prune(DGModuleMap) -- Pruning a DG module map is the identity

Function: prune
Usage:

fp = prune f

fp = minimalPresentation f
Inputs:
- f, an instance of the type DGModuleMap,
Optional inputs:
- Exclude => ..., default value {},
Outputs:
- fp, an instance of the type DGModuleMap, The same DG module map f.

Description

Since prune(DGModule) is the identity, and a DGModuleMap is stored as an A.natural-linear matrix between the naturals of its source and target, there is nothing for prune to minimize. The method is installed as the identity so that pruning commutes uniformly.

minimalPresentation is a synonym for prune.

i1 : R = ZZ/101[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 : idM = identityDGModuleMap M

                         2
o4 = {Source => (R[T   ])      }
                    1,1
                         2
      Target => (R[T   ])
                    1,1
      Natural => {0, 0} | 1 0 |
                 {1, 0} | 0 1 |

o4 : DGModuleMap

i5 : (prune idM) === idM

o5 = true

i6 : (minimalPresentation idM) === idM

o6 = true

Ways to use this method:

prune(DGModuleMap) -- Pruning a DG module map is the identity

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:4827:0.

prune(DGModuleMap) -- Pruning a DG module map is the identity

Description

See also

Ways to use this method: