toComplex(DGModule) -- Export a DG module to a Complex of free base-ring modules

Function: toComplex
Usage:

C = toComplex M
Inputs:
- M, an instance of the type DGModule,
Outputs:
- C, a complex, A Complex of free A.ring-modules whose i-th differential is moduleDifferential(i+1, M).

Description

toComplex packages the per-degree module differentials as an ordinary Complex so that the result can flow through the rest of the Complexes package. The one-argument form uses maxDegree M as the truncation bound and errors out if that is infinity; use toComplex(DGModule,ZZ) to supply an explicit bound. The result is not cached by this method (use dgComplex for a cached variant).

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 : C = toComplex KM

      1      2      1
o3 = R  <-- R  <-- R
                    
     0      1      2

o3 : Complex

i4 : assert(instance(C, Complex))

i5 : assert(C.dd_1 == moduleDifferential(1, KM))

i6 : assert(C.dd_2 == moduleDifferential(2, KM))

Ways to use this method:

toComplex(DGModule) -- Export a DG module to a Complex of free base-ring modules

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:7764:0.

toComplex(DGModule) -- Export a DG module to a Complex of free base-ring modules

Description

See also

Ways to use this method: