Matroids : Index

• affineGeometry -- affine geometry of rank n+1 over F_p
• affineGeometry(ZZ,ZZ) -- affine geometry of rank n+1 over F_p
• allMatroids -- returns all n-element matroids of rank r
• allMatroids(ZZ) -- returns all n-element matroids of rank r
• allMatroids(ZZ,ZZ) -- returns all n-element matroids of rank r
• allMinors -- returns all minors of one matroid in another
• allMinors(Matroid,Matroid) -- returns all minors of one matroid in another
• areIsomorphic(Matroid,Matroid) -- whether two matroids are isomorphic
• Attempts -- search for a representation of a matroid over a finite field
• bases -- bases of matroid
• bases(Matroid) -- bases of matroid
• basisIndicatorMatrix -- matrix of basis polytope
• basisIndicatorMatrix(Matroid) -- matrix of basis polytope
• binarySpike -- spike matroid
• binarySpike(ZZ) -- spike matroid
• characteristicPolynomial(Matroid) -- computes characteristic polynomial of a matroid
• CheckWellDefined -- an optional argument
• ChowRingOptions -- the defining ideal of the Chow ring
• chromaticPolynomial -- computes chromatic polynomial of a graph
• chromaticPolynomial(Graph) -- computes chromatic polynomial of a graph
• circuits -- circuits of matroid
• circuits(Matroid) -- circuits of matroid
• closure -- closure of a subset of a matroid
• closure(Matroid,List) -- closure of a subset of a matroid
• closure(Matroid,Set) -- closure of a subset of a matroid
• coextension -- the free coextension of a matroid
• coextension(Matroid) -- the free coextension of a matroid
• cogeneratorChowRing -- cogenerator of the Chow ring of a matroid
• cogeneratorChowRing(Matroid) -- cogenerator of the Chow ring of a matroid
• coloops -- coloops of matroid
• coloops(Matroid) -- coloops of matroid
• components(Matroid) -- connected components of matroid
• contraction -- contraction of subset of matroid
• contraction(Matroid,List) -- contraction of subset of matroid
• contraction(Matroid,Set) -- contraction of subset of matroid
• deletion -- deletion of subset of matroid
• deletion(Matroid,List) -- deletion of subset of matroid
• deletion(Matroid,Set) -- deletion of subset of matroid
• dual(Matroid) -- dual matroid
• elementaryQuotient -- associated to a modular cut or linear subclass
• elementaryQuotient(...,CheckWellDefined=>...) -- check whether the list is a modular cut or linear subclass
• elementaryQuotient(...,EntryMode=>...) -- use a modular cut or linear subclass
• elementaryQuotient(Matroid,List) -- associated to a modular cut or linear subclass
• extension -- of a matroid relative to a flat or modular cut
• extension(...,CheckWellDefined=>...) -- check whether the list is a modular cut or linear subclass
• extension(...,EntryMode=>...) -- use a modular cut or linear subclass
• extension(Matroid) -- of a matroid relative to a flat or modular cut
• extension(Matroid,List) -- of a matroid relative to a flat or modular cut
• extension(Matroid,Set) -- of a matroid relative to a flat or modular cut
• FlatOrder -- the defining ideal of the Chow ring
• flats -- flats of a matroid
• flats(Matroid) -- flats of a matroid
• flats(Matroid,ZZ) -- flats of a matroid
• flats(Matroid,ZZ,String) -- flats of a matroid
• fromSageMatroid -- Sage format for matroid
• fromSageMatroid(String) -- Sage format for matroid
• fundamentalCircuit -- fundamental circuit of independent set
• fundamentalCircuit(Matroid,List,Thing) -- fundamental circuit of independent set
• fundamentalCircuit(Matroid,Set,ZZ) -- fundamental circuit of independent set
• fVector(Matroid) -- f-vector of a matroid
• getCycles -- find cycles of graph
• getCycles(Graph) -- find cycles of graph
• getIsos -- all isomorphisms between two matroids
• getIsos(Matroid,Matroid) -- all isomorphisms between two matroids
• getRepresentation -- retrieves stored representation
• getRepresentation(Matroid) -- retrieves stored representation
• getSeparation -- finds a k-separation of a matroid
• getSeparation(Matroid,ZZ) -- finds a k-separation of a matroid
• groundSet -- (internal) ground set
• groundSet(Matroid) -- (internal) ground set
• hasMinor -- whether a matroid has a given minor
• hasMinor(...,Strategy=>...) -- whether a matroid has a given minor
• hasMinor(Matroid,Matroid) -- whether a matroid has a given minor
• hyperplanes -- hyperplanes of a matroid
• hyperplanes(Matroid) -- hyperplanes of a matroid
• ideal(Matroid) -- Stanley-Reisner (circuit) ideal of matroid
• idealChowRing -- the defining ideal of the Chow ring
