Posets : Index
- adjoinMax -- computes the poset with a new maximum element
- adjoinMax(Poset) -- computes the poset with a new maximum element
- adjoinMax(Poset,Thing) -- computes the poset with a new maximum element
- adjoinMin -- computes the poset with a new minimum element
- adjoinMin(Poset) -- computes the poset with a new minimum element
- adjoinMin(Poset,Thing) -- computes the poset with a new minimum element
- allRelations -- computes all relations of a poset
- allRelations(Poset) -- computes all relations of a poset
- allRelations(Poset,Boolean) -- computes all relations of a poset
- antichains -- computes all antichains of a poset
- antichains(Poset) -- computes all antichains of a poset
- antichains(Poset,ZZ) -- computes all antichains of a poset
- AntisymmetryStrategy -- creates a new Poset object
- areIsomorphic -- determines if two posets are isomorphic
- areIsomorphic(Poset,Poset) -- determines if two posets are isomorphic
- atoms -- computes the list of elements covering the minimal elements of a poset
- atoms(Poset) -- computes the list of elements covering the minimal elements of a poset
- augmentPoset -- computes the poset with an adjoined minimum and maximum
- augmentPoset(Poset) -- computes the poset with an adjoined minimum and maximum
- augmentPoset(Poset,Thing,Thing) -- computes the poset with an adjoined minimum and maximum
- Bias -- generates a random poset with a given relation probability
- booleanLattice -- generates the boolean lattice on $n$ elements
- booleanLattice(ZZ) -- generates the boolean lattice on $n$ elements
- boundedRegions -- computes the number of bounded regions a hyperplane arrangement divides the space into
- boundedRegions(List,Ring) -- computes the number of bounded regions a hyperplane arrangement divides the space into
- chain -- generates the chain poset on $n$ elements
- chain(ZZ) -- generates the chain poset on $n$ elements
- chains -- computes all chains of a poset
- chains(Poset) -- computes all chains of a poset
- chains(Poset,ZZ) -- computes all chains of a poset
- characteristicPolynomial -- computes the characteristic polynomial of a ranked poset with a unique minimal element
- characteristicPolynomial(..., VariableName => ...) -- computes the characteristic polynomial of a ranked poset with a unique minimal element
- characteristicPolynomial(Poset) -- computes the characteristic polynomial of a ranked poset with a unique minimal element
- closedInterval -- computes the subposet contained between two points
- closedInterval(Poset,Thing,Thing) -- computes the subposet contained between two points
- comparabilityGraph -- produces the comparability graph of a poset
- comparabilityGraph(Poset) -- produces the comparability graph of a poset
- compare -- compares two elements in a poset
- compare(Poset,Thing,Thing) -- compares two elements in a poset
- connectedComponents(Poset) -- generates a list of connected components of a poset
- coveringRelations -- computes the minimal list of generating relations of a poset
- coveringRelations(Poset) -- computes the minimal list of generating relations of a poset
- diamondProduct -- computes the diamond product of two ranked posets
- diamondProduct(Poset,Poset) -- computes the diamond product of two ranked posets
- dilworthLattice -- computes the Dilworth lattice of a poset
- dilworthLattice(Poset) -- computes the Dilworth lattice of a poset
- dilworthNumber -- computes the Dilworth number of a poset
- dilworthNumber(Poset) -- computes the Dilworth number of a poset
- displayPoset -- generates a PDF representation of a poset and attempts to display it
- displayPoset(..., Jitter => ...) -- generates a PDF representation of a poset and attempts to display it
- displayPoset(..., PDFDirectory => ...) -- generates a PDF representation of a poset and attempts to display it
- displayPoset(..., PDFViewer => ...) -- generates a PDF representation of a poset and attempts to display it
- displayPoset(..., SuppressLabels => ...) -- generates a PDF representation of a poset and attempts to display it
- displayPoset(Poset) -- generates a PDF representation of a poset and attempts to display it
- distributiveLattice -- computes the lattice of order ideals of a poset
- distributiveLattice(Poset) -- computes the lattice of order ideals of a poset
- divisorPoset -- generates the poset of divisors
- divisorPoset(List,List,PolynomialRing) -- generates the poset of divisors
