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mingens(DGIdeal) -- Basic accessors on a DG ideal

Description

Thin wrappers around the corresponding Ideal operations on I.natural, with the exception of ambient I, which returns the ambient DGAlgebra (not its underlying ring).

mingens I returns the minimal-generator matrix of I.natural. Note that the d-saturation in dgIdeal may have produced redundant generators; mingens I re-extracts a minimal set.

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})

o4 = DGIdeal of Anat
     generators => | x |

o4 : DGIdeal
 
i5 : mingens I

o5 = | x |

                1         1
o5 : Matrix Anat  <-- Anat
 
i6 : numgens I

o6 = 1

numgens I equals numgens I.natural — the number of (stored, possibly redundant) generators of the underlying ideal.

i7 : numgens I == numgens I.natural

o7 = true

module I returns the underlying Module-view of the ideal, and ring I, ambient I, generators I expose the ground ring, the ambient DG algebra, and the chosen generator matrix, respectively.

i8 : ring I === R

o8 = true
 
i9 : ambient I === A

o9 = true
 
i10 : module I

o10 = image | x |

                                    1
o10 : Anat-module, submodule of Anat

See also

Ways to use this method:

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:2730:0.