RingElement % DGIdeal -- Reduce a ring element modulo a DG ideal

Operator: %
Usage:

r = f % I
Inputs:
- f, a ring element, A RingElement of I.dgAlgebra.natural, or an integer (coerced into I.dgAlgebra.natural before reduction).
- I, an instance of the type DGIdeal,
Outputs:
- r, a ring element, The normal form of f modulo I.natural.

Description

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 : (x_Anat^2 % I) == 0

o5 = true

i6 : (y_Anat^2 % I) == y_Anat^2

o6 = true

Ways to use this method:

RingElement % DGIdeal -- Reduce a ring element modulo a DG ideal
ZZ % DGIdeal

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:2685:0.

RingElement % DGIdeal -- Reduce a ring element modulo a DG ideal

Description

See also

Ways to use this method: