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FastMinors : Index
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chooseGoodMinors
-- returns an ideal generated by interesting minors in a matrix
chooseGoodMinors(...,DetStrategy=>...)
-- DetStrategy is a strategy for allowing the user to choose how determinants (or rank), is computed
chooseGoodMinors(...,PeriodicCheckFunction=>...)
-- returns an ideal generated by interesting minors in a matrix
chooseGoodMinors(...,PointOptions=>...)
-- options to pass to functions in the package RandomPoints
chooseGoodMinors(...,Strategy=>...)
-- strategies for choosing submatrices
chooseGoodMinors(...,Verbose=>...)
-- returns an ideal generated by interesting minors in a matrix
chooseGoodMinors(ZZ,ZZ,Matrix)
-- returns an ideal generated by interesting minors in a matrix
chooseGoodMinors(ZZ,ZZ,Matrix,Ideal)
-- returns an ideal generated by interesting minors in a matrix
chooseRandomSubmatrix
-- returns coordinates for a random submatrix
chooseRandomSubmatrix(ZZ,Matrix)
-- returns coordinates for a random submatrix
chooseSubmatrixLargestDegree
-- returns coordinates for higher degree submatrix of a matrix
chooseSubmatrixLargestDegree(ZZ,Matrix)
-- returns coordinates for higher degree submatrix of a matrix
chooseSubmatrixSmallestDegree
-- returns coordinates for low degree submatrix of a matrix
chooseSubmatrixSmallestDegree(ZZ,Matrix)
-- returns coordinates for low degree submatrix of a matrix
CodimCheckFunction
-- attempts to show that the ring is regular in codimension n
DetStrategy
-- DetStrategy is a strategy for allowing the user to choose how determinants (or rank), is computed
FastMinors
-- faster linear algebra, especially for computation of minors
FastMinorsStrategyTutorial
-- How to use and construct strategies for selecting submatrices in various functions
getSubmatrixOfRank
-- tries to find a submatrix of the given rank
getSubmatrixOfRank(...,DetStrategy=>...)
-- DetStrategy is a strategy for allowing the user to choose how determinants (or rank), is computed
getSubmatrixOfRank(...,MaxMinors=>...)
-- an option to control depth of search
getSubmatrixOfRank(...,PointOptions=>...)
-- options to pass to functions in the package RandomPoints
getSubmatrixOfRank(...,Strategy=>...)
-- strategies for choosing submatrices
getSubmatrixOfRank(...,Threads=>...)
-- tries to find a submatrix of the given rank
getSubmatrixOfRank(...,Verbose=>...)
-- tries to find a submatrix of the given rank
getSubmatrixOfRank(ZZ,Matrix)
-- tries to find a submatrix of the given rank
GRevLexLargest
-- strategies for choosing submatrices
GRevLexSmallest
-- strategies for choosing submatrices
GRevLexSmallestTerm
-- strategies for choosing submatrices
isCodimAtLeast
-- returns true if we can quickly see whether the codim is at least a given number
isCodimAtLeast(...,PairLimit=>...)
-- returns true if we can quickly see whether the codim is at least a given number
isCodimAtLeast(...,SPairsFunction=>...)
-- returns true if we can quickly see whether the codim is at least a given number
isCodimAtLeast(...,Verbose=>...)
-- returns true if we can quickly see whether the codim is at least a given number
isCodimAtLeast(ZZ,Ideal)
-- returns true if we can quickly see whether the codim is at least a given number
isDimAtMost
-- returns true if we can quickly see whether the dim is at most a given number
isDimAtMost(...,PairLimit=>...)
-- returns true if we can quickly see whether the dim is at most a given number
isDimAtMost(...,SPairsFunction=>...)
-- returns true if we can quickly see whether the dim is at most a given number
isDimAtMost(...,Verbose=>...)
-- returns true if we can quickly see whether the dim is at most a given number
isDimAtMost(ZZ,Ideal)
-- returns true if we can quickly see whether the dim is at most a given number
isRankAtLeast
-- determines if the matrix has rank at least a number
isRankAtLeast(...,DetStrategy=>...)
-- DetStrategy is a strategy for allowing the user to choose how determinants (or rank), is computed
isRankAtLeast(...,MaxMinors=>...)
-- an option to control depth of search
isRankAtLeast(...,PointOptions=>...)
-- options to pass to functions in the package RandomPoints
isRankAtLeast(...,Strategy=>...)
-- strategies for choosing submatrices
isRankAtLeast(...,Threads=>...)
-- determines if the matrix has rank at least a number
isRankAtLeast(...,Verbose=>...)
-- determines if the matrix has rank at least a number
isRankAtLeast(ZZ,Matrix)
-- determines if the matrix has rank at least a number
LexLargest
-- strategies for choosing submatrices
LexSmallest
-- strategies for choosing submatrices
LexSmallestTerm
-- strategies for choosing submatrices
MaxMinors
-- an option to control depth of search
MinDimension
-- an option for projDim
MinMinorsFunction
-- attempts to show that the ring is regular in codimension n
MinorsCache
-- uses a recursive cofactor algorithm to compute the ideal of minors of a matrix
Modulus
-- an option for regularInCodimension
PeriodicCheckFunction
-- returns an ideal generated by interesting minors in a matrix
PointOptions
-- options to pass to functions in the package RandomPoints
Points
-- strategies for choosing submatrices
projDim
-- finds an upper bound for the projective dimension of a module
projDim(...,DetStrategy=>...)
-- DetStrategy is a strategy for allowing the user to choose how determinants (or rank), is computed
projDim(...,MaxMinors=>...)
-- an option to control depth of search
projDim(...,MinDimension=>...)
-- finds an upper bound for the projective dimension of a module
projDim(...,PointOptions=>...)
-- options to pass to functions in the package RandomPoints
projDim(...,Strategy=>...)
-- strategies for choosing submatrices
projDim(...,Verbose=>...)
-- finds an upper bound for the projective dimension of a module
projDim(Module)
-- finds an upper bound for the projective dimension of a module
Random
-- strategies for choosing submatrices
RandomNonzero
-- strategies for choosing submatrices
Rank
-- DetStrategy is a strategy for allowing the user to choose how determinants (or rank), is computed
Recursive
-- DetStrategy is a strategy for allowing the user to choose how determinants (or rank), is computed
recursiveMinors
-- uses a recursive cofactor algorithm to compute the ideal of minors of a matrix
recursiveMinors(...,MinorsCache=>...)
-- uses a recursive cofactor algorithm to compute the ideal of minors of a matrix
recursiveMinors(...,Threads=>...)
-- uses a recursive cofactor algorithm to compute the ideal of minors of a matrix
recursiveMinors(...,Verbose=>...)
-- uses a recursive cofactor algorithm to compute the ideal of minors of a matrix
recursiveMinors(ZZ,Matrix)
-- uses a recursive cofactor algorithm to compute the ideal of minors of a matrix
regularInCodimension
-- attempts to show that the ring is regular in codimension n
regularInCodimension(...,CodimCheckFunction=>...)
-- attempts to show that the ring is regular in codimension n
regularInCodimension(...,DetStrategy=>...)
-- DetStrategy is a strategy for allowing the user to choose how determinants (or rank), is computed
regularInCodimension(...,MaxMinors=>...)
-- an option to control depth of search
regularInCodimension(...,MinMinorsFunction=>...)
-- attempts to show that the ring is regular in codimension n
regularInCodimension(...,Modulus=>...)
-- attempts to show that the ring is regular in codimension n
regularInCodimension(...,PairLimit=>...)
-- attempts to show that the ring is regular in codimension n
regularInCodimension(...,PointOptions=>...)
-- options to pass to functions in the package RandomPoints
regularInCodimension(...,SPairsFunction=>...)
-- attempts to show that the ring is regular in codimension n
regularInCodimension(...,Strategy=>...)
-- strategies for choosing submatrices
regularInCodimension(...,UseOnlyFastCodim=>...)
-- attempts to show that the ring is regular in codimension n
regularInCodimension(...,Verbose=>...)
-- attempts to show that the ring is regular in codimension n
regularInCodimension(ZZ,Ring)
-- attempts to show that the ring is regular in codimension n
RegularInCodimensionTutorial
-- A tutorial for how to use the advanced options of the regularInCodimension function
reorderPolynomialRing
-- produces an isomorphic polynomial ring with a different, randomized, monomial order
reorderPolynomialRing(Symbol,Ring)
-- produces an isomorphic polynomial ring with a different, randomized, monomial order
SPairsFunction
-- returns true if we can quickly see whether the codim is at least a given number
StrategyCurrent
-- strategies for choosing submatrices
StrategyDefault
-- strategies for choosing submatrices
StrategyDefaultNonRandom
-- strategies for choosing submatrices
StrategyDefaultWithPoints
-- strategies for choosing submatrices
StrategyGRevLexSmallest
-- strategies for choosing submatrices
StrategyLexSmallest
-- strategies for choosing submatrices
StrategyPoints
-- strategies for choosing submatrices
StrategyRandom
-- strategies for choosing submatrices
Threads
-- an option for various functions
UseOnlyFastCodim
-- attempts to show that the ring is regular in codimension n