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
- 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
- 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
- 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
- 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
- layeredResolution -- 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
- makeFiniteResolution -- finite resolution of a matrix factorization module M
- makeFiniteResolution(List,Matrix) -- finite resolution of a matrix factorization module M
- makeFiniteResolutionCodim2 -- Maps associated to the finite resolution of a high syzygy module in codim 2
- makeFiniteResolutionCodim2(List,Matrix) -- 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(..., Check => ...) -- 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
- 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