- divisorPoset(RingElement) -- generates the poset of divisors
- divisorPoset(RingElement,RingElement) -- generates the poset of divisors with a lower and upper bound
- divisorPoset(ZZ) -- generates the poset of divisors
- dominanceLattice -- generates the dominance lattice of partitions of $n$
- dominanceLattice(ZZ) -- generates the dominance lattice of partitions of $n$
- dropElements -- computes the induced subposet of a poset given a list of elements to remove
- dropElements(Poset,Function) -- computes the induced subposet of a poset given a list of elements to remove
- dropElements(Poset,List) -- computes the induced subposet of a poset given a list of elements to remove
- dual(Poset) -- produces the derived poset with relations reversed
- Example: Constructing common posets
- Example: Hibi ideals
- Example: Intersection lattices
- Example: LCM-lattices
- facePoset -- generates the face poset of a simplicial complex
- facePoset(SimplicialComplex) -- generates the face poset of a simplicial complex
- filter -- computes the elements above given elements in a poset
- filter(Poset,List) -- computes the elements above given elements in a poset
- filtration -- generates the filtration of a poset
- filtration(Poset) -- generates the filtration of a poset
- flagChains -- computes the maximal chains in a list of flags of a ranked poset
- flagChains(Poset,List) -- computes the maximal chains in a list of flags of a ranked poset
- flagfPolynomial -- computes the flag-f polynomial of a ranked poset
- flagfPolynomial(..., VariableName => ...) -- computes the flag-f polynomial of a ranked poset
- flagfPolynomial(Poset) -- computes the flag-f polynomial of a ranked poset
- flaghPolynomial -- computes the flag-h polynomial of a ranked poset
- flaghPolynomial(..., VariableName => ...) -- computes the flag-h polynomial of a ranked poset
- flaghPolynomial(Poset) -- computes the flag-h polynomial of a ranked poset
- flagPoset -- computes the subposet of specified ranks of a ranked poset
- flagPoset(Poset,List) -- computes the subposet of specified ranks of a ranked poset
- fPolynomial -- computes the f-polynomial of a poset
- fPolynomial(..., VariableName => ...) -- computes the f-polynomial of a poset
- fPolynomial(Poset) -- computes the f-polynomial of a poset
- gapConvertPoset -- converts between Macaulay2's Posets and GAP's Posets
- gapConvertPoset(Array) -- converts between Macaulay2's Posets and GAP's Posets
- gapConvertPoset(Poset) -- converts between Macaulay2's Posets and GAP's Posets
- gapConvertPoset(String) -- converts between Macaulay2's Posets and GAP's Posets
- greeneKleitmanPartition -- computes the Greene-Kleitman partition of a poset
- greeneKleitmanPartition(..., Strategy => ...) -- computes the Greene-Kleitman partition of a poset
- greeneKleitmanPartition(Poset) -- computes the Greene-Kleitman partition of a poset
- GroundSet -- a class for partially ordered sets (posets)
- hasseDiagram -- produces the Hasse diagram of a poset
- hasseDiagram(Poset) -- produces the Hasse diagram of a poset
- height(Poset) -- computes the height of a poset
- hibiIdeal -- produces the Hibi ideal of a poset
- hibiIdeal(..., CoefficientRing => ...) -- produces the Hibi ideal of a poset
- hibiIdeal(Poset) -- produces the Hibi ideal of a poset
- hibiRing -- produces the Hibi ring of a poset
- hibiRing(..., CoefficientRing => ...) -- produces the Hibi ring of a poset
- hibiRing(..., Strategy => ...) -- produces the Hibi ring of a poset
- hibiRing(Poset) -- produces the Hibi ring of a poset
- hPolynomial -- computes the h-polynomial of a poset
- hPolynomial(..., VariableName => ...) -- computes the h-polynomial of a poset
- hPolynomial(Poset) -- computes the h-polynomial of a poset
- incomparabilityGraph -- produces the incomparability graph of a poset
- incomparabilityGraph(Poset) -- produces the incomparability graph of a poset
- indexLabeling -- relabels a poset with the labeling based on the indices of the vertices
- indexLabeling(Poset) -- relabels a poset with the labeling based on the indices of the vertices
- intersectionLattice -- generates the intersection lattice of a hyperplane arrangement
- intersectionLattice(List,Ring) -- generates the intersection lattice of a hyperplane arrangement
- isAntichain -- determines if a given list of vertices is an antichain of a poset
- isAntichain(Poset,List) -- determines if a given list of vertices is an antichain of a poset
- isAtomic -- determines if a lattice is atomic
- isAtomic(Poset) -- determines if a lattice is atomic
- isBounded -- determines if a poset is bounded
- isBounded(Poset) -- determines if a poset is bounded
- isComparabilityGraph -- determines if a graph is the comparability graph of a poset
- isComparabilityGraph(Graph) -- determines if a graph is the comparability graph of a poset
- isConnected(Poset) -- determines if a poset is connected
- isDistributive -- determines if a lattice is distributive
- isDistributive(Poset) -- determines if a lattice is distributive
- isEulerian(Poset) -- determines if a ranked poset is Eulerian
- isGeometric -- determines if a lattice is geometric
- isGeometric(Poset) -- determines if a lattice is geometric
- isGraded -- determines if a poset is graded
- isGraded(Poset) -- determines if a poset is graded
- isLattice -- determines if a poset is a lattice
- isLattice(Poset) -- determines if a poset is a lattice
- isLowerSemilattice -- determines if a poset is a lower (or meet) semilattice
- isLowerSemilattice(Poset) -- determines if a poset is a lower (or meet) semilattice
- isLowerSemimodular -- determines if a ranked lattice is lower semimodular
- isLowerSemimodular(Poset) -- determines if a ranked lattice is lower semimodular
- isModular -- determines if a lattice is modular
- isModular(Poset) -- determines if a lattice is modular
- isomorphism -- computes an isomorphism between isomorphic posets
- isomorphism(Poset,Poset) -- computes an isomorphism between isomorphic posets
- isRanked -- determines if a poset is ranked
- isRanked(Poset) -- determines if a poset is ranked
- isSperner -- determines if a ranked poset has the Sperner property
- isSperner(Poset) -- determines if a ranked poset has the Sperner property
- isStrictSperner -- determines if a ranked poset has the strict Sperner property
- isStrictSperner(Poset) -- determines if a ranked poset has the strict Sperner property
- isUpperSemilattice -- determines if a poset is an upper (or join) semilattice
- isUpperSemilattice(Poset) -- determines if a poset is an upper (or join) semilattice
- isUpperSemimodular -- determines if a lattice is upper semimoudlar
- isUpperSemimodular(Poset) -- determines if a lattice is upper semimoudlar
- Jitter -- generates a string containing a TikZ-figure of a poset
- joinExists -- determines if the join exists for two elements of a poset
- joinExists(Poset,Thing,Thing) -- determines if the join exists for two elements of a poset
- joinIrreducibles -- determines the join irreducible elements of a poset
- joinIrreducibles(Poset) -- determines the join irreducible elements of a poset
- labelPoset -- relabels a poset with the specified labeling
- labelPoset(Poset,HashTable) -- relabels a poset with the specified labeling
- lcmLattice -- generates the lattice of lcms in an ideal
- lcmLattice(..., Strategy => ...) -- generates the lattice of lcms in an ideal
- lcmLattice(Ideal) -- generates the lattice of lcms in an ideal
- linearExtensions -- computes all linear extensions of a poset
- linearExtensions(Poset) -- computes all linear extensions of a poset
- maximalAntichains -- computes all maximal antichains of a poset
- maximalAntichains(Poset) -- computes all maximal antichains of a poset
- maximalChains -- computes all maximal chains of a poset
- maximalChains(Poset) -- computes all maximal chains of a poset
- maximalElements -- determines the maximal elements of a poset
- maximalElements(Poset) -- determines the maximal elements of a poset
- meetExists -- determines if the meet exists for two elements of a poset
- meetExists(Poset,Thing,Thing) -- determines if the meet exists for two elements of a poset
- meetIrreducibles -- determines the meet irreducible elements of a poset
- meetIrreducibles(Poset) -- determines the meet irreducible elements of a poset
- minimalElements -- determines the minimal elements of a poset
- minimalElements(Poset) -- determines the minimal elements of a poset
- moebiusFunction -- computes the Moebius function at every pair of elements of a poset
- moebiusFunction(Poset) -- computes the Moebius function at every pair of elements of a poset
- naturalLabeling -- relabels a poset with a natural labeling
- naturalLabeling(Poset) -- relabels a poset with a natural labeling
- naturalLabeling(Poset,ZZ) -- relabels a poset with a natural labeling
- NCPartition -- generates the non-crossing partitions of size $n$
- ncPartitions -- generates the non-crossing partitions of size $n$
- ncPartitions(ZZ) -- generates the non-crossing partitions of size $n$
- ncpLattice -- computes the non-crossing partition lattice of set-partitions of size $n$
- ncpLattice(ZZ) -- computes the non-crossing partition lattice of set-partitions of size $n$
- openInterval -- computes the subposet contained strictly between two points
- openInterval(Poset,Thing,Thing) -- computes the subposet contained strictly between two points
- orderComplex -- produces the order complex of a poset
- orderComplex(..., CoefficientRing => ...) -- produces the order complex of a poset
- orderComplex(..., VariableName => ...) -- produces the order complex of a poset
- orderComplex(Poset) -- produces the order complex of a poset
- orderIdeal -- computes the elements below given elements in a poset
- orderIdeal(Poset,List) -- computes the elements below given elements in a poset
- OriginalPoset -- computes the lattice of order ideals of a poset
- outputTexPoset -- writes a LaTeX file with a TikZ-representation of a poset
- outputTexPoset(..., Jitter => ...) -- writes a LaTeX file with a TikZ-representation of a poset
- outputTexPoset(..., SuppressLabels => ...) -- writes a LaTeX file with a TikZ-representation of a poset
- outputTexPoset(Poset,String) -- writes a LaTeX file with a TikZ-representation of a poset
- partitionLattice -- computes the lattice of set-partitions of size $n$
- partitionLattice(ZZ) -- computes the lattice of set-partitions of size $n$
- PDFDirectory -- generates a PDF representation of a poset and attempts to display it
- PDFViewer -- generates a PDF representation of a poset and attempts to display it
- plueckerPoset -- computes a poset associated to the Pluecker relations
- plueckerPoset(ZZ) -- computes a poset associated to the Pluecker relations
- poincare(Poset) -- computes the Poincare polynomial of a ranked poset with a unique minimal element
- poincarePolynomial -- computes the Poincare polynomial of a ranked poset with a unique minimal element
- poincarePolynomial(..., VariableName => ...) -- computes the Poincare polynomial of a ranked poset with a unique minimal element
- poincarePolynomial(Poset) -- computes the Poincare polynomial of a ranked poset with a unique minimal element
- Poset -- a class for partially ordered sets (posets)
- poset -- creates a new Poset object
- Poset * Poset -- computes the product of two posets
- Poset + Poset -- computes the union of two posets
- Poset - List -- computes the induced subposet of a poset given a list of elements to remove
- Poset == Poset -- determines if two posets are isomorphic
- Poset _ List -- returns elements of the ground set
- Poset _ ZZ -- returns an element of the ground set
- Poset _* -- returns the ground set of a poset
- poset(..., AntisymmetryStrategy => ...) -- creates a new Poset object
- poset(List) -- creates a new Poset object
- poset(List,Function) -- creates a new Poset object
- poset(List,List) -- creates a new Poset object
- poset(List,List,Matrix) -- creates a new Poset object
- posetJoin -- determines the join for two elements of a poset
- posetJoin(Poset,Thing,Thing) -- determines the join for two elements of a poset
- posetMeet -- determines the meet for two elements of a poset
- posetMeet(Poset,Thing,Thing) -- determines the meet for two elements of a poset
- Posets -- a package for working with partially ordered sets
- pPartitionRing -- produces the p-partition ring of a poset
- pPartitionRing(..., CoefficientRing => ...) -- produces the p-partition ring of a poset
- pPartitionRing(Poset) -- produces the p-partition ring of a poset
- Precompute -- a package-wide configuration that toggles precomputation
- principalFilter -- computes the elements above a given element in a poset
- principalFilter(Poset,Thing) -- computes the elements above a given element in a poset
- principalOrderIdeal -- computes the elements below a given element in a poset
- principalOrderIdeal(Poset,Thing) -- computes the elements below a given element in a poset
- product(Poset,Poset) -- computes the product of two posets
- projectivizeArrangement -- computes the intersection poset of a projectivized hyperplane arrangement
- projectivizeArrangement(List,Ring) -- computes the intersection poset of a projectivized hyperplane arrangement
- randomPoset -- generates a random poset with a given relation probability
- randomPoset(..., Bias => ...) -- generates a random poset with a given relation probability
