Matroids : Table of Contents

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