org.mathIT.numbers

Class Factors

java.lang.Object

java.util.AbstractMap<K,V>

java.util.TreeMap<BigInteger,Integer>

org.mathIT.numbers.Factors

All Implemented Interfaces:

Serializable, Cloneable, Map<BigInteger,Integer>, NavigableMap<BigInteger,Integer>, SortedMap<BigInteger,Integer>

public class Factors
extends TreeMap<BigInteger,Integer>

An object of this class contains a list of all prime factors and their exponents. By the Fundamental Theorem of Arithmetic, any positive integer n has a unique decomposition into prime factors, i.e.,

n = p₁^e₁ + ... + p_k^e_k

where p₁ < ... < p_k are prime numbers and the exponents e₁, ..., e_k are positive integers. Technically, the prime factors are given as a TreeMap<BigInteger, Integer> where the keys are the different unique primes and the values the respective exponents, i.e.,

[<p₁, e₁>, ..., <p_k, e_k>]

Version:

1.1

Author:

Andreas de Vries

See Also:

Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class java.util.AbstractMap

AbstractMap.SimpleEntry<K,V>, AbstractMap.SimpleImmutableEntry<K,V>

Constructor Summary

Constructors

Constructor and Description
Factors(BigInteger n) Computes prime factors of n and stores them into this map.
Factors(long n) Computes prime factors of n and stores them into this map.

Method Summary

Modifier and Type	Method and Description
BigInteger	lambda() The Carmichael function λ(n).
BigInteger	phi() The Euler function φ(n), sometimes also called totient function.
String	toHTMLString() Returns a HTML string representation of this factor list.
String	toString() Returns a string representation of this factor list.
BigInteger	value() Returns the integer value determined by these prime factors.

Methods inherited from class java.util.TreeMap

ceilingEntry, ceilingKey, clear, clone, comparator, containsKey, containsValue, descendingKeySet, descendingMap, entrySet, firstEntry, firstKey, floorEntry, floorKey, forEach, get, headMap, headMap, higherEntry, higherKey, keySet, lastEntry, lastKey, lowerEntry, lowerKey, navigableKeySet, pollFirstEntry, pollLastEntry, put, putAll, remove, replace, replace, replaceAll, size, subMap, subMap, tailMap, tailMap, values

Methods inherited from class java.util.AbstractMap

equals, hashCode, isEmpty

Methods inherited from class java.lang.Object

finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface java.util.Map

compute, computeIfAbsent, computeIfPresent, equals, getOrDefault, hashCode, isEmpty, merge, putIfAbsent, remove

Constructor Detail

Factors

public Factors(BigInteger n)

Computes prime factors of n and stores them into this map.

Parameters:

n - the number which is to be factorized

Factors

public Factors(long n)

Computes prime factors of n and stores them into this map.

Parameters:

n - the number which is to be factorized

Method Detail

lambda

public BigInteger lambda()

The Carmichael function λ(n). For a definition and an introduction to this function see http://www.math-it.org/Mathematik/Zahlentheorie/Carmichael.html

Returns:

λ(n) where n is the number represented by this factors

phi

public BigInteger phi()

The Euler function φ(n), sometimes also called totient function. For a definition and an introduction to this function see http://www.math-it.org/Mathematik/Zahlentheorie/Euler.html

Returns:

φ(n) where n is the number represented by this factors

value

public BigInteger value()

Returns the integer value determined by these prime factors.

Returns:

the integer value determined by these factors

toHTMLString

public String toHTMLString()

Returns a HTML string representation of this factor list.

Returns:

a HTML string representation of this factor list

toString

public String toString()

Returns a string representation of this factor list.

Overrides:

toString in class AbstractMap<BigInteger,Integer>

Returns:

a string representation of this factor list