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CompleteIntersectionResolutions : Index
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ARanks
-- ranks of the modules A_i(d) in a matrixFactorization
ARanks(List)
-- ranks of the modules A_i(d) in a matrixFactorization
Augmentation
-- Option for matrixFactorization
BGGL
-- Exterior module to linear complex
bMaps
-- list the maps d_p:B_1(p)-->B_0(p) in a matrixFactorization
bMaps(List)
-- list the maps d_p:B_1(p)-->B_0(p) in a matrixFactorization
BRanks
-- ranks of the modules B_i(d) in a matrixFactorization
BRanks(List)
-- ranks of the modules B_i(d) in a matrixFactorization
Check
-- Option for matrixFactorization
CompleteIntersectionResolutions
-- "Resolution over a Complete Intersection"
complexity
-- complexity of a module over a complete intersection
complexity(List)
-- complexity of a module over a complete intersection
complexity(Module)
-- complexity of a module over a complete intersection
cosyzygyRes
-- cosyzygy chain of a Cohen-Macaulay module over a Gorenstein ring
cosyzygyRes(Module)
-- cosyzygy chain of a Cohen-Macaulay module over a Gorenstein ring
cosyzygyRes(ZZ,Module)
-- cosyzygy chain of a Cohen-Macaulay module over a Gorenstein ring
dMaps
-- list the maps d(p):A_1(p)--> A_0(p) in a matrixFactorization
dMaps(List)
-- list the maps d(p):A_1(p)--> A_0(p) in a matrixFactorization
dualWithComponents
-- dual module preserving direct sum information
dualWithComponents(Module)
-- dual module preserving direct sum information
EisenbudShamash
-- Computes the Eisenbud-Shamash Complex
EisenbudShamash(Matrix,ChainComplex,ZZ)
-- Computes the Eisenbud-Shamash Complex
EisenbudShamash(Ring,ChainComplex,ZZ)
-- Computes the Eisenbud-Shamash Complex
EisenbudShamashTotal
-- Precursor complex of total Ext
EisenbudShamashTotal(...,Check=>...)
-- Precursor complex of total Ext
EisenbudShamashTotal(...,Grading=>...)
-- Precursor complex of total Ext
EisenbudShamashTotal(...,Variables=>...)
-- Precursor complex of total Ext
EisenbudShamashTotal(Module)
-- Precursor complex of total Ext
evenExtModule
-- even part of Ext^*(M,k) over a complete intersection as module over CI operator ring
evenExtModule(...,OutRing=>...)
-- even part of Ext^*(M,k) over a complete intersection as module over CI operator ring
evenExtModule(Module)
-- even part of Ext^*(M,k) over a complete intersection as module over CI operator ring
expo
-- returns a set corresponding to the basis of a divided power
expo(ZZ,List)
-- returns a set corresponding to the basis of a divided power
expo(ZZ,ZZ)
-- returns a set corresponding to the basis of a divided power
exteriorExtModule
-- Ext(M,k) or Ext(M,N) as a module over an exterior algebra
exteriorExtModule(Matrix,Module)
-- Ext(M,k) or Ext(M,N) as a module over an exterior algebra
exteriorExtModule(Matrix,Module,Module)
-- Ext(M,k) or Ext(M,N) as a module over an exterior algebra
exteriorHomologyModule
-- Make the homology of a complex into a module over an exterior algebra
exteriorHomologyModule(Matrix,ChainComplex)
-- Make the homology of a complex into a module over an exterior algebra
exteriorTorModule
-- Tor as a module over an exterior algebra or bigraded algebra
exteriorTorModule(Matrix,Module)
-- Tor as a module over an exterior algebra or bigraded algebra
exteriorTorModule(Matrix,Module,Module)
-- Tor as a module over an exterior algebra or bigraded algebra
extIsOnePolynomial
-- check whether the Hilbert function of Ext(M,k) is one polynomial
extIsOnePolynomial(Module)
-- check whether the Hilbert function of Ext(M,k) is one polynomial
ExtModule
-- Ext^*(M,k) over a complete intersection as module over CI operator ring
ExtModule(Module)
-- Ext^*(M,k) over a complete intersection as module over CI operator ring
ExtModuleData
-- Even and odd Ext modules and their regularity
ExtModuleData(Module)
-- Even and odd Ext modules and their regularity
extVsCohomology
-- compares Ext_S(M,k) as exterior module with coh table of sheaf Ext_R(M,k)
extVsCohomology(Matrix,Module)
-- compares Ext_S(M,k) as exterior module with coh table of sheaf Ext_R(M,k)
finiteBettiNumbers
-- betti numbers of finite resolution computed from a matrix factorization
finiteBettiNumbers(List)
-- betti numbers of finite resolution computed from a matrix factorization
freeExteriorSummand
-- find the free summands of a module over an exterior algebra
freeExteriorSummand(Module)
-- find the free summands of a module over an exterior algebra
Grading
-- Option for EisenbudShamashTotal, newExt
hf
-- Computes the hilbert function in a range of degrees
hf(List,Module)
-- Computes the hilbert function in a range of degrees
hf(Sequence,Module)
-- Computes the hilbert function in a range of degrees
hfModuleAsExt
-- predict betti numbers of moduleAsExt(M,R)
hfModuleAsExt(ZZ,Module,ZZ)
-- predict betti numbers of moduleAsExt(M,R)
highSyzygy
-- Returns a syzygy module one beyond the regularity of Ext(M,k)
highSyzygy(...,Optimism=>...)
-- Returns a syzygy module one beyond the regularity of Ext(M,k)
highSyzygy(Module)
-- Returns a syzygy module one beyond the regularity of Ext(M,k)
hMaps
-- list the maps h(p): A_0(p)--> A_1(p) in a matrixFactorization
hMaps(List)
-- list the maps h(p): A_0(p)--> A_1(p) in a matrixFactorization
HomWithComponents
-- computes Hom, preserving direct sum information
HomWithComponents(Module,Module)
-- computes Hom, preserving direct sum information
infiniteBettiNumbers
-- betti numbers of finite resolution computed from a matrix factorization
infiniteBettiNumbers(List,ZZ)
-- betti numbers of finite resolution computed from a matrix factorization
isLinear
-- check whether matrix entries have degree 1
isLinear(Matrix)
-- check whether matrix entries have degree 1
isQuasiRegular
-- tests a matrix or sequence or list for quasi-regularity on a module
isQuasiRegular(List,Module)
-- tests a matrix or sequence or list for quasi-regularity on a module
isQuasiRegular(Matrix,Module)
-- tests a matrix or sequence or list for quasi-regularity on a module
isQuasiRegular(Sequence,Module)
-- tests a matrix or sequence or list for quasi-regularity on a module
isStablyTrivial
-- returns true if the map goes to 0 under stableHom
isStablyTrivial(Matrix)
-- returns true if the map goes to 0 under stableHom
koszulExtension
-- creates the Koszul extension complex of a map
koszulExtension(ChainComplex,ChainComplex,Matrix,Matrix)
-- creates the Koszul extension complex of a map
Layered
-- Option for matrixFactorization
layeredResolution
-- layered finite and infinite layered resolutions of CM modules
layeredResolution(...,Check=>...)
-- layered finite and infinite layered resolutions of CM modules
layeredResolution(...,Verbose=>...)
-- layered finite and infinite layered resolutions of CM modules
layeredResolution(Matrix,Module)
-- layered finite and infinite layered resolutions of CM modules
layeredResolution(Matrix,Module,ZZ)
-- layered finite and infinite layered resolutions of CM modules
Lift
-- Option for newExt
makeFiniteResolution
-- finite resolution of a matrix factorization module M
makeFiniteResolution(Matrix,List)
-- finite resolution of a matrix factorization module M
makeFiniteResolutionCodim2
-- Maps associated to the finite resolution of a high syzygy module in codim 2
makeFiniteResolutionCodim2(...,Check=>...)
-- Maps associated to the finite resolution of a high syzygy module in codim 2
makeFiniteResolutionCodim2(Matrix,List)
-- Maps associated to the finite resolution of a high syzygy module in codim 2
makeHomotopies
-- returns a system of higher homotopies
makeHomotopies(Matrix,ChainComplex)
-- returns a system of higher homotopies
makeHomotopies(Matrix,ChainComplex,ZZ)
-- returns a system of higher homotopies
makeHomotopies1
-- returns a system of first homotopies
makeHomotopies1(Matrix,ChainComplex)
-- returns a system of first homotopies
makeHomotopies1(Matrix,ChainComplex,ZZ)
-- returns a system of first homotopies
makeHomotopiesOnHomology
-- Homology of a complex as exterior module
makeHomotopiesOnHomology(Matrix,ChainComplex)
-- Homology of a complex as exterior module
makeModule
-- makes a Module out of a collection of modules and maps
makeModule(HashTable,Matrix,HashTable)
-- makes a Module out of a collection of modules and maps
makeT
-- make the CI operators on a complex
makeT(Matrix,ChainComplex,ZZ)
-- make the CI operators on a complex
matrixFactorization
-- Maps in a higher codimension matrix factorization
matrixFactorization(...,Augmentation=>...)
-- Maps in a higher codimension matrix factorization
matrixFactorization(...,Check=>...)
-- Maps in a higher codimension matrix factorization
matrixFactorization(...,Layered=>...)
-- Maps in a higher codimension matrix factorization
matrixFactorization(...,Verbose=>...)
-- Maps in a higher codimension matrix factorization
matrixFactorization(Matrix,Module)
-- Maps in a higher codimension matrix factorization
mfBound
-- determines how high a syzygy to take for "matrixFactorization"
mfBound(Module)
-- determines how high a syzygy to take for "matrixFactorization"
moduleAsExt
-- Find a module with given asymptotic resolution
moduleAsExt(Module,Ring)
-- Find a module with given asymptotic resolution
newExt
-- Global Ext for modules over a complete Intersection
newExt(...,Check=>...)
-- Global Ext for modules over a complete Intersection
newExt(...,Grading=>...)
-- Global Ext for modules over a complete Intersection
newExt(...,Lift=>...)
-- Global Ext for modules over a complete Intersection
newExt(...,Variables=>...)
-- Global Ext for modules over a complete Intersection
newExt(Module,Module)
-- Global Ext for modules over a complete Intersection
oddExtModule
-- odd part of Ext^*(M,k) over a complete intersection as module over CI operator ring
oddExtModule(...,OutRing=>...)
-- odd part of Ext^*(M,k) over a complete intersection as module over CI operator ring
oddExtModule(Module)
-- odd part of Ext^*(M,k) over a complete intersection as module over CI operator ring
Optimism
-- Option to highSyzygy
OutRing
-- Option allowing specification of the ring over which the output is defined
psiMaps
-- list the maps psi(p): B_1(p) --> A_0(p-1) in a matrixFactorization
psiMaps(List)
-- list the maps psi(p): B_1(p) --> A_0(p-1) in a matrixFactorization
regularitySequence
-- regularity of Ext modules for a sequence of MCM approximations
regularitySequence(List,Module)
-- regularity of Ext modules for a sequence of MCM approximations
S2
-- Universal map to a module satisfying Serre's condition S2
S2(ZZ,Module)
-- Universal map to a module satisfying Serre's condition S2
Shamash
-- Computes the Shamash Complex
Shamash(Matrix,ChainComplex,ZZ)
-- Computes the Shamash Complex
Shamash(Ring,ChainComplex,ZZ)
-- Computes the Shamash Complex
splittings
-- compute the splittings of a split right exact sequence
splittings(Matrix,Matrix)
-- compute the splittings of a split right exact sequence
stableHom
-- map from Hom(M,N) to the stable Hom module
stableHom(Module,Module)
-- map from Hom(M,N) to the stable Hom module
sumTwoMonomials
-- tally the sequences of BRanks for certain examples
sumTwoMonomials(ZZ,ZZ)
-- tally the sequences of BRanks for certain examples
TateResolution
-- TateResolution of a module over an exterior algebra
TateResolution(Module)
-- TateResolution of a module over an exterior algebra
TateResolution(Module,ZZ)
-- TateResolution of a module over an exterior algebra
TateResolution(Module,ZZ,ZZ)
-- TateResolution of a module over an exterior algebra
tensorWithComponents
-- forms the tensor product, preserving direct sum information
tensorWithComponents(Module,Module)
-- forms the tensor product, preserving direct sum information
toArray
-- makes an array from a List or from a single integer
toArray(List)
-- makes an array from a List or from a single integer
toArray(ZZ)
-- makes an array from a List or from a single integer
twoMonomials
-- tally the sequences of BRanks for certain examples
twoMonomials(...,Optimism=>...)
-- tally the sequences of BRanks for certain examples
twoMonomials(ZZ,ZZ)
-- tally the sequences of BRanks for certain examples