• idealChowRing(...,ChowRingOptions=>...) -- the defining ideal of the Chow ring
• idealChowRing(...,CoefficientRing=>...) -- the defining ideal of the Chow ring
• idealChowRing(...,FlatOrder=>...) -- the defining ideal of the Chow ring
• idealChowRing(...,Presentation=>...) -- the defining ideal of the Chow ring
• idealChowRing(...,Variable=>...) -- the defining ideal of the Chow ring
• idealChowRing(Matroid) -- the defining ideal of the Chow ring
• idealOrlikSolomonAlgebra (missing documentation)
• independenceComplex(Matroid) -- independence complex of matroid
• independentSets(Matroid) -- independent subsets of a matroid
• independentSets(Matroid,List) -- independent subsets of a matroid
• independentSets(Matroid,Set) -- independent subsets of a matroid
• independentSets(Matroid,ZZ) -- independent subsets of a matroid
• indicesOf -- indices of a sublist
• indicesOf(List,List) -- indices of a sublist
• indicesOf(Matroid,List) -- indices of a sublist
• is3Connected -- whether a matroid is 3-connected
• is3Connected(Matroid) -- whether a matroid is 3-connected
• isBinary -- whether a matroid is representable over F_2
• isBinary(Matroid) -- whether a matroid is representable over F_2
• isConnected(Matroid) -- whether a matroid is connected
• isDependent -- whether a subset is dependent
• isDependent(Matroid,List) -- whether a subset is dependent
• isDependent(Matroid,Set) -- whether a subset is dependent
• isElementaryQuotient -- whether a matroid is an elementary quotient of another matroid
• isElementaryQuotient(Matroid,Matroid) -- whether a matroid is an elementary quotient of another matroid
• isLinearSubclass -- whether a list of hyperplanes of a matroid is a linear subclass
• isLinearSubclass(Matroid,List) -- whether a list of hyperplanes of a matroid is a linear subclass
• isModularCut -- whether a list of flats of a matroid is a modular cut
• isModularCut(Matroid,List) -- whether a list of flats of a matroid is a modular cut
• isNonCrossing -- whether 2 subsets are non-crossing
• isNonCrossing(List,List) -- whether 2 subsets are non-crossing
• isNonCrossing(Set,Set) -- whether 2 subsets are non-crossing
• isomorphism(Matroid,Matroid) -- computes an isomorphism between isomorphic matroids
• isoTypes -- distinct isomorphism classes
• isoTypes(List) -- distinct isomorphism classes
• isPositivelyOrientable -- whether a matroid is positively orientable
• isPositivelyOrientable(Matroid) -- whether a matroid is positively orientable
• isPositivelyOriented -- whether a matroid is positively oriented
• isPositivelyOriented(Matroid) -- whether a matroid is positively oriented
• isQuotient -- whether a matroid is a quotient of another matroid
• isQuotient(Matroid,Matroid) -- whether a matroid is a quotient of another matroid
• isSimple(Matroid) -- whether a matroid is simple
• isWellDefined(Matroid) -- whether the input is a well-defined matroid
• latticeOfFlats -- lattice of flats of a matroid
• latticeOfFlats(Matroid) -- lattice of flats of a matroid
• linearSubclass -- associated to an elementary quotient or modular cut
• linearSubclass(...,CheckWellDefined=>...) -- check whether the list is a modular cut
• linearSubclass(Matroid,List) -- associated to an elementary quotient or modular cut
• linearSubclass(Matroid,Matroid) -- associated to an elementary quotient or modular cut
• Loops -- constructs a matroid
• loops -- loops of matroid
• loops(Matroid) -- loops of matroid
• Matroid -- the class of all matroids
• matroid -- constructs a matroid
• Matroid + Matroid -- union of matroids
• Matroid ++ Matroid -- direct sum of matroids
• Matroid / List -- contraction of subset of matroid
• Matroid / Set -- contraction of subset of matroid
• Matroid == Matroid -- whether two matroids are equal
• Matroid \ List -- deletion of subset of matroid
• Matroid \ Set -- deletion of subset of matroid
• Matroid _ List -- elements of matroid
• Matroid _ Set -- elements of matroid
• Matroid _ ZZ -- elements of matroid
• Matroid _* -- elements of matroid
• Matroid | List -- restriction to subset of matroid
• Matroid | Set -- restriction to subset of matroid
• matroid(...,EntryMode=>...) -- select method of specifying matroid
• matroid(...,Loops=>...) -- constructs a matroid
• matroid(...,ParallelEdges=>...) -- constructs a matroid
• matroid(Graph) -- constructs a matroid
• matroid(Ideal) -- constructs a matroid
• matroid(List) -- constructs a matroid
• matroid(List,List) -- constructs a matroid
• matroid(List,List,ZZ) -- constructs a matroid
