MatrixSchubert : Index

• Algorithm -- computes the Grothendieck polynomial of a permutation
• antiDiagInit -- compute the (unique) antidiagonal initial ideal of an ASM ideal
• antiDiagInit(...,CoefficientRing=>...) -- compute the (unique) antidiagonal initial ideal of an ASM ideal
• antiDiagInit(...,Variable=>...) -- compute the (unique) antidiagonal initial ideal of an ASM ideal
• antiDiagInit(List) -- compute the (unique) antidiagonal initial ideal of an ASM ideal
• antiDiagInit(Matrix) -- compute the (unique) antidiagonal initial ideal of an ASM ideal
• ASMFullList -- lists all ASMs of a fixed size
• ASMFullList(ZZ) -- lists all ASMs of a fixed size
• ASMRandomList -- lists random ASMs of a fixed size
• ASMRandomList(ZZ,ZZ) -- lists random ASMs of a fixed size
• ASMToMonotoneTriangle -- converts an ASM to a monotone triangle
• ASMToMonotoneTriangle(Matrix) -- converts an ASM to a monotone triangle
• augmentedEssentialSet -- find the essential set and rank conditions for a partial ASM or a permutation
• augmentedEssentialSet(List) -- find the essential set and rank conditions for a partial ASM or a permutation
• augmentedEssentialSet(Matrix) -- find the essential set and rank conditions for a partial ASM or a permutation
• augmentedRotheDiagram -- find the Rothe diagram and rank table for a partial ASM or permutation
• augmentedRotheDiagram(List) -- find the Rothe diagram and rank table for a partial ASM or permutation
• augmentedRotheDiagram(Matrix) -- find the Rothe diagram and rank table for a partial ASM or permutation
• avoidsAllPatterns -- whether a permutation avoids all of the given patterns
• avoidsAllPatterns(List,List) -- whether a permutation avoids all of the given patterns
• CoefficientRing -- Diagonal initial ideal of an ASM ideal with respect to revlex, ordering variables from NW corner
• cohenMacaulayASMsList -- lists all Cohen-Macaulay ASMs of a fixed size which are not permutation matrices
• cohenMacaulayASMsList(ZZ) -- lists all Cohen-Macaulay ASMs of a fixed size which are not permutation matrices
• composePerms -- computes the composition of two permutations
• composePerms(List,List) -- computes the composition of two permutations
• descentSet -- the descent set of a permutation
• descentSet(List) -- the descent set of a permutation
• diagLexInitNW -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from NW corner
• diagLexInitNW(...,CoefficientRing=>...) -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from NW corner
• diagLexInitNW(...,Variable=>...) -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from NW corner
• diagLexInitNW(List) -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from NW corner
• diagLexInitNW(Matrix) -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from NW corner
• diagLexInitSE -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from SE corner
• diagLexInitSE(...,CoefficientRing=>...) -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from SE corner
• diagLexInitSE(...,Variable=>...) -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from SE corner
• diagLexInitSE(List) -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from SE corner
• diagLexInitSE(Matrix) -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from SE corner
• diagRevLexInit -- Diagonal initial ideal of an ASM ideal with respect to revlex, ordering variables from NW corner
• diagRevLexInit(...,CoefficientRing=>...) -- Diagonal initial ideal of an ASM ideal with respect to revlex, ordering variables from NW corner
• diagRevLexInit(...,Variable=>...) -- Diagonal initial ideal of an ASM ideal with respect to revlex, ordering variables from NW corner
• diagRevLexInit(List) -- Diagonal initial ideal of an ASM ideal with respect to revlex, ordering variables from NW corner
• diagRevLexInit(Matrix) -- Diagonal initial ideal of an ASM ideal with respect to revlex, ordering variables from NW corner
• doubleSchubertPolynomial -- computes the double Schubert polynomial of a permutation
• doubleSchubertPolynomial(List) -- computes the double Schubert polynomial of a permutation
• entrywiseMaxRankTable -- compute the entrywise maximum rank table of a list of ASMs
• entrywiseMaxRankTable(List) -- compute the entrywise maximum rank table of a list of ASMs
• entrywiseMinRankTable -- compute the entrywise minimum rank table of a list of ASMs
• entrywiseMinRankTable(List) -- compute the entrywise minimum rank table of a list of ASMs
• essentialSet -- compute the essential set in the Rothe Diagram for a partial ASM or a permutation.
• essentialSet(List) -- compute the essential set in the Rothe Diagram for a partial ASM or a permutation.
• essentialSet(Matrix) -- compute the essential set in the Rothe Diagram for a partial ASM or a permutation.
