isValidDGModule -- Structural-invariant check on a DG module

Usage:

b = isValidDGModule M
Inputs:
- M, an instance of the type DGModule,
Outputs:
- b, a Boolean value, true if the stored DGModule has all required keys with the expected types; false otherwise.

Description

isValidDGModule parallels isValidDGAlgebra: it confirms that M carries the keys dgAlgebra, ring, natural, Degrees, and diff with the expected types, that the referenced DGAlgebra is itself structurally valid, and that the generator-degree list has the same length as the differential list. It does not verify the semantic property d_M^2 = 0; that is the job of isWellDefinedDifferential, and the two together are what the user-facing isWellDefined(DGModule) calls.

i1 : R = QQ[x, y] / ideal(x^2, y^2)

o1 = R

o1 : QuotientRing

i2 : KM = koszulComplexDGM R^1

o2 = {Base ring => R                    }
      DG algebra => R[T   ..T   ]
                       1,1   1,2
                                       1
      Natural module => (R[T   ..T   ])
                            1,1   1,2
      Generator degrees => {{0, 0}}
      Differentials on gens => {0}

o2 : DGModule

i3 : assert(isValidDGModule KM)

Ways to use isValidDGModule:

isValidDGModule(DGModule)

For the programmer

The object isValidDGModule is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:7058:0.

isValidDGModule -- Structural-invariant check on a DG module

Description

See also

Ways to use isValidDGModule:

For the programmer