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