# multiplierIdeal(Ideal,QQ) -- multiplier ideal

## Synopsis

• Function: multiplierIdeal
• Usage:
mI = multiplierIdeal(I,c)
• Inputs:
• I, an ideal, an ideal in a polynomial ring
• c, , 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.