CompleteIntersectionResolutions : Index

• 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