DGIdeal == DGIdeal -- Equality and containment of DG ideals

Operator: ==
Usage:

b = I == J

b = isSubset(I, J)
Inputs:
- I, an instance of the type DGIdeal,
- J, an instance of the type DGIdeal,
Outputs:
- b, a Boolean value,

Description

Both compare DGIdeals via their underlying Ideals I.natural and J.natural. Equality additionally requires the DG algebras to be the same object (=== — object identity, not just isomorphism). Containment also asserts that I and J share an ambient DG algebra.

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, {x_Anat, y_Anat})

o5 = DGIdeal of Anat
     generators => | y x |

o5 : DGIdeal

i6 : isSubset(I, J)

o6 = true

i7 : I != J

o7 = true

i8 : I == I

o8 = true

Ways to use this method:

DGIdeal == DGIdeal -- Equality and containment of DG ideals

The source of this document is in DGAlgebras/doc.m2:2656:0.

DGIdeal == DGIdeal -- Equality and containment of DG ideals

Description

See also

Ways to use this method: