displayModuleBlockDiff -- Pretty-print the labeled block matrix of a DG module differential

Usage:

tab = displayModuleBlockDiff(M, n)

entry = displayModuleBlockDiff(M, srcLbl, tgtLbl)
Inputs:
- M, an instance of the type DGModule, A DG module; must be free.
- n, an integer, A hom-degree.
- srcLbl, a list, A pair {i, v} identifying a single source block (a generator index and a chunk-degree vector).
- tgtLbl, a list, A pair {j, w} identifying a single target block.
Outputs:
- tab, a net, A centered table whose first row lists source labels and whose first column lists target labels; inner entries are the corresponding blocks of moduleBlockDiff(M, n).
- entry, a matrix, In the three-argument form, returns the single block b^[tgtLbl]_[srcLbl] extracted from the labeled block matrix.

Description

The two-argument form lays out moduleBlockDiff as a labeled table, parallel to displayBlockDiff for DG algebras. The three-argument form bypasses the table and returns a single block directly, which is handy for programmatic inspection.

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

o1 = R

o1 : QuotientRing

i2 : k = R^1 / ideal(x, y)

o2 = cokernel | x y |

                            1
o2 : R-module, quotient of R

i3 : A = koszulComplexDGA R

o3 = {Ring => R                          }
      Underlying algebra => R[T   ..T   ]
                               1,1   1,2
      Differential => {x, y}

o3 : DGAlgebra

i4 : Mdg = minimalSemifreeResolution(A, k, EndDegree => 2)

o4 = {Base ring => R                                          }
      DG algebra => R[T   ..T   ]
                       1,1   1,2
                                       3
      Natural module => (R[T   ..T   ])
                            1,1   1,2
      Generator degrees => {{0, 0}, {2, 2}, {2, 2}}
      Differentials on gens => {0, | xT_(1,1) |, | yT_(1,2) |}
                                   |     0    |  |     0    |
                                   |     0    |  |     0    |

o4 : DGModule

i5 : instance(displayModuleBlockDiff(Mdg, 2), Net)

o5 = true

Ways to use displayModuleBlockDiff:

displayModuleBlockDiff(DGModule,List,List)
displayModuleBlockDiff(DGModule,ZZ)

For the programmer

The object displayModuleBlockDiff is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:6387:0.

displayModuleBlockDiff -- Pretty-print the labeled block matrix of a DG module differential

Description

See also

Ways to use displayModuleBlockDiff:

For the programmer