Natural (core 4.1 API)

java.lang.Object
- java.lang.Number
- - fj.data.Natural

All Implemented Interfaces:

java.io.Serializable
```
public final class Natural
extends java.lang.Number
```
Represents a natural number (zero, one, two, etc.)

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`static F<Natural,F<Natural,Natural>>`	`add` A function that adds two natural numbers.
`static F<Natural,java.math.BigInteger>`	`bigIntegerValue` A function that returns the BigInteger value of a given Natural.
`static F<Natural,F<Natural,Natural>>`	`divide` A function that divides its second argument by its first.
`static F<Natural,F<Natural,V2<Natural>>>`	`divmod` A function that divides its second argument by its first, yielding both the quotient and the remainder.
`static F<java.math.BigInteger,Option<Natural>>`	`fromBigInt` A function that returns the natural number equal to a given BigInteger
`static F<Natural,F<Natural,Natural>>`	`mod` A function that yields the remainder of division of its second argument by its first.
`static F<Natural,F<Natural,Natural>>`	`multiply` A function that multiplies a natural number by another.
`static Natural`	`ONE` The natural number one
`static F<Natural,F<Natural,Option<Natural>>>`	`subtract` A function that subtracts its first argument from its second.
`static Natural`	`ZERO` The natural number zero

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`Natural`	`add(Natural n)` Add two natural numbers together.
`java.math.BigInteger`	`bigIntegerValue()` Return the BigInteger value of this natural number.
`Natural`	`divide(Natural n)` Divide a natural number by another.
`V2<Natural>`	`divmod(Natural n)` Divide a natural number by another yielding both the quotient and the remainder.
`double`	`doubleValue()` Return the double value of this natural number.
`float`	`floatValue()` Return the float value of this natural number.
`int`	`intValue()` Return the int value of this natural number.
`long`	`longValue()` Return the long value of this natural number.
`Natural`	`mod(Natural n)` Take the remainder of a natural number division.
`Natural`	`multiply(Natural n)` Multiply a natural number by another.
`static Option<Natural>`	`natural(java.math.BigInteger i)` Returns the natural number equal to the given BigInteger
`static Option<Natural>`	`natural(long i)` Returns the natural number equal to the given long
`static F<Natural,Option<Natural>>`	`pred_()` First-class predecessor function.
`Option<Natural>`	`pred()` Return the predecessor of this natural number
`static Natural`	`product(List<Natural> ns)` Takes the product of a list of natural numbers.
`static Natural`	`product(Stream<Natural> ns)` Takes the product of a stream of natural numbers.
`Option<Natural>`	`subtract(Natural n)` Subtract a natural number from another.
`static F<Natural,Natural>`	`succ_()` First-class successor function.
`Natural`	`succ()` Return the successor of this natural number
`static Natural`	`sum(List<Natural> ns)` Sums a list of natural numbers.
`static Natural`	`sum(Stream<Natural> ns)` Sums a stream of natural numbers.

Methods inherited from class java.lang.Number
byteValue, shortValue

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

- Field Detail
  - fromBigInt
```
public static final F<java.math.BigInteger,Option<Natural>> fromBigInt
```
    A function that returns the natural number equal to a given BigInteger
  - ZERO
```
public static final Natural ZERO
```
    The natural number zero
  - ONE
```
public static final Natural ONE
```
    The natural number one
  - add
```
public static final F<Natural,F<Natural,Natural>> add
```
    A function that adds two natural numbers.
  - subtract
```
public static final F<Natural,F<Natural,Option<Natural>>> subtract
```
    A function that subtracts its first argument from its second.
  - multiply
```
public static final F<Natural,F<Natural,Natural>> multiply
```
    A function that multiplies a natural number by another.
  - divide
```
public static final F<Natural,F<Natural,Natural>> divide
```
    A function that divides its second argument by its first.
  - mod
```
public static final F<Natural,F<Natural,Natural>> mod
```
    A function that yields the remainder of division of its second argument by its first.
  - divmod
```
public static final F<Natural,F<Natural,V2<Natural>>> divmod
```
    A function that divides its second argument by its first, yielding both the quotient and the remainder.
  - bigIntegerValue
```
public static final F<Natural,java.math.BigInteger> bigIntegerValue
```
    A function that returns the BigInteger value of a given Natural.
- Method Detail
  - natural
```
public static Option<Natural> natural(java.math.BigInteger i)
```
    Returns the natural number equal to the given BigInteger
    
    Parameters:
    
    i - A given BigInteger
    
    Returns:
    
    An optional natural number, or none if the given BigInteger is less than zero.
  - natural
```
public static Option<Natural> natural(long i)
```
    Returns the natural number equal to the given long
    
    Parameters:
    
    i - A given long
    
    Returns:
    
    An optional natural number, or none if the given long is less than zero.
  - succ
```
public Natural succ()
```
    Return the successor of this natural number
    
    Returns:
    
    the successor of this natural number
  - succ_
```
public static F<Natural,Natural> succ_()
```
    First-class successor function.
    
    Returns:
    
    A function that returns the successor of a given natural number.
  - pred
```
public Option<Natural> pred()
```
    Return the predecessor of this natural number
    
    Returns:
    
    the predecessor of this natural number
  - pred_
```
public static F<Natural,Option<Natural>> pred_()
```
    First-class predecessor function.
    
    Returns:
    
    A function that returns the predecessor of a given natural number, or None if it's zero.
  - add
```
public Natural add(Natural n)
```
    Add two natural numbers together.
    
    Parameters:
    
    n - A natural number to add to this one.
    
    Returns:
    
    the sum of the two natural numbers.
  - subtract
```
public Option<Natural> subtract(Natural n)
```
    Subtract a natural number from another.
    
    Parameters:
    
    n - A natural number to subtract from this one.
    
    Returns:
    
    The difference between the two numbers, if this number is larger than the given one. Otherwise none.
  - multiply
```
public Natural multiply(Natural n)
```
    Multiply a natural number by another.
    
    Parameters:
    
    n - A natural number to multiply by this one.
    
    Returns:
    
    The product of the two numbers.
  - divide
```
public Natural divide(Natural n)
```
    Divide a natural number by another.
    
    Parameters:
    
    n - A natural number to divide this one by.
    
    Returns:
    
    The quotient of this number and the highest number, less than or equal to the given number, that divides this number.
  - mod
```
public Natural mod(Natural n)
```
    Take the remainder of a natural number division.
    
    Parameters:
    
    n - A natural number to divide this one by.
    
    Returns:
    
    The remainder of division of this number by the given number.
  - divmod
```
public V2<Natural> divmod(Natural n)
```
    Divide a natural number by another yielding both the quotient and the remainder.
    
    Parameters:
    
    n - A natural number to divide this one by.
    
    Returns:
    
    The quotient and the remainder, in that order.
  - bigIntegerValue
```
public java.math.BigInteger bigIntegerValue()
```
    Return the BigInteger value of this natural number.
    
    Returns:
    
    the BigInteger value of this natural number.
  - longValue
```
public long longValue()
```
    Return the long value of this natural number.
    
    Specified by:
    
    longValue in class java.lang.Number
    
    Returns:
    
    the long value of this natural number.
  - floatValue
```
public float floatValue()
```
    Return the float value of this natural number.
    
    Specified by:
    
    floatValue in class java.lang.Number
    
    Returns:
    
    the float value of this natural number.
  - doubleValue
```
public double doubleValue()
```
    Return the double value of this natural number.
    
    Specified by:
    
    doubleValue in class java.lang.Number
    
    Returns:
    
    the double value of this natural number.
  - intValue
```
public int intValue()
```
    Return the int value of this natural number.
    
    Specified by:
    
    intValue in class java.lang.Number
    
    Returns:
    
    the int value of this natural number.
  - sum
```
public static Natural sum(Stream<Natural> ns)
```
    Sums a stream of natural numbers.
    
    Parameters:
    
    ns - A stream of natural numbers.
    
    Returns:
    
    The sum of all the natural numbers in the stream.
  - product
```
public static Natural product(Stream<Natural> ns)
```
    Takes the product of a stream of natural numbers.
    
    Parameters:
    
    ns - A stream of natural numbers.
    
    Returns:
    
    The product of all the natural numbers in the stream.
  - sum
```
public static Natural sum(List<Natural> ns)
```
    Sums a list of natural numbers.
    
    Parameters:
    
    ns - A list of natural numbers.
    
    Returns:
    
    The sum of all the natural numbers in the list.
  - product
```
public static Natural product(List<Natural> ns)
```
    Takes the product of a list of natural numbers.
    
    Parameters:
    
    ns - A list of natural numbers.
    
    Returns:
    
    The product of all the natural numbers in the list.

Class Natural

Field Summary

Method Summary

Methods inherited from class java.lang.Number

Methods inherited from class java.lang.Object

Field Detail

fromBigInt

ZERO

ONE

add

subtract

multiply

divide

mod

divmod

bigIntegerValue

Method Detail

natural

natural

succ

succ_

pred

pred_

add

subtract

multiply

divide

mod

divmod

bigIntegerValue

longValue

floatValue

doubleValue

intValue

sum

product

sum

product