- randomPoset(List) -- generates a random poset with a given relation probability
- randomPoset(ZZ) -- generates a random poset with a given relation probability
- rank(Poset) -- generates a list of lists representing the ranks of a ranked poset
- rankFunction -- computes the rank function of a ranked poset
- rankFunction(Poset) -- computes the rank function of a ranked poset
- rankGeneratingFunction -- computes the rank generating function of a ranked poset
- rankGeneratingFunction(..., VariableName => ...) -- computes the rank generating function of a ranked poset
- rankGeneratingFunction(Poset) -- computes the rank generating function of a ranked poset
- rankPoset -- generates a list of lists representing the ranks of a ranked poset
- rankPoset(Poset) -- generates a list of lists representing the ranks of a ranked poset
- realRegions -- computes the number of regions a hyperplane arrangement divides the space into
- realRegions(List,Ring) -- computes the number of regions a hyperplane arrangement divides the space into
- RelationMatrix -- a class for partially ordered sets (posets)
- Relations -- a class for partially ordered sets (posets)
- removeIsomorphicPosets -- returns a sub-list of non-isomorphic posets
- removeIsomorphicPosets(List) -- returns a sub-list of non-isomorphic posets
- resolutionPoset -- generates a poset from a resolution
- resolutionPoset(ChainComplex) -- generates a poset from a resolution
- resolutionPoset(Ideal) -- generates a poset from a resolution
- resolutionPoset(MonomialIdeal) -- generates a poset from a resolution
- setPartition -- computes the list of set-partitions of size $n$
- setPartition(List) -- computes the list of set-partitions of size $n$
- setPartition(ZZ) -- computes the list of set-partitions of size $n$
- setPDFViewer -- sets the default PDFViewer option
- setPDFViewer(String) -- sets the default PDFViewer option
- setPrecompute -- sets the Precompute configuration
- setPrecompute(Boolean) -- sets the Precompute configuration
- setSuppressLabels -- sets the SuppressLabels configuration
- setSuppressLabels(Boolean) -- sets the SuppressLabels configuration
- standardMonomialPoset -- generates the poset of divisibility in the monomial basis of an ideal
- standardMonomialPoset(MonomialIdeal) -- generates the poset of divisibility in the monomial basis of an ideal
- standardMonomialPoset(MonomialIdeal,ZZ,ZZ) -- generates the poset of divisibility in the monomial basis of an ideal
- subposet -- computes the induced subposet of a poset given a list of elements
- subposet(Poset,List) -- computes the induced subposet of a poset given a list of elements
- SuppressLabels -- generates a string containing a TikZ-figure of a poset
- tex(Poset) -- generates a string containing a TikZ-figure of a poset
- texPoset -- generates a string containing a TikZ-figure of a poset
- texPoset(..., Jitter => ...) -- generates a string containing a TikZ-figure of a poset
- texPoset(..., SuppressLabels => ...) -- generates a string containing a TikZ-figure of a poset
- texPoset(Poset) -- generates a string containing a TikZ-figure of a poset
- transitiveClosure -- computes the transitive closure of a set of relations
- transitiveClosure(List,List) -- computes the transitive closure of a set of relations
- transitiveOrientation -- generates a poset whose comparability graph is the given graph
- transitiveOrientation(..., Random => ...) -- generates a poset whose comparability graph is the given graph
- transitiveOrientation(..., Strategy => ...) -- generates a poset whose comparability graph is the given graph
- transitiveOrientation(Graph) -- generates a poset whose comparability graph is the given graph
- tuttePolynomial -- computes the Tutte polynomial of a poset
- tuttePolynomial(Poset) -- computes the Tutte polynomial of a poset
- union -- computes the union of two posets
- union(Poset,Poset) -- computes the union of two posets
- vertices(Poset) -- returns the ground set of a poset
- youngSubposet -- generates a subposet of Young's lattice
- youngSubposet(List) -- generates a subposet of Young's lattice
- youngSubposet(List,List) -- generates a subposet of Young's lattice
- youngSubposet(ZZ) -- generates a subposet of Young's lattice
- zetaPolynomial -- computes the zeta polynomial of a poset
- zetaPolynomial(..., VariableName => ...) -- computes the zeta polynomial of a poset
- zetaPolynomial(Poset) -- computes the zeta polynomial of a poset