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LinearTruncations : Index
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B
C
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Z
compMax
-- takes componentwise minimum or maximum of a list of lists
compMax(List)
-- takes componentwise minimum or maximum of a list of lists
compMax(List,List)
-- takes componentwise minimum or maximum of a list of lists
compMin
-- takes componentwise minimum or maximum of a list of lists
compMin(List)
-- takes componentwise minimum or maximum of a list of lists
compMin(List,List)
-- takes componentwise minimum or maximum of a list of lists
diagonalMultidegrees
-- t-tuples of non-negative integers with sum equal to d
diagonalMultidegrees(ZZ,List)
-- t-tuples of non-negative integers with sum equal to d
diagonalMultidegrees(ZZ,ZZ)
-- t-tuples of non-negative integers with sum equal to d
findMins
-- calculates the minimal elements of a subset of ZZ^r
findMins(Ideal)
-- calculates the minimal elements of a subset of ZZ^r
findMins(List)
-- calculates the minimal elements of a subset of ZZ^r
findRegion
-- finds minimal multidegree(s) in a given region where an ideal or module satisfies a Boolean function
findRegion(List,Ideal,Function)
-- finds minimal multidegree(s) in a given region where an ideal or module satisfies a Boolean function
findRegion(List,Module,Function)
-- finds minimal multidegree(s) in a given region where an ideal or module satisfies a Boolean function
Inner
-- finds minimal multidegree(s) in a given region where an ideal or module satisfies a Boolean function
IrrelevantIdeal
-- checks whether degrees in the resolution of a truncation are at most those of the irrelevant ideal
irrelevantIdeal
-- gives the irrelevant ideal of the coordinate ring of a product of projective spaces
irrelevantIdeal(Ring)
-- gives the irrelevant ideal of the coordinate ring of a product of projective spaces
isLinearComplex
-- tests whether a complex of graded modules is linear
isLinearComplex(ChainComplex)
-- tests whether a complex of graded modules is linear
isQuasiLinear
-- checks whether degrees in the resolution of a truncation are at most those of the irrelevant ideal
isQuasiLinear(...,IrrelevantIdeal=>...)
-- checks whether degrees in the resolution of a truncation are at most those of the irrelevant ideal
isQuasiLinear(BettiTally)
-- checks whether degrees in the resolution of a truncation are at most those of the irrelevant ideal
isQuasiLinear(ChainComplex)
-- checks whether degrees in the resolution of a truncation are at most those of the irrelevant ideal
isQuasiLinear(List,Module)
-- checks whether degrees in the resolution of a truncation are at most those of the irrelevant ideal
LinearTruncations
-- truncations of a multigraded module that give linear resolutions
linearTruncations
-- finds minimal multidegree(s) in a given range where the resolution of a truncated module is linear
linearTruncations(List,Module)
-- finds minimal multidegree(s) in a given range where the resolution of a truncated module is linear
linearTruncations(Module)
-- finds minimal multidegree(s) in a given range where the resolution of a truncated module is linear
linearTruncationsBound
-- bounds the region where truncations of a module have linear resolutions
linearTruncationsBound(Module)
-- bounds the region where truncations of a module have linear resolutions
multigradedPolynomialRing
-- produces polynomial rings with standard multigradings
multigradedPolynomialRing(...,CoefficientField=>...)
-- produces polynomial rings with standard multigradings
multigradedPolynomialRing(...,Standard=>...)
-- produces polynomial rings with standard multigradings
multigradedPolynomialRing(...,Variables=>...)
-- produces polynomial rings with standard multigradings
multigradedPolynomialRing(List)
-- produces polynomial rings with standard multigradings
multigradedPolynomialRing(ZZ)
-- produces polynomial rings with standard multigradings
Outer
-- finds minimal multidegree(s) in a given region where an ideal or module satisfies a Boolean function
partialRegularities
-- calculates Castelnuovo-Mumford regularity in each component of a multigrading
partialRegularities(ChainComplex)
-- calculates Castelnuovo-Mumford regularity in each component of a multigrading
partialRegularities(Module)
-- calculates Castelnuovo-Mumford regularity in each component of a multigrading
regularityBound
-- bounds the multigraded regularity of a module
regularityBound(Module)
-- bounds the multigraded regularity of a module
supportOfTor
-- computes multidegrees in the support of Tor_i(M,k), where k is the residue field
supportOfTor(ChainComplex)
-- computes multidegrees in the support of Tor_i(M,k), where k is the residue field
supportOfTor(Module)
-- computes multidegrees in the support of Tor_i(M,k), where k is the residue field