• firstDescent -- finds the location of the first descent of a permutation
• firstDescent(List) -- finds the location of the first descent of a permutation
• fultonGens -- compute the Fulton generators of an ASM ideal (for example, a Schubert determinantal ideal)
• fultonGens(...,CoefficientRing=>...) -- compute the Fulton generators of an ASM ideal (for example, a Schubert determinantal ideal)
• fultonGens(...,Variable=>...) -- compute the Fulton generators of an ASM ideal (for example, a Schubert determinantal ideal)
• fultonGens(List) -- compute the Fulton generators of an ASM ideal (for example, a Schubert determinantal ideal)
• fultonGens(Matrix) -- compute the Fulton generators of an ASM ideal (for example, a Schubert determinantal ideal)
• Functions for investigating permutations -- basic functions for permutations
• getASM -- get the ASM of an ideal (if it exists)
• getASM(Ideal) -- get the ASM of an ideal (if it exists)
• grothendieckPolynomial -- computes the Grothendieck polynomial of a permutation
• grothendieckPolynomial(...,Algorithm=>...) -- computes the Grothendieck polynomial of a permutation
• grothendieckPolynomial(List) -- computes the Grothendieck polynomial of a permutation
• Initial ideals of ASM ideals -- basic functions for investigating initial ideals of ASM varieties
• initialIdealsList -- lists all antidiagonal initial ideals of ASMs of a fixed size
• initialIdealsList(ZZ) -- lists all antidiagonal initial ideals of ASMs of a fixed size
• inverseOf -- to return the inverse of a permutation in 1-line notation.
• inverseOf(List) -- to return the inverse of a permutation in 1-line notation.
• Investigating ASM varieties -- basic functions for alternating sign matrix ideals
• Investigating matrix Schubert varieties -- basic functions for Schubert determinantal ideals
• isASM -- whether a matrix is an ASM
• isASM(Matrix) -- whether a matrix is an ASM
• isASMIdeal -- whether an ideal is an ASM ideal
• isASMIdeal(Ideal) -- whether an ideal is an ASM ideal
• isASMUnion -- whether the union of matrix Schubert varieties is an ASM variety
• isASMUnion(List) -- whether the union of matrix Schubert varieties is an ASM variety
• isCartwrightSturmfels -- whether a permutation is Cartwright-Sturmfels
• isCartwrightSturmfels(List) -- whether a permutation is Cartwright-Sturmfels
• isCDG -- whether a permutation is CDG
• isCDG(List) -- whether a permutation is CDG
• isIntersectionOfSchubertDeterminantalIdeals -- whether an ideal is the intersection of Schubert determinantal ideals
• isIntersectionOfSchubertDeterminantalIdeals(Ideal) -- whether an ideal is the intersection of Schubert determinantal ideals
• isMinRankTable -- whether a matrix is the canonical rank table of some partial ASM
• isMinRankTable(Matrix) -- whether a matrix is the canonical rank table of some partial ASM
• isPartialASM -- whether a matrix is a partial alternating sign matrix
• isPartialASM(Matrix) -- whether a matrix is a partial alternating sign matrix
• isPatternAvoiding -- whether a permutation avoids certain patterns, e.g. $2143$-avoiding or $312$- and $231$-avoiding
• isPatternAvoiding(List,List) -- whether a permutation avoids certain patterns, e.g. $2143$-avoiding or $312$- and $231$-avoiding
• isPerm -- whether a list is a permutation in 1-line notation
• isPerm(List) -- whether a list is a permutation in 1-line notation
• isSchubertCM -- whether an ASM variety is Cohen-Macaulay
• isSchubertCM(List) -- whether an ASM variety is Cohen-Macaulay
• isSchubertCM(Matrix) -- whether an ASM variety is Cohen-Macaulay
• isVexillary -- whether a permutation is vexillary, i.e. 2143-avoiding
• isVexillary(List) -- whether a permutation is vexillary, i.e. 2143-avoiding
• KPolynomialASM -- compute the K Polynomial of an ASM variety
• KPolynomialASM(Matrix) -- compute the K Polynomial of an ASM variety
• lastDescent -- finds the location of the last descent of a permutation
• lastDescent(List) -- finds the location of the last descent of a permutation
• longestPerm -- to return the longest permutation of length n
• longestPerm(ZZ) -- to return the longest permutation of length n
• MatrixSchubert -- matrix Schubert varieties and ASM varieties
• monotoneTriangleToASM -- converts a monotone triangle to an ASM
• monotoneTriangleToASM(List) -- converts a monotone triangle to an ASM
• nonCohenMacaulayASMsList -- lists all non-Cohen-Macaulay ASMs of a fixed size
• nonCohenMacaulayASMsList(ZZ) -- lists all non-Cohen-Macaulay ASMs of a fixed size
• padASM -- pad an ASM with an identity matrix
• padASM(Matrix,ZZ) -- pad an ASM with an identity matrix
• partialASMToASM -- extend a partial alternating sign matrix to an alternating sign matrix
• partialASMToASM(Matrix) -- extend a partial alternating sign matrix to an alternating sign matrix
• permLength -- to find the length of a permutation in 1-line notation.
