# jumpingCoefficients(Ideal) -- jumping coefficients and corresponding multiplier ideals

## Synopsis

• Function: jumpingCoefficients
• Usage:
(cs, mI) = jumpingCoefficients I, (cs, mI) = jumpingCoefficients(I,a,b)
• Inputs:
• I, an ideal, an ideal in a polynomial ring
• Optional inputs:
• DegreeLimit => ..., default value null, multiplier ideal
• Strategy => ..., default value ViaElimination, multiplier ideal
• Outputs:
• cs, a list, the list of jumping coefficients
• mI, a list, the list of corresponding multiplier ideals

## Description

Computes the jumping coefficients and their multiplier ideals in an open interval (a,b). By default a = 0, b = analyticSpread I. The options are passed to multiplierIdeal.

See Berkesch and Leykin Algorithms for Bernstein-Sato polynomials and multiplier ideals'' for details.
 i1 : R = QQ[x_1..x_4]; i2 : jumpingCoefficients ideal {x_1^3 - x_2^2, x_2^3 - x_3^2} 4 29 31 11 35 2 o2 = ({-, --, --, --, --}, {ideal (x , x , x ), ideal (x , x , x ), ideal 3 18 18 6 18 3 2 1 3 2 1 ------------------------------------------------------------------------ 2 2 2 2 3 2 (x , x , x x , x ), ideal (x , x x , x x , x , x x , x ), ideal (x , 3 2 1 2 1 3 2 3 1 3 2 1 2 1 3 ------------------------------------------------------------------------ 2 2 3 x x , x x , x , x x , x )}) 2 3 1 3 2 1 2 1 o2 : Sequence