplex,SimplicialComplex) -- compute the relative homology of two simplicial complexes
• HH_ZZ SimplicialMap -- Compute the induced map on homology of a simplicial map.
• HH_ZZ(SimplicialComplex,Ring) -- compute the reduced homology of an abstract simplicial complex
• homology(SimplicialComplex,Ring) -- compute the reduced homology of an abstract simplicial complex
• homology(SimplicialComplex,SimplicialComplex) -- compute the relative homology of two simplicial complexes
• id _ SimplicialComplex -- make the identity map from a SimplicialComplex to itself
• ideal(SimplicialComplex) -- get the Stanley–Reisner ideal
• image(SimplicialMap) -- construct the image of a simplicial map
• inducedSubcomplex(SimplicialComplex,List) -- make the induced simplicial complex on a subset of vertices
• isInjective(SimplicialMap) -- checks if a simplicial map is injective
• isProper(SimplicialComplex) -- whether an abstract simplicial complex is properly colored
• isPure(SimplicialComplex) -- whether the facets are equidimensional
• isSurjective(SimplicialMap) -- checks if a simplicial map is surjective
• isWellDefined(SimplicialComplex) -- whether underlying data is uncontradictory
• isWellDefined(SimplicialMap) -- whether underlying data is uncontradictory
• kleinBottleComplex(PolynomialRing) -- make a minimal triangulation of the Klein bottle
• link(SimplicialComplex,RingElement) -- make the link of a face in an abstract simplicial complex
• lyubeznikResolution -- create the Lyubeznik resolution of an ordered set of monomials.
• lyubeznikSimplicialComplex -- create a simplicial complex supporting a Lyubeznik resolution of a monomial ideal
• Making an abstract simplicial complex -- information about the basic constructors
• map(SimplicialComplex,SimplicialComplex,Matrix) -- create a simplicial map between simplicial complexes
• map(SimplicialMap) -- the underlying ring map associated to a simplicial map
• matrix(SimplicialMap) -- get the underlying map of rings
• monomialIdeal(SimplicialComplex) -- get the Stanley–Reisner monomial ideal
• net(SimplicialComplex) -- make a symbolic representation of an abstract simplicial complex
• net(SimplicialMap) -- make a symbolic representation for a map of abstract simplicial complexes
• nonPiecewiseLinearSphereComplex(PolynomialRing) -- make a non-piecewise-linear 5-sphere with 18 vertices
• poincareSphereComplex(PolynomialRing) -- make a homology 3-sphere with 16 vertices
• prune(SimplicialComplex) -- make a minimal presentation of an abstract simplicial complex
• realProjectiveSpaceComplex(ZZ,PolynomialRing) -- make a small triangulation of real projective space
• ring(SimplicialComplex) -- get the polynomial ring of its Stanley–Reisner ideal
• rudinBallComplex(PolynomialRing) -- make a nonshellable 3-ball with 14 vertices and 41 facets
• scarfChainComplex -- create the Scarf chain complex for a list of monomials.
• scarfSimplicialComplex -- create the Scarf simplicial complex for a list of monomials
• simplexComplex(ZZ,PolynomialRing) -- make the simplex as an abstract simplicial complex
• SimplicialComplex -- the class of all abstract simplicial complexes
• SimplicialComplex * SimplicialComplex -- make the join for two abstract simplicial complexes
• simplicialComplex(List) -- make an abstract simplicial complex from a list of faces
• simplicialComplex(MonomialIdeal) -- make a simplicial complex from its Stanley–Reisner ideal
• SimplicialMap -- the class of all maps between simplicial complexes
• skeleton(ZZ,SimplicialComplex) -- make a new simplicial complex generated by all faces of a bounded dimension
• smallManifold(ZZ,ZZ,ZZ,PolynomialRing) -- get a small manifold from the Frank Lutz database
• source(SimplicialMap) -- get the source of the map
• star(SimplicialComplex,RingElement) -- make the star of a face
• substitute(SimplicialComplex,PolynomialRing) -- change the ring of a simplicial complex
• target(SimplicialMap) -- get the target of the map
• taylorResolution -- create the Taylor resolution of a monomial ideal
• vertices(SimplicialComplex) -- get the list of the vertices for an abstract simplicial complex
• wedge(SimplicialComplex,SimplicialComplex,RingElement,RingElement) -- make the wedge sum of two abstract simplicial complexes
• Working with associated chain complexes -- information about the chain complexes and their homogenizations
• Working with simplicial maps -- information about simplicial maps and the induced operations
• zieglerBallComplex(PolynomialRing) -- make a nonshellable 3-ball with 10 vertices and 21 facets