• permLength(List) -- to find the length of a permutation in 1-line notation.
• permSetOfASM -- finds the permutation set of an alternating sign matrix
• permSetOfASM(Matrix) -- finds the permutation set of an alternating sign matrix
• permToMatrix -- converts a permutation in 1-line notation into a permutation matrix
• permToMatrix(List) -- converts a permutation in 1-line notation into a permutation matrix
• PipeDream -- the class representing a pipe dream
• pipeDreams -- computes the set of reduced pipe dreams corresponding to a permutation
• pipeDreams(List) -- computes the set of reduced pipe dreams corresponding to a permutation
• pipeDreamsNonReduced -- computes the set of all pipe dreams corresponding to a permutation
• pipeDreamsNonReduced(List) -- computes the set of all pipe dreams corresponding to a permutation
• rajcode -- finds the Rajchgot code of a permutation
• rajcode(List) -- finds the Rajchgot code of a permutation
• rajIndex -- finds the Rajchgot index of a permutation
• rajIndex(List) -- finds the Rajchgot index of a permutation
• rankTable -- compute a table of rank conditions that determines the corresponding ASM or matrix Schubert variety
• rankTable(List) -- compute a table of rank conditions that determines the corresponding ASM or matrix Schubert variety
• rankTable(Matrix) -- compute a table of rank conditions that determines the corresponding ASM or matrix Schubert variety
• rankTableFromMatrix -- returns the minimal rank table from an arbitrary integer matrix
• rankTableFromMatrix(Matrix) -- returns the minimal rank table from an arbitrary integer matrix
• rankTableToASM -- to find the a partial ASM associated to a given rank table
• rankTableToASM(Matrix) -- to find the a partial ASM associated to a given rank table
• rotheDiagram -- find the Rothe diagram of a partial alternating sign matrix
• rotheDiagram(List) -- find the Rothe diagram of a partial alternating sign matrix
• rotheDiagram(Matrix) -- find the Rothe diagram of a partial alternating sign matrix
• schubertAdd -- compute the sum of ASM ideals
• schubertAdd(List) -- compute the sum of ASM ideals
• schubertCodim -- compute the codimension (i.e., height) of a Schubert determinantal ideal or ASM ideal
• schubertCodim(List) -- compute the codimension (i.e., height) of a Schubert determinantal ideal or ASM ideal
• schubertCodim(Matrix) -- compute the codimension (i.e., height) of a Schubert determinantal ideal or ASM ideal
• schubertDecompose -- finds the decomposition of an ASM ideal into Schubert determinantal ideals
• schubertDecompose(Ideal) -- finds the decomposition of an ASM ideal into Schubert determinantal ideals
• schubertDecompose(Matrix) -- finds the decomposition of an ASM ideal into Schubert determinantal ideals
• schubertDeterminantalIdeal -- compute an alternating sign matrix ideal (for example, a Schubert determinantal ideal)
• schubertDeterminantalIdeal(...,CoefficientRing=>...) -- compute an alternating sign matrix ideal (for example, a Schubert determinantal ideal)
• schubertDeterminantalIdeal(...,Variable=>...) -- compute an alternating sign matrix ideal (for example, a Schubert determinantal ideal)
• schubertDeterminantalIdeal(List) -- compute an alternating sign matrix ideal (for example, a Schubert determinantal ideal)
• schubertDeterminantalIdeal(Matrix) -- compute an alternating sign matrix ideal (for example, a Schubert determinantal ideal)
• schubertIntersect -- compute the intersection of ASM ideals
• schubertIntersect(List) -- compute the intersection of ASM ideals
• schubertPolynomial -- computes the Schubert polynomial of a permutation
• schubertPolynomial(...,Algorithm=>...) -- computes the Schubert polynomial of a permutation
• schubertPolynomial(List) -- computes the Schubert polynomial of a permutation
• schubertRegularity -- compute the Castelnuovo-Mumford regularity of the quotient by an ASM ideal
• schubertRegularity(List) -- compute the Castelnuovo-Mumford regularity of the quotient by an ASM ideal
• schubertRegularity(Matrix) -- compute the Castelnuovo-Mumford regularity of the quotient by an ASM ideal
• subwordComplex -- to find the subword complex associated to w
• subwordComplex(List) -- to find the subword complex associated to w
• toOneLineNotation -- rewrites a transposition or permutation matrix in 1-line notation
• toOneLineNotation(List,ZZ) -- rewrites a transposition or permutation matrix in 1-line notation
• toOneLineNotation(Matrix) -- rewrites a transposition or permutation matrix in 1-line notation
• Variable -- Diagonal initial ideal of an ASM ideal with respect to revlex, ordering variables from NW corner