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isHomogeneous(DGIdeal) -- Predicates on a DG ideal

Description

isHomogeneous I returns isHomogeneous I.natural — i.e. tests whether the underlying ideal is homogeneous with respect to the grading of A.natural.

isZero I returns true iff I.natural is the zero ideal (equivalently, numgens I.natural == 0).

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, y_Anat})

o4 = DGIdeal of Anat
     generators => | y x |

o4 : DGIdeal
 
i5 : isHomogeneous I

o5 = true
 
i6 : isZero I

o6 = false
 
i7 : Z = dgIdeal(A, {})

o7 = DGIdeal of Anat
     generators => 0

o7 : DGIdeal
 
i8 : isZero Z

o8 = true

See also

Ways to use this method:

The source of this document is in DGAlgebras/doc.m2:2839:0.