Rational

java.lang.Object
- etomica.veos.bigdecimal.Rational

All Implemented Interfaces:

java.lang.Cloneable, java.lang.Comparable<Rational>
```
public class Rational
extends java.lang.Object
implements java.lang.Cloneable, java.lang.Comparable<Rational>
```
Fractions (rational numbers). They are divisions of two BigInteger numbers, reduced to coprime numerator and denominator.

Since:

2006-06-25

Field Summary

Fields
Modifier and Type	Field	Description
`static Rational`	`HALF`	The constant 1/2
`static java.math.BigInteger`	`MAX_INT`	The maximum and minimum value of a standard Java integer, 2^31.
`static java.math.BigInteger`	`MIN_INT`
`static Rational`	`ZERO`	The constant 0.

Constructor Summary

Constructors
Constructor	Description
`Rational()`	Default ctor, which represents the zero.
`Rational(int n)`	ctor from an integer.
`Rational(int a, int b)`	ctor from a numerator and denominator.
`Rational(java.lang.String str)`	ctor from a string representation.
`Rational(java.lang.String str, int radix)`	ctor from a string representation in a specified base.
`Rational(java.math.BigInteger a)`	ctor from a numerator.
`Rational(java.math.BigInteger a, java.math.BigInteger b)`	ctor from a numerator and denominator.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`Rational`	`abs()`	Absolute value.
`Rational`	`add(int val)`	Add another integer.
`Rational`	`add(Rational val)`	Add another fraction.
`Rational`	`add(java.math.BigInteger val)`	Add another integer.
`java.math.BigDecimal`	`BigDecimalValue(java.math.MathContext mc)`	Return a representation as BigDecimal.
`static Rational`	`binomial(Rational n, int m)`	binomial (n choose m).
`static Rational`	`binomial(Rational n, java.math.BigInteger m)`	binomial (n choose m).
`java.math.BigInteger`	`ceil()`	ceil(): the nearest integer not smaller than this.
`Rational`	`clone()`	Create a copy.
`int`	`compareTo(Rational val)`	Compares the value of this with another constant.
`int`	`compareTo(java.math.BigInteger val)`	Compares the value of this with another constant.
`java.math.BigInteger`	`denom()`	Get the denominator.
`Rational`	`divide(int val)`	Divide by an integer.
`Rational`	`divide(Rational val)`	Divide by another fraction.
`Rational`	`divide(java.math.BigInteger val)`	Divide by an integer.
`double`	`doubleValue()`	Return a double value representation.
`float`	`floatValue()`	Return a float value representation.
`java.math.BigInteger`	`floor()`	floor(): the nearest integer not greater than this.
`static Rational`	`hankelSymb(Rational n, int k)`	Hankel's symbol (n,k)
`boolean`	`isBigInteger()`	True if the value is integer.
`boolean`	`isInteger()`	True if the value is integer and in the range of the standard integer.
`boolean`	`isIntegerFrac()`	True if the value is a fraction of two integers in the range of the standard integer.
`static java.math.BigInteger`	`lcmDenom(Rational[] vals)`	Common lcm of the denominators of a set of rational values.
`Rational`	`max(Rational val)`	Compares the value of this with another constant.
`Rational`	`min(Rational val)`	Compares the value of this with another constant.
`Rational`	`multiply(int val)`	Multiply by an integer.
`Rational`	`multiply(Rational val)`	Multiply by another fraction.
`Rational`	`multiply(java.math.BigInteger val)`	Multiply by a BigInteger.
`Rational`	`negate()`	Compute the negative.
`protected void`	`normalize()`	Normalize to coprime numerator and denominator.
`java.math.BigInteger`	`numer()`	Get the numerator.
`Rational`	`Pochhammer(int n)`	Compute pochhammer's symbol (this)_n.
`Rational`	`Pochhammer(java.math.BigInteger n)`	Compute Pochhammer's symbol (this)_n.
`Rational`	`pow(int exponent)`	Power to an integer.
`Rational`	`pow(Rational exponent)`	Raise to a rational power.
`Rational`	`pow(java.math.BigInteger exponent)`	Power to an integer.
`Rational`	`root(java.math.BigInteger r)`	r-th root.
`int`	`signum()`	The sign: 1 if the number is >0, 0 if ==0, -1 if <0
`Rational`	`subtract(int val)`	Subtract an integer.
`Rational`	`subtract(Rational val)`	Subtract another fraction.
`Rational`	`subtract(java.math.BigInteger val)`	Subtract an integer.
`java.lang.String`	`toFString(int digits)`	Return a string in floating point format.
`java.lang.String`	`toString()`	Return a string in the format number/denom.
`java.math.BigInteger`	`trunc()`	Remove the fractional part.

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

- Field Detail
  - MAX_INT
```
public static java.math.BigInteger MAX_INT
```
    The maximum and minimum value of a standard Java integer, 2^31.
    
    Since:
    
    2009-05-18
  - MIN_INT
```
public static java.math.BigInteger MIN_INT
```
  - ZERO
```
public static Rational ZERO
```
    The constant 0.
  - HALF
```
public static Rational HALF
```
    The constant 1/2
    
    Since:
    
    2010-05-25
- Constructor Detail
  - Rational
```
public Rational()
```
    Default ctor, which represents the zero.
    
    Since:
    
    2007-11-17
  - Rational
```
public Rational(java.math.BigInteger a,
                java.math.BigInteger b)
```
    ctor from a numerator and denominator.
    
    Parameters:
    
    a - the numerator.
    
    b - the denominator.
  - Rational
```
public Rational(java.math.BigInteger a)
```
    ctor from a numerator.
    
    Parameters:
    
    a - the BigInteger.
  - Rational
```
public Rational(int a,
                int b)
```
    ctor from a numerator and denominator.
    
    Parameters:
    
    a - the numerator.
    
    b - the denominator.
  - Rational
```
public Rational(int n)
```
    ctor from an integer.
    
    Parameters:
    
    n - the integer to be represented by the new instance.
    
    Since:
    
    2010-07-18
  - Rational
```
public Rational(java.lang.String str)
         throws java.lang.NumberFormatException
```
    ctor from a string representation.
    
    Parameters:
    
    str - the string. This either has a slash in it, separating two integers, or, if there is no slash, is representing the numerator with implicit denominator equal to 1. Warning: this does not yet test for a denominator equal to zero
    
    Throws:
    
    java.lang.NumberFormatException
  - Rational
```
public Rational(java.lang.String str,
                int radix)
         throws java.lang.NumberFormatException
```
    ctor from a string representation in a specified base.
    
    Parameters:
    
    str - the string. This either has a slash in it, separating two integers, or, if there is no slash, is just representing the numerator.
    
    radix - the number base for numerator and denominator Warning: this does not yet test for a denominator equal to zero
    
    Throws:
    
    java.lang.NumberFormatException
- Method Detail
  - clone
```
public Rational clone()
```
    Create a copy.
    
    Overrides:
    
    clone in class java.lang.Object
    
    Since:
    
    2008-11-07
  - multiply
```
public Rational multiply(Rational val)
```
    Multiply by another fraction.
    
    Parameters:
    
    val - a second rational number.
    
    Returns:
    
    the product of this with the val.
  - multiply
```
public Rational multiply(java.math.BigInteger val)
```
    Multiply by a BigInteger.
    
    Parameters:
    
    val - a second number.
    
    Returns:
    
    the product of this with the value.
  - multiply
```
public Rational multiply(int val)
```
    Multiply by an integer.
    
    Parameters:
    
    val - a second number.
    
    Returns:
    
    the product of this with the value.
  - pow
```
public Rational pow(int exponent)
```
    Power to an integer.
    
    Parameters:
    
    exponent - the exponent.
    
    Returns:
    
    this value raised to the power given by the exponent. If the exponent is 0, the value 1 is returned.
  - pow
```
public Rational pow(java.math.BigInteger exponent)
             throws java.lang.NumberFormatException
```
    Power to an integer.
    
    Parameters:
    
    exponent - the exponent.
    
    Returns:
    
    this value raised to the power given by the exponent. If the exponent is 0, the value 1 is returned.
    
    Throws:
    
    java.lang.NumberFormatException
    
    Since:
    
    2009-05-18
  - root
```
public Rational root(java.math.BigInteger r)
              throws java.lang.NumberFormatException
```
    r-th root.
    
    Parameters:
    
    r - the inverse of the exponent. 2 for the square root, 3 for the third root etc
    
    Returns:
    
    this value raised to the inverse power given by the root argument, this^(1/r).
    
    Throws:
    
    java.lang.NumberFormatException
    
    Since:
    
    2009-05-18
  - pow
```
public Rational pow(Rational exponent)
             throws java.lang.NumberFormatException
```
    Raise to a rational power.
    
