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MCMApproximations : Index
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approximation
-- returns pair of components of the map from the MCM approximation
approximation(...,CoDepth=>...)
-- returns pair of components of the map from the MCM approximation
approximation(...,Total=>...)
-- returns pair of components of the map from the MCM approximation
approximation(Module)
-- returns pair of components of the map from the MCM approximation
approximationSequence
-- Short exact sequence of the MCM approximation
auslanderInvariant
-- measures failure of surjectivity of the essential MCM approximation
auslanderInvariant(...,CoDepth=>...)
-- measures failure of surjectivity of the essential MCM approximation
auslanderInvariant(Module)
-- measures failure of surjectivity of the essential MCM approximation
Characteristic
-- Option for setupRings(c,d,Characteristic=>q)
coApproximation
-- Maximal Cohen-Macaulay co-approximation of M
coApproximation(...,CoDepth=>...)
-- Maximal Cohen-Macaulay co-approximation of M
coApproximation(...,Total=>...)
-- Maximal Cohen-Macaulay co-approximation of M
coApproximation(Module)
-- Maximal Cohen-Macaulay co-approximation of M
coApproximationSequence
-- Short exact sequence of the MCM coapproximation
CoDepth
-- Option for syzygyModule(-k,M,CoDepth => m)
MCMApproximations
-- Maximal Cohen-Macaulay Approximations and Complete Intersections
profondeur
-- computes the profondeur with respect to an ideal
profondeur(Ideal,Module)
-- computes the profondeur with respect to an ideal
profondeur(Module)
-- computes the profondeur with respect to an ideal
profondeur(Ring)
-- computes the profondeur with respect to an ideal
Randomize
-- Option for setupRings(c,d,Characteristic=>q, Randomize=>false)
setupModules
-- Creates a list of modules and maps over complete intersection for experiments
setupModules(List,Module)
-- Creates a list of modules and maps over complete intersection for experiments
setupRings
-- Sets up a complete intersection for experiments
setupRings(...,Characteristic=>...)
-- Sets up a complete intersection for experiments
setupRings(...,Randomize=>...)
-- Sets up a complete intersection for experiments
setupRings(Matrix)
-- Sets up a complete intersection for experiments
setupRings(ZZ,ZZ)
-- Sets up a complete intersection for experiments
socleDegrees
-- lists the degrees of the socle generators
socleDegrees(Module)
-- lists the degrees of the socle generators
syzygyModule
-- Produces the k-th syzygy module (k \in ZZ)
syzygyModule(...,CoDepth=>...)
-- Produces the k-th syzygy module (k \in ZZ)
syzygyModule(ZZ,Module)
-- Produces the k-th syzygy module (k \in ZZ)
Total
-- option for approximation