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DGIdeal + DGIdeal -- Sum of two DG ideals

Description

Preserves d-closure because d(I + J) \subset dI + dJ \subset I + J.

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})

o4 = DGIdeal of Anat
     generators => | x |

o4 : DGIdeal
 
i5 : J = dgIdeal(A, {y_Anat})

o5 = DGIdeal of Anat
     generators => | y |

o5 : DGIdeal
 
i6 : K = I + J

o6 = DGIdeal of Anat
     generators => | y x |

o6 : DGIdeal
 
i7 : isWellDefined K

o7 = true
 
i8 : (I + J) == (J + I)

o8 = true

The zero DGIdeal is a two-sided identity for +.

i9 : Z = dgIdeal(A, {})

o9 = DGIdeal of Anat
     generators => 0

o9 : DGIdeal
 
i10 : (Z + I) == I

o10 = true

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.m2:2470:0.