    Parameters:
    
    exponent - The exponent.
    
    Returns:
    
    This value raised to the power given by the exponent. If the exponent is 0, the value 1 is returned.
    
    Throws:
    
    java.lang.NumberFormatException
    
    Since:
    
    2009-05-18
  - divide
```
public Rational divide(Rational val)
```
    Divide by another fraction.
    
    Parameters:
    
    val - A second rational number.
    
    Returns:
    
    The value of this/val
  - divide
```
public Rational divide(java.math.BigInteger val)
```
    Divide by an integer.
    
    Parameters:
    
    val - a second number.
    
    Returns:
    
    the value of this/val
  - divide
```
public Rational divide(int val)
```
    Divide by an integer.
    
    Parameters:
    
    val - A second number.
    
    Returns:
    
    The value of this/val
  - add
```
public Rational add(Rational val)
```
    Add another fraction.
    
    Parameters:
    
    val - The number to be added
    
    Returns:
    
    this+val.
  - add
```
public Rational add(java.math.BigInteger val)
```
    Add another integer.
    
    Parameters:
    
    val - The number to be added
    
    Returns:
    
    this+val.
  - add
```
public Rational add(int val)
```
    Add another integer.
    
    Parameters:
    
    val - The number to be added
    
    Returns:
    
    this+val.
    
    Since:
    
    May 26 2010
  - negate
```
public Rational negate()
```
    Compute the negative.
    
    Returns:
    
    -this.
  - subtract
```
public Rational subtract(Rational val)
```
    Subtract another fraction.
    
    Parameters:
    
    val - the number to be subtracted from this
    
    Returns:
    
    this - val.
  - subtract
```
public Rational subtract(java.math.BigInteger val)
```
    Subtract an integer.
    
    Parameters:
    
    val - the number to be subtracted from this
    
    Returns:
    
    this - val.
  - subtract
```
public Rational subtract(int val)
```
    Subtract an integer.
    
    Parameters:
    
    val - the number to be subtracted from this
    
    Returns:
    
    this - val.
  - binomial
```
public static Rational binomial(Rational n,
                                java.math.BigInteger m)
```
    binomial (n choose m).
    
    Parameters:
    
    n - the numerator. Equals the size of the set to choose from.
    
    m - the denominator. Equals the number of elements to select.
    
    Returns:
    
    the binomial coefficient.
    
    Since:
    
    2006-06-27
  - binomial
```
public static Rational binomial(Rational n,
                                int m)
```
    binomial (n choose m).
    
    Parameters:
    
    n - the numerator. Equals the size of the set to choose from.
    
    m - the denominator. Equals the number of elements to select.
    
    Returns:
    
    the binomial coefficient.
    
    Since:
    
    2009-05-19
  - hankelSymb
```
public static Rational hankelSymb(Rational n,
                                  int k)
```
    Hankel's symbol (n,k)
    
    Parameters:
    
    n - the first parameter.
    
    k - the second parameter, greater or equal to 0.
    
    Returns:
    
    Gamma(n+k+1/2)/k!/GAMMA(n-k+1/2)
    
    Since:
    
    2010-07-18
  - numer
```
public java.math.BigInteger numer()
```
    Get the numerator.
    
    Returns:
    
    The numerator of the reduced fraction.
  - denom
```
public java.math.BigInteger denom()
```
    Get the denominator.
    
    Returns:
    
    The denominator of the reduced fraction.
  - abs
```
public Rational abs()
```
    Absolute value.
    
    Returns:
    
    The absolute (non-negative) value of this.
  - floor
```
public java.math.BigInteger floor()
```
    floor(): the nearest integer not greater than this.
    
    Returns:
    
    The integer rounded towards negative infinity.
  - ceil
```
public java.math.BigInteger ceil()
```
    ceil(): the nearest integer not smaller than this.
    
    Returns:
    
    The integer rounded towards positive infinity.
    
    Since:
    
    2010-05-26
  - trunc
```
public java.math.BigInteger trunc()
```
    Remove the fractional part.
    
    Returns:
    
    The integer rounded towards zero.
  - compareTo
```
public int compareTo(Rational val)
```
    Compares the value of this with another constant.
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<Rational>
    
    Parameters:
    
    val - the other constant to compare with
    
    Returns:
    
    -1, 0 or 1 if this number is numerically less than, equal to, or greater than val.
  - compareTo
```
public int compareTo(java.math.BigInteger val)
```
    Compares the value of this with another constant.
    
