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Dmodules :: multiplierIdeal(Ideal,QQ)

multiplierIdeal(Ideal,QQ) -- multiplier ideal



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


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.

See also