prune(DGIdeal) -- Trim a DG ideal down to a minimal generating set

Function: prune
Usage:

J = prune I

J = minimalPresentation I
Inputs:
- I, an instance of the type DGIdeal,
Optional inputs:
- Exclude => ..., default value {},
Outputs:
- J, an instance of the type DGIdeal, A DGIdeal with J.natural == I.natural (as ideals) but with a possibly smaller generator list obtained by trim.

Description

prune computes trim I.natural and wraps the result. It caches a pruningMap in J.cache giving the canonical comparison map J -> I; since DGIdeals have the same ambient DG algebra before and after pruning, this is recorded as the identity DGAlgebraMap on I.dgAlgebra.

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 : Anat = A.natural

o3 = Anat

o3 : PolynomialRing, 2 skew commutative variable(s)

i4 : I = dgIdeal(A, {x_Anat, x_Anat * y_Anat, x_Anat^2})

o4 = DGIdeal of Anat
     generators => | x |

o4 : DGIdeal

i5 : J = prune I

o5 = DGIdeal of Anat
     generators => | x |

o5 : DGIdeal

i6 : isWellDefined J

o6 = true

i7 : J.natural == I.natural

o7 = true

Idempotent: pruning an already-minimal DGIdeal is a no-op at the ideal level (the stored generator list already agrees with mingens). Repeated pruning is safe.

i8 : isWellDefined prune prune prune J

o8 = true

minimalPresentation is a synonym for prune on DGIdeals.

Ways to use this method:

prune(DGIdeal) -- Trim a DG ideal down to a minimal generating set

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:2775:0.

prune(DGIdeal) -- Trim a DG ideal down to a minimal generating set

Description

See also

Ways to use this method: