prune(DGAlgebraMap) -- Pruning a DG algebra map is the identity

Function: prune
Usage:

fp = prune f

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

Description

Since prune(DGAlgebra) is the identity, and a DGAlgebraMap is stored as a ring map between the underlying graded algebras 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, y]

o1 = R

o1 : PolynomialRing

i2 : A = koszulComplexDGA R

o2 = {Ring => R                          }
      Underlying algebra => R[T   ..T   ]
                               1,1   1,2
      Differential => {x, y}

o2 : DGAlgebra

i3 : phi = identityDGAlgebraMap A

o3 = map (R[T   ..T   ], R[T   ..T   ], {T   , T   , x, y})
             1,1   1,2      1,1   1,2     1,1   1,2

o3 : DGAlgebraMap

i4 : (prune phi) === phi

o4 = true

i5 : (minimalPresentation phi) === phi

o5 = true

Ways to use this method:

prune(DGAlgebraMap) -- Pruning a DG algebra map is the identity

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:4791:0.

prune(DGAlgebraMap) -- Pruning a DG algebra map is the identity

Description

See also

Ways to use this method: