CompleteIntersectionResolutions : Table of Contents

• CompleteIntersectionResolutions -- "Resolution over a Complete Intersection"
• ARanks -- 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
• BRanks -- ranks of the modules B_i(d) in a matrixFactorization
• Check -- Option for matrixFactorization
• complexity -- complexity of a module over a complete intersection
• cosyzygyRes -- 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
• dualWithComponents -- dual module preserving direct sum information
• EisenbudShamash -- Computes the Eisenbud-Shamash Complex
• EisenbudShamashTotal -- Precursor complex of total Ext
• evenExtModule -- 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
• exteriorExtModule -- 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
• exteriorTorModule -- Tor as a module over an exterior algebra or bigraded algebra
• extIsOnePolynomial -- 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
• ExtModuleData -- 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)
• finiteBettiNumbers -- betti numbers of finite resolution computed from a matrix factorization
• freeExteriorSummand -- 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
• hfModuleAsExt -- predict betti numbers of moduleAsExt(M,R)
• highSyzygy -- 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
• HomWithComponents -- computes Hom, preserving direct sum information
• infiniteBettiNumbers -- betti numbers of finite resolution computed from a matrix factorization
• isLinear -- check whether matrix entries have degree 1
• isQuasiRegular -- tests a matrix or sequence or list for quasi-regularity on a module
• isStablyTrivial -- returns true if the map goes to 0 under stableHom
• koszulExtension -- creates the Koszul extension complex of a map
• Layered -- Option for matrixFactorization
• layeredResolution -- layered finite and infinite layered resolutions of CM modules
• Lift -- Option for newExt
• makeFiniteResolution -- finite resolution of a matrix factorization module M
• makeFiniteResolutionCodim2 -- Maps associated to the finite resolution of a high syzygy module in codim 2
• makeHomotopies -- returns a system of higher homotopies
• makeHomotopies1 -- returns a system of first homotopies
• makeHomotopiesOnHomology -- Homology of a complex as exterior module
• makeModule -- makes a Module out of a collection of modules and maps
• makeT -- make the CI operators on a complex
• matrixFactorization -- Maps in a higher codimension matrix factorization
• mfBound -- determines how high a syzygy to take for "matrixFactorization"
• moduleAsExt -- Find a module with given asymptotic resolution
• newExt -- 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
• 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
• regularitySequence -- regularity of Ext modules for a sequence of MCM approximations
• S2 -- Universal map to a module satisfying Serre's condition S2
• Shamash -- Computes the Shamash Complex
• splittings -- compute the splittings of a split right exact sequence
• stableHom -- map from Hom(M,N) to the stable Hom module
• sumTwoMonomials -- tally the sequences of BRanks for certain examples
• TateResolution -- TateResolution of a module over an exterior algebra
• tensorWithComponents -- forms the tensor product, preserving direct sum information
• toArray -- makes an array from a List or from a single integer
• twoMonomials -- tally the sequences of BRanks for certain examples