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# MultiplicityJN -- Computes the multiplicity as a jumping number.

- 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.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/MultiplierIdealsDim2.m2:673:0.