maxDegree(DGModule) -- Largest hom-degree present in a DG module

Function: maxDegree
Usage:

n = maxDegree M
Inputs:
- M, an instance of the type DGModule,
Outputs:
- n, an integer or an infinite number, maxDegree A + max(first d | d in M.Degrees) when A has finite max hom-degree; infinity otherwise.

Description

maxDegree of a DG module combines the hom-degree bound of the ambient DGAlgebra with the largest hom-degree shift of a natural generator. When the underlying DG algebra has an even-degree generator it has infinity as its max degree, and so does every DG module over it.

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(maxDegree KM == maxDegree KM.dgAlgebra)

i4 : A = koszulComplexDGA R

o4 = {Ring => R                          }
      Underlying algebra => R[T   ..T   ]
                               1,1   1,2
      Differential => {x, y}

o4 : DGAlgebra

i5 : M = freeDGModule(A, {0, 3})

o5 = {Base ring => R                       }
      DG algebra => R[T   ..T   ]
                       1,1   1,2
                                       2
      Natural module => (R[T   ..T   ])
                            1,1   1,2
      Generator degrees => {{0, 0}, {3, 0}}
      Differentials on gens => {0, 0}

o5 : DGModule

i6 : maxDegree M

o6 = 5

Ways to use this method:

maxDegree(DGModule) -- Largest hom-degree present in a DG module

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:7650:0.

maxDegree(DGModule) -- Largest hom-degree present in a DG module

Description

See also

Ways to use this method: