# JNandMI -- HashTable containing all the information about the Jumping Numbers

## Description

This HashTable contains all the information about the jumping numbers that computes MultiplierIdeals. As a key, it contains the Jumping Number and for each Jumping Number it contains the multiplicity, the divisor associated to the ideal, the Maximal and Minimal Jumping Divisors and (if it applies) the critical chains.
 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 : MultiplierIdeals(F,E,BiggestJN => 1) 1 o3 = Jumping number: - Multiplicity: 1 Multiplier ideal: | 1 1 2 1 2 | Maximal jumping divisor: {| 1 0 1 0 1 |} 2 Minimal jumping divisor: {| 1 0 1 0 1 |} 7 Jumping number: -- Multiplicity: 2 Multiplier ideal: | 2 2 4 2 4 | Maximal jumping divisor: {| 0 0 1 0 1 |} 10 Minimal jumping divisor: {| 0 0 1 0 1 |} 9 Jumping number: -- Multiplicity: 2 Multiplier ideal: | 2 3 5 3 5 | Maximal jumping divisor: {| 0 0 1 0 1 |} 10 Minimal jumping divisor: {| 0 0 1 0 1 |} Jumping number: 1 Multiplicity: 1 Multiplier ideal: | 3 3 6 3 6 | Maximal jumping divisor: {| 1 1 1 1 1 |} Minimal jumping divisor: {| 1 0 1 0 1 |} o3 : Type of HashTable i4 : JNandMI 1 o4 = HashTable{{-} => {1, | 1 1 2 1 2 |, | 1 0 1 0 1 |, | 1 0 1 0 1 |} } 2 {1} => {1, | 3 3 6 3 6 |, | 1 1 1 1 1 |, | 1 0 1 0 1 |} 7 {--} => {2, | 2 2 4 2 4 |, | 0 0 1 0 1 |, | 0 0 1 0 1 |} 10 9 {--} => {2, | 2 3 5 3 5 |, | 0 0 1 0 1 |, | 0 0 1 0 1 |} 10 o4 : HashTable

## For the programmer

The object JNandMI is .