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

Synopsis

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

Description

Compute a set of Noetherian operators for the $P$-primary component of $I$.

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

The optional argument Strategy can be used to choose different algorithms. Each strategy may accept additional optional arguments, see the documentation page for each strategy for details.

If the prime $P$ is known to be a rational point, the optional argument Rational can be set to true. This may offer a speed-up in the computation.

Ways to use this method: