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

- 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

## See also

- multiplierIdeal -- multiplier ideal

## Ways to use this method:

- jumpingCoefficients(Ideal) -- jumping coefficients and corresponding multiplier ideals
- `jumpingCoefficients(Ideal,QQ,QQ)`
- `jumpingCoefficients(Ideal,QQ,ZZ)`
- `jumpingCoefficients(Ideal,ZZ,QQ)`
- `jumpingCoefficients(Ideal,ZZ,ZZ)`

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/BernsteinSato/DOC/multiplierIdeals.m2:61:0.