MultiplicityJN -- Computes the multiplicity as a jumping number.

Synopsis

Usage:

MultIdeal(F,E,jn)
Inputs:
- F, Matrix
- E, Matrix
- jn, Real number
Outputs:
- The multiplicity of jn as a jumping number.

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 jn, it returns the multiplicity of jn as a jumping number. It is important to notice that if jn is not a jumping number, then the multiplicity will be zero.

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 : MultiplicityJN(F,E,1 / 2)

o3 = 1

o3 : QQ

For the programmer

The object MultiplicityJN is a function closure.