• matroid(List,MonomialIdeal) -- constructs a matroid
• matroid(Matrix) -- constructs a matroid
• matroid(ZZ,List) -- constructs a matroid
• Matroids -- a package for computations with matroids
• maxWeightBasis -- maximum weight basis using greedy algorithm
• maxWeightBasis(Matroid,List) -- maximum weight basis using greedy algorithm
• minor -- minor of matroid
• minor(Matroid,List,List) -- minor of matroid
• minor(Matroid,Set,Set) -- minor of matroid
• modularCut -- associated to an elementary quotient or linear subclass
• modularCut(...,CheckWellDefined=>...) -- check whether the list is a linear subclass
• modularCut(Matroid,List) -- associated to an elementary quotient or linear subclass
• modularCut(Matroid,Matroid) -- associated to an elementary quotient or linear subclass
• nonbases -- nonbases of matroid
• nonbases(Matroid) -- nonbases of matroid
• parallelConnection -- parallel connection of two matroids
• parallelConnection(Matroid,Matroid) -- parallel connection of two matroids
• ParallelEdges -- constructs a matroid
• positiveOrientation -- a positive orientation of a matroid
• positiveOrientation(Matroid) -- a positive orientation of a matroid
• Presentation -- the defining ideal of the Chow ring
• projectiveGeometry -- projective geometry of dimension n over F_p
• projectiveGeometry(ZZ,ZZ) -- projective geometry of dimension n over F_p
• quickIsomorphismTest -- quick checks for isomorphism between matroids
• quickIsomorphismTest(Matroid,Matroid) -- quick checks for isomorphism between matroids
• rank(Matroid) -- rank of a matroid
• rank(Matroid,List) -- rank of a subset of a matroid
• rank(Matroid,Set) -- rank of a subset of a matroid
• readFromFile -- save matroid to file
• readFromFile(String) -- save matroid to file
• relabel -- relabel a matroid
• relabel(Matroid) -- relabel a matroid
• relabel(Matroid,HashTable) -- relabel a matroid
• relabel(Matroid,List) -- relabel a matroid
• relaxation -- relaxation of matroid
• relaxation(...,CheckWellDefined=>...) -- an optional argument
• relaxation(Matroid) -- relaxation of matroid
• relaxation(Matroid,List) -- relaxation of matroid
• relaxation(Matroid,Set) -- relaxation of matroid
• restriction -- restriction to subset of matroid
• restriction(Matroid,List) -- restriction to subset of matroid
• restriction(Matroid,Set) -- restriction to subset of matroid
• saveMatroid -- save matroid to file
• saveMatroid(Matroid) -- save matroid to file
• saveMatroid(Matroid,String) -- save matroid to file
• searchRepresentation -- search for a representation of a matroid over a finite field
• searchRepresentation(...,Attempts=>...) -- search for a representation of a matroid over a finite field
• searchRepresentation(Matroid,GaloisField) -- search for a representation of a matroid over a finite field
• seriesConnection -- series connection of two matroids
• seriesConnection(Matroid,Matroid) -- series connection of two matroids
• setRepresentation -- stores user-defined representation
• setRepresentation(Matroid,Matrix) -- stores user-defined representation
• simpleMatroid -- simple matroid associated to a matroid
• simpleMatroid(Matroid) -- simple matroid associated to a matroid
• specificMatroid -- creates built-in matroid
• specificMatroid(String) -- creates built-in matroid
• specificMatroid(Symbol) -- creates built-in matroid
• spike -- spike matroid
• spike(ZZ) -- spike matroid
• spike(ZZ,List) -- spike matroid
• storedRepresentation -- stores user-defined representation
• sum2 -- 2-sum of matroids
• sum2(Matroid,Matroid) -- 2-sum of matroids
• swirl -- swirl matroid
• swirl(ZZ) -- swirl matroid
• thetaMatroid -- theta matroid
• thetaMatroid(ZZ) -- theta matroid
• toSageMatroid -- Sage format for matroid
• toSageMatroid(Matroid) -- Sage format for matroid
• truncate(Matroid) -- the truncation of a matroid with respect to a flat
• truncate(Set,Matroid) -- the truncation of a matroid with respect to a flat
• truncate(ZZ,Matroid) -- the truncation of a matroid with respect to a flat
• tutteEvaluate -- evaluate Tutte polynomial
• tutteEvaluate(Matroid,Thing,Thing) -- evaluate Tutte polynomial
• tuttePolynomial(Matroid) -- Tutte polynomial of a matroid
• tuttePolynomial(Matroid,Ring) -- Tutte polynomial of a matroid
• uniformMatroid -- uniform matroid
• uniformMatroid(ZZ,ZZ) -- uniform matroid
• wheel -- wheels/whirls
• wheel(ZZ) -- wheels/whirls
• whirl -- wheels/whirls
• whirl(ZZ) -- wheels/whirls
• Working with Chow rings of matroids