noetherianOperators(Ideal,Ideal) -- Noetherian operators of a primary component

• Function: noetherianOperators

• Usage:

  noetherianOperators (I, P)

  noetherianOperators (I, P, Strategy => "MacaulayMatrix")

  noetherianOperators (I, P, Rational => false)

• Inputs:
  • I, an ideal,
  • P, an ideal, a minimal prime of $I$
• Outputs:
  • a list, of differential operators

i1 : R = QQ[x,y,t];

i2 : I1 = ideal(x^2, y^2-x*t);

o2 : Ideal of R

i3 : I2 = ideal((x-t)^2);

o3 : Ideal of R

i4 : I = intersect(I1, I2);

o4 : Ideal of R

i5 : noetherianOperators(I, radical I1)

o5 = {| 1 |, | dy |, | tdy^2+2dx |, | tdy^3+6dxdy |}

o5 : List

i6 : noetherianOperators(I, radical I2) == noetherianOperators(I2)

o6 = true