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.

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

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

See also

• jumpingCoefficients -- jumping coefficients and corresponding multiplier ideals