TateOnProducts : Table of Contents

• TateOnProducts -- Computation of parts of the Tate resolution on products
• actionOnDirectImage -- recover the module structure via a Noether normalization
• beilinson -- apply the beilinson functor
• beilinsonBundle -- compute a basic Beilinson bundle
• beilinsonContraction -- compute a Beilinson contraction
• beilinsonWindow -- extract the subquotient complex which contributes to the Beilinson window
• bgg -- make a linear free complex from a module over an exterior algebra or a symmetric algebra
• BundleType -- Option in beilinson with values PrunedQuotient, QuotientBundle, DummyQuotientBundle, SubBundle, FreeBundle, or MapsBetweenFreeBundles
• coarseMultigradedRegularity -- A truncation that has linear resolution
• CoefficientField -- Option for productOfProjectiveSpaces
• cohomologyHashTable -- cohomology groups of a sheaf on a product of projective spaces, or of (part) of a Tate resolution
• cohomologyMatrix -- cohomology groups of a sheaf on P^{n_1}xP^{n_2}, or of (part) of a Tate resolution
• CohomologyVariables -- Option for productOfProjectiveSpaces
• composedFunctions -- composed functions
• ContractionData -- name of a cached datum
• contractionData -- Compute the action of monomials in the exterior algebra on the Beilinson monad
• cornerComplex -- form the corner complex
• directImageComplex -- compute the direct image complex
• DummyQuotientBundle -- value for the option BundleType in beilinson
• eulerPolynomialTable -- cohomology groups of a sheaf on a product of projective spaces, or of (part) of a Tate resolution
• firstQuadrantComplex -- form the first quadrant complex
• FreeBundle -- value for the option BundleType in beilinson
• InitialDegree -- Option for chainComplexMap
• isAction -- test whether a list of square matrices induces an action
• isIsomorphic -- probabilistic test for homogeneous isomorphism
• isQuism -- Test to see if the ChainComplexMap is a quasiisomorphism.
• lastQuadrantComplex -- form the last quadrant complex
• lowerCorner -- compute the lower corner
• MapsBetweenFreeBundles -- value for the option BundleType in beilinson
• productOfProjectiveSpaces -- Cox ring of a product of projective spaces and it Koszul dual exterior algebra
• PrunedQuotient -- value for the option BundleType in beilinson
• QuotientBundle -- value for the option BundleType in beilinson
• regionComplex -- region complex
• Rings -- Option for productOfProjectiveSpaces
• strand -- take the strand
• SubBundle -- value for the option BundleType in beilinson
• symExt -- from linear presentation matrices over S to linear presentation matrices over E and conversely
• tallyDegrees -- collect the degrees of the generators of the terms in a free complex
• TateData -- symbol used in beilinsonBundle
• tateData -- reads TateData from the cache of an appropriate ring
• tateExtension -- extend the terms in the Beilinson window to a part of a corner complex of the corresponding Tate resolution
• tateResolution -- compute the Tate resolution
• trivialHomologicalTruncation -- return the trivial truncation of a chain complex
• upperCorner -- compute the upper corner