getBasis(ZZ,DGModule) -- Basis of the hom-degree-n piece of a DG module

Function: getBasis
Usage:

b = getBasis(n, M)
Inputs:
- n, an integer, A homological degree.
- M, an instance of the type DGModule,
Optional inputs:
- Limit => ..., default value -1, Maximum number of basis elements to return from getBasis
Outputs:
- b, a matrix, A one-row matrix over M.natural whose entries are the basis elements of F_n(M), the hom-degree-n piece of M.natural over A.ring.

Description

getBasis(n, M) delegates to basis on the underlying A.natural-module M.natural, restricting to the variables of A.natural. The result is the piece of M on which moduleDifferential(n, M) acts as its source-side basis.

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 : b = getBasis(1, KM)

o3 = | T_(1,1) T_(1,2) |

                           1                    2
o3 : Matrix (R[T   ..T   ])  <-- (R[T   ..T   ])
                1,1   1,2            1,1   1,2

i4 : assert(instance(b, Matrix))

i5 : assert(numcols b == 2)

Ways to use this method:

getBasis(ZZ,DGModule) -- Basis of the hom-degree-n piece of a DG module

The source of this document is in DGAlgebras/doc.m2:7724:0.

getBasis(ZZ,DGModule) -- Basis of the hom-degree-n piece of a DG module

Description

See also

Ways to use this method: