toComplex(DGModule,ZZ) -- Export a DG module to a Complex with an explicit hom-degree bound

Function: toComplex
Usage:

C = toComplex(M, n)
Inputs:
- M, an instance of the type DGModule,
- n, an integer, A hom-degree upper bound.
Outputs:
- C, a complex, A Complex of free A.ring-modules, truncated at hom-degree n.

Description

The explicit-bound form of toComplex(DGModule). Supplying a bound is required when the ambient DG algebra has infinite hom-degree (as for an acyclicClosure), and convenient when a low bound suffices.

i1 : R = QQ[x, y, z]

o1 = R

o1 : PolynomialRing

i2 : KM = koszulComplexDGM R^1

o2 = {Base ring => R                    }
      DG algebra => R[T   ..T   ]
                       1,1   1,3
                                       1
      Natural module => (R[T   ..T   ])
                            1,1   1,3
      Generator degrees => {{0, 0}}
      Differentials on gens => {0}

o2 : DGModule

i3 : C = toComplex(KM, 2)

      1      3      3
o3 = R  <-- R  <-- R
                    
     0      1      2

o3 : Complex

i4 : assert(instance(C, Complex))

i5 : assert(max C == 2)

Ways to use this method:

toComplex(DGModule,ZZ) -- Export a DG module to a Complex with an explicit hom-degree bound

The source of this document is in DGAlgebras/doc.m2:7799:0.

toComplex(DGModule,ZZ) -- Export a DG module to a Complex with an explicit hom-degree bound

Description

See also

Ways to use this method: