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 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.

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