    Parameters:
    
    val - the other constant to compare with
    
    Returns:
    
    -1, 0 or 1 if this number is numerically less than, equal to, or greater than val.
  - toString
```
public java.lang.String toString()
```
    Return a string in the format number/denom. If the denominator equals 1, print just the numerator without a slash.
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    the human-readable version in base 10
  - doubleValue
```
public double doubleValue()
```
    Return a double value representation.
    
    Returns:
    
    The value with double precision.
    
    Since:
    
    2008-10-26
  - floatValue
```
public float floatValue()
```
    Return a float value representation.
    
    Returns:
    
    The value with single precision.
    
    Since:
    
    2009-08-06
  - BigDecimalValue
```
public java.math.BigDecimal BigDecimalValue(java.math.MathContext mc)
```
    Return a representation as BigDecimal.
    
    Parameters:
    
    mc - the mathematical context which determines precision, rounding mode etc
    
    Returns:
    
    A representation as a BigDecimal floating point number.
    
    Since:
    
    2008-10-26
  - toFString
```
public java.lang.String toFString(int digits)
```
    Return a string in floating point format.
    
    Parameters:
    
    digits - The precision (number of digits)
    
    Returns:
    
    The human-readable version in base 10.
    
    Since:
    
    2008-10-25
  - max
```
public Rational max(Rational val)
```
    Compares the value of this with another constant.
    
    Parameters:
    
    val - The other constant to compare with
    
    Returns:
    
    The arithmetic maximum of this and val.
    
    Since:
    
    2008-10-19
  - min
```
public Rational min(Rational val)
```
    Compares the value of this with another constant.
    
    Parameters:
    
    val - The other constant to compare with
    
    Returns:
    
    The arithmetic minimum of this and val.
    
    Since:
    
    2008-10-19
  - Pochhammer
```
public Rational Pochhammer(java.math.BigInteger n)
```
    Compute Pochhammer's symbol (this)_n.
    
    Parameters:
    
    n - The number of product terms in the evaluation.
    
    Returns:
    
    Gamma(this+n)/Gamma(this) = this*(this+1)*...*(this+n-1).
    
    Since:
    
    2008-10-25
  - Pochhammer
```
public Rational Pochhammer(int n)
```
    Compute pochhammer's symbol (this)_n.
    
    Parameters:
    
    n - The number of product terms in the evaluation.
    
    Returns:
    
    Gamma(this+n)/GAMMA(this).
    
    Since:
    
    2008-11-13
  - isBigInteger
```
public boolean isBigInteger()
```
    True if the value is integer. Equivalent to the indication whether a conversion to an integer can be exact.
    
    Since:
    
    2010-05-26
  - isInteger
```
public boolean isInteger()
```
    True if the value is integer and in the range of the standard integer. Equivalent to the indication whether a conversion to an integer can be exact.
    
    Since:
    
    2010-05-26
  - isIntegerFrac
```
public boolean isIntegerFrac()
```
    True if the value is a fraction of two integers in the range of the standard integer.
    
    Since:
    
    2010-05-26
  - signum
```
public int signum()
```
    The sign: 1 if the number is >0, 0 if ==0, -1 if <0
    
    Returns:
    
    the signum of the value.
    
    Since:
    
    2010-05-26
  - lcmDenom
```
public static java.math.BigInteger lcmDenom(Rational[] vals)
```
    Common lcm of the denominators of a set of rational values.
    
    Parameters:
    
    vals - The list/set of the rational values.
    
    Returns:
    
    LCM(denom of first, denom of second, ..,denom of last)
    
    Since:
    
    2012-03-02
  - normalize
```
protected void normalize()
```
    Normalize to coprime numerator and denominator. Also copy a negative sign of the denominator to the numerator.
    
    Since:
    
    2008-10-19

Class Rational

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

MAX_INT

MIN_INT

ZERO

HALF

Constructor Detail

Rational

Rational

Rational

Rational

Rational

Rational

Rational

Method Detail

clone

multiply

multiply

multiply

pow

pow

root

pow

divide

divide

divide

add

add

add

negate

subtract

subtract

subtract

binomial

binomial

hankelSymb

numer

denom

abs

floor

ceil

trunc

compareTo

compareTo

toString

doubleValue

floatValue

BigDecimalValue

toFString

max

min

Pochhammer

Pochhammer

isBigInteger

isInteger

isIntegerFrac

signum

lcmDenom

normalize