generatorTable -- Display the generator list of a DG module with hom-degrees and differentials

Usage:

t = generatorTable M
Inputs:
- M, an instance of the type DGModule,
Outputs:
- t, a net, A centered table with one row per generator. Columns are the generator index i, the hom-degree, the remaining external degree, and the differential M.diff#i.

Description

A convenient overview of the generator structure of a semifree DG module. Particularly useful for inspecting the output of minimalSemifreeResolution or semifreeResolution, where each iteration of killCycles(DGModule) appends further generators.

i1 : R = QQ[x]

o1 = R

o1 : PolynomialRing

i2 : A = koszulComplexDGA R

o2 = {Ring => R                    }
      Underlying algebra => R[T   ]
                               1,1
      Differential => {x}

o2 : DGAlgebra

i3 : M = freeDGModule(A, {0, 1})

o3 = {Base ring => R                       }
      DG algebra => R[T   ]
                       1,1
                                 2
      Natural module => (R[T   ])
                            1,1
      Generator degrees => {{0, 0}, {1, 0}}
      Differentials on gens => {0, 0}

o3 : DGModule

i4 : natGens = apply(rank M.natural, i -> (M.natural)_i)

o4 = {| 1 |, | 0 |}
      | 0 |  | 1 |

o4 : List

i5 : setDiff(M, {0, x * natGens#0})

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

o5 : DGModule

i6 : instance(generatorTable M, Net)

o6 = true

When M has no generators, the result is a single-row placeholder.

Ways to use generatorTable:

generatorTable(DGModule)

For the programmer

The object generatorTable is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:6239:0.

generatorTable -- Display the generator list of a DG module with hom-degrees and differentials

Description

See also

Ways to use generatorTable:

For the programmer