MultIdeal -- Computes the multiplier ideal of a given number.

Synopsis

Usage:

MultIdeal(F,E,jn)
Inputs:
- F, Matrix
- E, Matrix
- jn, Real number
Optional inputs:
- MaxIterations => ..., default value 10000, Limits the number of iterations of the Unloading algorithm.
Outputs:
- The multiplier ideal associated to jn.

Description

Starting form the divisor encoded as a matrix of dimensions 1 x m, the intersection matrix as presented in [AAD14] and a real number, it returns the multiplier ideal associated to this number.

i1 : E = matrix({{ -5,  0,  1,  0,  1},
                     {  0, -2,  1,  0,  0},
                     {  1,  1, -1,  0,  0},
                     {  0,  0,  0, -2,  1},
                     {  1,  0,  0,  1, -1}})

o1 = | -5 0  1  0  1  |
     | 0  -2 1  0  0  |
     | 1  1  -1 0  0  |
     | 0  0  0  -2 1  |
     | 1  0  0  1  -1 |

              5       5
o1 : Matrix ZZ  <-- ZZ

i2 : F = matrix({{4,5,10,5,10}})

o2 = | 4 5 10 5 10 |

              1       5
o2 : Matrix ZZ  <-- ZZ

i3 : MultIdeal(F,E,1 / 2)

o3 = | 1 1 2 1 2 |

o3 : MutableMatrix

For the programmer

The object MultIdeal is a function closure.