multiplierIdeal(Ideal,QQ) -- multiplier ideal

Synopsis

Function: multiplierIdeal
Usage:

mI = multiplierIdeal(I,c)
Inputs:
- I, an ideal, an ideal in a polynomial ring
- c, a rational number, coefficient (or a list of coefficients)
Optional inputs:
- DegreeLimit => ..., default value null
- Strategy => ..., default value ViaElimination
Outputs:
- mI, an ideal, multiplier ideal J_I(c) (or a list of)

Description

Computes the multiplier ideal for given ideal and coefficient.

There are three options for Strategy:

ViaElimination -- the default;
ViaLinearAlgebra -- skips one expensive elimination step by using linear algebra;
ViaColonIdeal -- same as elimination, but may be slightly faster.

The option DegreeLimit specifies the maximal degree of polynomials to consider for membership in the multiplier ideal.See Berkesch and Leykin ``Algorithms for Bernstein-Sato polynomials and multiplier ideals'' for details.

i1 : R = QQ[x_1..x_4];

i2 : multiplierIdeal(ideal {x_1^3 - x_2^2, x_2^3 - x_3^2}, 31/18)

                 2         2
o2 = ideal (x , x , x x , x )
             3   2   1 2   1

o2 : Ideal of R

Caveat

When Strategy=>ViaLinearAlgebra the option DegreeLimit must be specified. The output it guaranteed to be the whole multiplier ideal only when dim(I)=0. For positive-dimensional input the up-to-specified-degree part of the multiplier ideal is returned.

Ways to use this method: