noetherianOperators(Module) -- Noetherian operators of a primary submodule

Synopsis

Function: noetherianOperators
Usage:

noetherianOperators U
Inputs:
- U, a module, a primary submodule
Outputs:
- a list, of differential operators

Description

Compute a set of Noetherian operators for the primary submodule U.

This method contains an implementation of Algorithm 4.1 in the paper Primary decomposition of modules: a computational differential approach. For more details, see Section 4 of the paper Primary decomposition of modules: a computational differential approach.

i1 : R = QQ[x_1,x_2,x_3]

o1 = R

o1 : PolynomialRing

i2 : U = image matrix {{x_1, x_2^2, 0}, {x_3, x_3^2, x_2^2-x_1*x_3}}

o2 = image | x_1 x_2^2 0            |
           | x_3 x_3^2 x_2^2-x_1x_3 |

                             2
o2 : R-module, submodule of R

i3 : noetherianOperators U

o3 = {| -x_3 |}
      |  x_1 |

o3 : List

Ways to use this method: