# 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, assumed to be unmixed
• P, an ideal, a minimal prime of $I$
• Outputs:

## Description

Compute a set of Noetherian operators for $P$-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) 2 3 o5 = {1, dy, t*dy + 2*dx, t*dy + 6*dx*dy} 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 ration point, the optional argument Rational can be set to true. This may offer a speed up in the computation.