DG module primitives and chain-complex export -- Installing differentials, reading degree data, and exporting to Complex

This page collects the remaining DG module primitives (installing a differential, asking for the largest hom-degree, reading off a per-degree basis) together with the methods that export a DG algebra, DG module, DG module map, or DG ideal to the ordinary Complex / ComplexMap world.

Installing a differential. setDiff(DGModule,List) is the DG module analogue of setDiff(DGAlgebra,List): it records the image of each natural generator under d_M and invalidates every cached derived value.

Reading degree data. maxDegree(DGModule) and maxDegree(DGQuotientModule) report the largest hom-degree present (or infinity if the underlying DG algebra has an even-degree generator). getBasis(ZZ,DGModule) returns an A.ring-basis of the hom-degree-n piece of M.natural.

Exporting to Complex. The toComplex family packages per-degree differentials as a plain Complex of free base-ring modules; the toComplexMap family packages per-degree induced maps as a ComplexMap. Together they let the chain-level results of the DG machinery be handed off to the rest of the Complexes package.

Block-diagonal display. displayBlockDiff prints the per-internal-multidegree block decomposition of a DG algebra differential at a given homological degree, convenient for inspecting the acyclic closure of a multigraded quotient.