java.lang.Object
- org.nevec.rjm.Ifactor

All Implemented Interfaces:

java.lang.Cloneable, java.lang.Comparable<Ifactor>
```
public class Ifactor
extends java.lang.Object
implements java.lang.Cloneable, java.lang.Comparable<Ifactor>
```
Factored integers. This class contains a non-negative integer with the prime factor decomposition attached.

Since:

2006-08-14, 2012-02-14 The internal representation contains the bases, and becomes sparser if few prime factors are present.

Author:

Richard J. Mathar

Field Summary

Fields
Modifier and Type	Field	Description
`java.math.BigInteger`	`n`	The standard representation of the number
`static Ifactor`	`ONE`
`java.util.Vector<java.lang.Integer>`	`primeexp`
`static Ifactor`	`ZERO`

Constructor Summary

Constructors
Constructor	Description
`Ifactor(int number)`	Constructor given an integer.
`Ifactor(java.math.BigInteger number)`	Constructor given a BigInteger .
`Ifactor(java.util.Vector<java.lang.Integer> pows)`	Constructor given a list of exponents of the prime factor decomposition.
`Ifactor(Ifactor oth)`	Copy constructor.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`Ifactor`	`add(java.math.BigInteger oth)`	Summation with another positive integer
`int`	`bigomega()`	The sum of the prime factor exponents, with multiplicity.
`Ifactor`	`clone()`	Deep copy.
`int`	`compareTo(Ifactor oth)`	Compare value against another Ifactor
`java.math.BigInteger`	`core()`	The square-free part.
`Ifactor`	`divide(Ifactor oth)`	Integer division through another positive integer.
`java.util.Vector<java.math.BigInteger>`	`divisors()`	The set of positive divisors.
`Ifactor`	`dropPrime()`	Divide through the highest possible power of the highest prime.
`boolean`	`equals(Ifactor oth)`	Comparison of two numbers.
`Ifactor`	`gcd(Ifactor oth)`	Greatest common divisor of this and oth.
`boolean`	`issquare()`	Test whether this is a square of an integer (perfect square).
`Ifactor`	`lcm(Ifactor oth)`	Lowest common multiple of this with oth.
`static void`	`main(java.lang.String[] args)`	Test program.
`static Ifactor`	`max(java.util.Vector<Ifactor> set)`	Maximum of a list of values.
`Ifactor`	`max(Ifactor oth)`	Maximum of two values.
`static Ifactor`	`min(java.util.Vector<Ifactor> set)`	Minimum of a list of values.
`Ifactor`	`min(Ifactor oth)`	Minimum of two values.
`int`	`moebius()`	The Moebius function.
`protected Ifactor`	`multGcdLcm(Ifactor oth, int type)`	Multiply with another positive integer.
`Ifactor`	`multiply(int oth)`	Multiply with another positive integer.
`Ifactor`	`multiply(java.math.BigInteger oth)`	Multiply with another positive integer.
`Ifactor`	`multiply(Ifactor oth)`	Multiply with another positive integer.
`int`	`omega()`	The sum of the prime factor exponents, without multiplicity.
`Ifactor`	`pow(int exponent)`	Exponentiation with a positive integer.
`Rational`	`root(int r)`	Pulling the r-th root.
`Ifactor`	`sigma()`	Sum of the divisors of the number.
`Ifactor`	`sigma(int k)`	Sum of the k-th powers of divisors of the number.
`java.lang.String`	`toString()`	Convert to printable format

Methods inherited from class java.lang.Object
equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Field Detail
  - n
```
public java.math.BigInteger n
```
    The standard representation of the number
  - primeexp
```
public java.util.Vector<java.lang.Integer> primeexp
```
  - ONE
```
public static final Ifactor ONE
```
  - ZERO
```
public static final Ifactor ZERO
```
- Constructor Detail
  - Ifactor
```
public Ifactor(int number)
```
    Constructor given an integer. constructor with an ordinary integer
    
    Parameters:
    
    number - the standard representation of the integer
  - Ifactor
```
public Ifactor(java.math.BigInteger number)
```
    Constructor given a BigInteger . Constructor with an ordinary integer, calling a prime factor decomposition.
    
    Parameters:
    
    number - the BigInteger representation of the integer
  - Ifactor
```
public Ifactor(java.util.Vector<java.lang.Integer> pows)
```
    Constructor given a list of exponents of the prime factor decomposition.
    
    Parameters:
    
    pows - the vector with the sorted list of exponents. pows[0] is the exponent of 2, pows[1] the exponent of 3, pows[2] the exponent of 5 etc. Note that this list does not include the primes, but assumes a continuous prime-smooth basis.
  - Ifactor
```
public Ifactor(Ifactor oth)
```
    Copy constructor.
    
    Parameters:
    
    oth - the value to be copied
- Method Detail
  - clone
```
public Ifactor clone()
```
    Deep copy.
    
    Overrides:
    
    clone in class java.lang.Object
    
    Since:
    
    2009-08-14
  - equals
```
public boolean equals(Ifactor oth)
```
    Comparison of two numbers. The value of this method is in allowing the Vector<>.contains() calls that use the value, not the reference for comparison.
    
    Parameters:
    
    oth - the number to compare this with.
    
    Returns:
    
    true if both are the same numbers, false otherwise.
  - multiply
```
public Ifactor multiply(java.math.BigInteger oth)
```
    Multiply with another positive integer.
    
    Parameters:
    
    oth - the second factor.
    
    Returns:
    
    the product of both numbers.
  - multiply
```
public Ifactor multiply(int oth)
```
    Multiply with another positive integer.
    
    Parameters:
    
    oth - the second factor.
    
    Returns:
    
    the product of both numbers.
  - multiply
```
public Ifactor multiply(Ifactor oth)
```
    Multiply with another positive integer.
    
    Parameters:
    
    oth - the second factor.
    
    Returns:
    
    the product of both numbers.
  - lcm
```
public Ifactor lcm(Ifactor oth)
```
    Lowest common multiple of this with oth.
    
    Parameters:
    
    oth - the second parameter of lcm(this,oth)
    
    Returns:
    
    the lowest common multiple of both numbers. Returns zero if any of both arguments is zero.
  - gcd
```
public Ifactor gcd(Ifactor oth)
```
    Greatest common divisor of this and oth.
    
    Parameters:
    
    oth - the second parameter of gcd(this,oth)
    
    Returns:
    
    the lowest common multiple of both numbers. Returns zero if any of both arguments is zero.
  - multGcdLcm
```
protected Ifactor multGcdLcm(Ifactor oth,
                             int type)
```
    Multiply with another positive integer.
    
    Parameters:
    
    oth - the second factor.
    
    type - 0 to multiply, 1 for gcd, 2 for lcm
    
    Returns:
    
    the product, gcd or lcm of both numbers.
  - divide
```
public Ifactor divide(Ifactor oth)
```
    Integer division through another positive integer.
    
    Parameters:
    
    oth - the denominator.
    
    Returns:
    
    the division of this through the oth, discarding the remainder.
  - add
```
public Ifactor add(java.math.BigInteger oth)
```
    Summation with another positive integer
    
    Parameters:
    
    oth - the other term.
    
    Returns:
    
    the sum of both numbers
  - pow
```
public Ifactor pow(int exponent)
            throws java.lang.ArithmeticException
```
    Exponentiation with a positive integer.
    
    Parameters:
    
    exponent - the non-negative exponent
    
    Returns:
    
    n^exponent. If exponent=0, the result is 1.
    
    Throws:
    
    java.lang.ArithmeticException
  - root
```
public Rational root(int r)
              throws java.lang.ArithmeticException
```
    Pulling the r-th root.
    
    Parameters:
    
    r - the positive or negative (nonzero) root.
    
    Returns:
    
    n^(1/r). The return value falls into the Ifactor class if r is positive, but if r is negative a Rational type is needed.
    
    Throws:
    
    java.lang.ArithmeticException
    
    Since:
    
    2009-05-18
  - divisors
```
public java.util.Vector<java.math.BigInteger> divisors()
```
    The set of positive divisors.
    
    Returns:
    
    the vector of divisors of the absolute value, sorted.
    
    Since:
    
    2010-08-27
  - sigma
```
public Ifactor sigma()
```
    Sum of the divisors of the number.
    
    Returns:
    
    the sum of all divisors of the number, 1+....+n.
  - sigma
```
public Ifactor sigma(int k)
```
    Sum of the k-th powers of divisors of the number.
    
    Returns:
    
    the sum of all divisors of the number, 1^k+....+n^k.
  - dropPrime
```
public Ifactor dropPrime()
```
    Divide through the highest possible power of the highest prime. If the current number is the prime factor product p1^e1 * p2*e2* p3^e3*...*py^ey * pz^ez, the value returned has the final factor pz^ez eliminated, which gives p1^e1 * p2*e2* p3^e3*...*py^ey.
    
    Returns:
    
    the new integer obtained by removing the highest prime power. If this here represents 0 or 1, it is returned without change.
    
    Since:
    
    2006-08-20
  - issquare
```
public boolean issquare()
```
    Test whether this is a square of an integer (perfect square).
    
    Returns:
    
    true if this is an integer squared (including 0), else false
  - bigomega
```
public int bigomega()
```
    The sum of the prime factor exponents, with multiplicity.
    
    Returns:
    
    the sum over the primeexp numbers
  - omega
```
public int omega()
```
    The sum of the prime factor exponents, without multiplicity.
    
    Returns:
    
    the number of distinct prime factors.
    
    Since:
    
    2008-10-16
  - core
```
public java.math.BigInteger core()
```
    The square-free part.
    
    Returns:
    
    the minimum m such that m times this number is a square.
    
    Since:
    
    2008-10-16
  - moebius
```
public int moebius()
```
    The Moebius function. 1 if n=1, else, if k is the number of distinct prime factors, return (-1)^k, else, if k has repeated prime factors, return 0.
    
    Returns:
    
    the moebius function.
  - max
```
public Ifactor max(Ifactor oth)
```
    Maximum of two values.
    
    Parameters:
    
    oth - the number to compare this with.
    
    Returns:
    
    the larger of the two values.
  - min
```
public Ifactor min(Ifactor oth)
```
    Minimum of two values.
    
    Parameters:
    
    oth - the number to compare this with.
    
    Returns:
    
    the smaller of the two values.
  - max
```
public static Ifactor max(java.util.Vector<Ifactor> set)
```
    Maximum of a list of values.
    
    Parameters:
    
    set - list of numbers.
    
    Returns:
    
    the largest in the list.
  - min
```
public static Ifactor min(java.util.Vector<Ifactor> set)
```
    Minimum of a list of values.
    
    Parameters:
    
    set - list of numbers.
    
    Returns:
    
    the smallest in the list.
  - compareTo
```
public int compareTo(Ifactor oth)
```
    Compare value against another Ifactor
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<Ifactor>
    
    Parameters:
    
    oth - The value to be compared agains.
    
    Returns:
    
    1, 0 or -1 according to being larger, equal to or smaller than oth.
    
    Since:
    
    2012-02-15
  - toString
```
public java.lang.String toString()
```
    Convert to printable format
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    a string of the form n:prime^pow*prime^pow*prime^pow...
  - main
```
public static void main(java.lang.String[] args)
                 throws java.lang.Exception
```
    Test program. It takes a single argument n and prints the integer factorizaton.
    java -cp . org.nevec.rjm.Ifactor n
    
    Throws:
    
    java.lang.Exception

Class Ifactor

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

n

primeexp

ONE

ZERO

Constructor Detail

Ifactor

Ifactor

Ifactor

Ifactor

Method Detail

clone

equals

multiply

multiply

multiply

lcm

gcd

multGcdLcm

divide

add

pow

root

divisors

sigma

sigma

dropPrime

issquare

bigomega

omega

core

moebius

max

min

max

min

compareTo

toString

main