Package cc.redberry.rings

Class ImageRing<F,I>

java.lang.Object

cc.redberry.rings.ImageRing<F,I>

All Implemented Interfaces:

IParser<I>, Stringifiable<I>, Ring<I>, Serializable, Iterable<I>, Comparator<I>

Direct Known Subclasses:

MultipleFieldExtension

public class ImageRing<F,I>
extends Object
implements Ring<I>

A ring obtained via isomorphism specified by image(Object) and inverse(Object) functions.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
Function<F,I>	imageFunc
Function<I,F>	inverseFunc
Ring<F>	ring	the ring

Constructor Summary

Constructors

Constructor	Description
ImageRing(Ring<F> ring, Function<I,F> inverseFunc, Function<F,I> imageFunc)

Method Summary

Modifier and Type	Method	Description
I	abs(I el)	Returns the abs value of element (no copy)
I	add(I... elements)	Total of the array of elements
I	add(I a, I b)	Add two elements
BigInteger	cardinality()	Returns the number of elements in this ring (cardinality) or null if ring is infinite
BigInteger	characteristic()	Returns characteristic of this ring
int	compare(I o1, I o2)
I	copy(I element)	Makes a deep copy of the specified element (for immutable instances the same reference returned).
I	decrement(I element)	Returns element - 1
I[]	divideAndRemainder(I dividend, I divider)	Returns quotient and remainder of dividend / divider
boolean	equals(Object o)
I[]	extendedGCD(I a, I b)	Returns array of [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b)
FactorDecomposition<I>	factor(I element)	Factor specified element
I	factorial(long num)	Gives a product of valueOf(1) * valueOf(2) * .... * valueOf(num)
FactorDecomposition<I>	factorSquareFree(I element)	Square-free factorization of specified element
I	gcd(I... elements)	Returns greatest common divisor of specified elements
I	gcd(I a, I b)	Returns the greatest common divisor of two elements
I	gcd(Iterable<I> elements)	Returns greatest common divisor of specified elements
I	getOne()	Returns unit element of this ring (one)
I	getZero()	Returns zero element of this ring
int	hashCode()
I	image(F el)
I[]	image(F[] el)
I	increment(I element)	Returns element + 1
F	inverse(I el)
F[]	inverse(I[] el)
boolean	isEuclideanRing()	Returns whether this ring is a Euclidean ring
boolean	isField()	Returns whether this ring is a field
boolean	isOne(I element)	Tests whether specified element is one (exactly)
boolean	isPerfectPower()	Returns whether the cardinality is a perfect power (p^k with k > 1)
boolean	isUnit(I element)	Tests whether specified element is a ring unit
boolean	isZero(I element)	Tests whether specified element is zero
Iterator<I>	iterator()	Returns iterator over ring elements (for finite rings, otherwise throws exception)
I	lcm(I a, I b)	Returns the least common multiple of two elements
I	multiply(I... elements)	Multiplies the array of elements
I	multiply(I a, I b)	Multiplies two elements
I	negate(I element)	Negates the given element
I	parse(String string)	Parse string into ring element
BigInteger	perfectPowerBase()	Returns base so that cardinality == base^exponent or null if cardinality is not finite
BigInteger	perfectPowerExponent()	Returns exponent so that cardinality == base^exponent or null if cardinality is not finite
I	pow(I base, int exponent)	Returns base in a power of exponent (non negative)
I	pow(I base, long exponent)	Returns base in a power of exponent (non negative)
I	pow(I base, BigInteger exponent)	Returns base in a power of exponent (non negative)
I	quotient(I dividend, I divider)	Returns the quotient of dividend / divider
I	randomElement(org.apache.commons.math3.random.RandomGenerator rnd)	Returns a random element from this ring
I	reciprocal(I element)	Gives the inverse element element ^ (-1)
I	remainder(I dividend, I divider)	Returns the remainder of dividend / divider
int	signum(I element)	Returns -1 if element < 0, 0 if element == 0 and 1 if element > 0, where comparison is specified by Comparator.compare(Object, Object)
I	subtract(I a, I b)	Subtracts b from a
I	valueOf(long val)	Returns ring element associated with specified long
I	valueOf(I val)	Converts a value from other ring to this ring.
I	valueOfBigInteger(BigInteger val)	Returns ring element associated with specified integer

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface java.util.Comparator

reversed, thenComparing, thenComparing, thenComparing, thenComparingDouble, thenComparingInt, thenComparingLong

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Methods inherited from interface cc.redberry.rings.Ring

addMutable, createArray, createArray, createArray, createArray, createArray2d, createArray2d, createZeroesArray, createZeroesArray2d, divideExact, divideExactMutable, divideOrNull, fillZeros, firstBezoutCoefficient, getNegativeOne, isFinite, isFiniteField, isMinusOne, isUnitOrZero, lcm, lcm, max, min, multiply, multiply, multiplyMutable, negateMutable, randomElement, randomElementTree, randomElementTree, randomNonZeroElement, setToValueOf, subtractMutable, valueOf

Methods inherited from interface cc.redberry.rings.io.Stringifiable

toString

Field Detail

ring

public final Ring<F> ring

the ring

imageFunc

public final Function<F,I> imageFunc

inverseFunc

public final Function<I,F> inverseFunc

Constructor Detail

ImageRing

public ImageRing(Ring<F> ring,
                 Function<I,F> inverseFunc,
                 Function<F,I> imageFunc)

Method Detail

image

public I image(F el)

image

public I[] image(F[] el)

inverse

public F inverse(I el)

inverse

public F[] inverse(I[] el)

isField

public boolean isField()

Description copied from interface: Ring

Returns whether this ring is a field

Specified by:

isField in interface Ring<F>

Returns:

whether this ring is a field

isEuclideanRing

public boolean isEuclideanRing()

Description copied from interface: Ring

Returns whether this ring is a Euclidean ring

Specified by:

isEuclideanRing in interface Ring<F>

Returns:

whether this ring is a Euclidean ring

cardinality

public BigInteger cardinality()

Description copied from interface: Ring

Returns the number of elements in this ring (cardinality) or null if ring is infinite

Specified by:

cardinality in interface Ring<F>

Returns:

the number of elements in this ring (cardinality) or null if ring is infinite

characteristic

public BigInteger characteristic()

Description copied from interface: Ring

Returns characteristic of this ring

Specified by:

characteristic in interface Ring<F>

Returns:

characteristic of this ring

isPerfectPower

public boolean isPerfectPower()

Description copied from interface: Ring

Returns whether the cardinality is a perfect power (p^k with k > 1)

Specified by:

isPerfectPower in interface Ring<F>

Returns:

whether the cardinality is a perfect power (p^k with k > 1)

perfectPowerBase

public BigInteger perfectPowerBase()

Description copied from interface: Ring

Returns base so that cardinality == base^exponent or null if cardinality is not finite

Specified by:

perfectPowerBase in interface Ring<F>

Returns:

base so that cardinality == base^exponent or null if cardinality is not finite

perfectPowerExponent

public BigInteger perfectPowerExponent()

Description copied from interface: Ring

Returns exponent so that cardinality == base^exponent or null if cardinality is not finite

Specified by:

perfectPowerExponent in interface Ring<F>

Returns:

exponent so that cardinality == base^exponent or null if cardinality is not finite

add

public I add(I a,
             I b)

Description copied from interface: Ring

Add two elements

Specified by:

add in interface Ring<F>

Parameters:

a - the first element

b - the second element

Returns:

a + b

subtract

public I subtract(I a,
                  I b)

Description copied from interface: Ring

Subtracts b from a

Specified by:

subtract in interface Ring<F>

Parameters:

a - the first element

b - the second element

Returns:

a - b

multiply

public I multiply(I a,
                  I b)

Description copied from interface: Ring

Multiplies two elements

Specified by:

multiply in interface Ring<F>

Parameters:

a - the first element

b - the second element

Returns:

a * b

negate

public I negate(I element)

Description copied from interface: Ring

Negates the given element

Specified by:

negate in interface Ring<F>

Parameters:

element - the ring element

Returns:

-val

increment

public I increment(I element)

Description copied from interface: Ring

Returns element + 1

Specified by:

increment in interface Ring<F>

Parameters:

element - the element

Returns:

element + 1

decrement

public I decrement(I element)

Description copied from interface: Ring

Returns element - 1

Specified by:

decrement in interface Ring<F>

Parameters:

element - the element

Returns:

element - 1

add

public I add(I... elements)

Description copied from interface: Ring

Total of the array of elements

Specified by:

add in interface Ring<F>

Parameters:

elements - elements to sum

Returns:

sum of the array

multiply

public I multiply(I... elements)

Description copied from interface: Ring

Multiplies the array of elements

Specified by:

multiply in interface Ring<F>

Parameters:

elements - the elements

Returns:

product of the array

abs

public I abs(I el)

Description copied from interface: Ring

Returns the abs value of element (no copy)

Specified by:

abs in interface Ring<F>

copy

public I copy(I element)

Description copied from interface: Ring

Makes a deep copy of the specified element (for immutable instances the same reference returned).

Specified by:

copy in interface Ring<F>

Parameters:

element - the element

Returns:

deep copy of specified element

divideAndRemainder

public I[] divideAndRemainder(I dividend,
                              I divider)

Description copied from interface: Ring

Returns quotient and remainder of dividend / divider

Specified by:

divideAndRemainder in interface Ring<F>

Parameters:

dividend - the dividend

divider - the divider

Returns:

{quotient, remainder}

quotient

public I quotient(I dividend,
                  I divider)

Description copied from interface: Ring

Returns the quotient of dividend / divider

Specified by:

quotient in interface Ring<F>

Parameters:

dividend - the dividend

divider - the divider

Returns:

the quotient of dividend / divider

remainder

public I remainder(I dividend,
                   I divider)

Description copied from interface: Ring

Returns the remainder of dividend / divider

Specified by:

remainder in interface Ring<F>

Parameters:

dividend - the dividend

divider - the divider

Returns:

the remainder of dividend / divider

reciprocal

public I reciprocal(I element)

Description copied from interface: Ring

Gives the inverse element element ^ (-1)

Specified by:

reciprocal in interface Ring<F>

Parameters:

element - the element

Returns:

element ^ (-1)

getZero

public I getZero()

Description copied from interface: Ring

Returns zero element of this ring

Specified by:

getZero in interface Ring<F>

Returns:

0

getOne

public I getOne()

Description copied from interface: Ring

Returns unit element of this ring (one)

Specified by:

getOne in interface Ring<F>

Returns:

1

isZero

public boolean isZero(I element)

Description copied from interface: Ring

Tests whether specified element is zero

Specified by:

isZero in interface Ring<F>

Parameters:

element - the ring element

Returns:

whether specified element is zero

isOne

public boolean isOne(I element)

Description copied from interface: Ring

Tests whether specified element is one (exactly)

Specified by:

isOne in interface Ring<F>

Parameters:

element - the ring element

Returns:

whether specified element is exactly one

See Also:

Ring.isUnit(Object)

isUnit

public boolean isUnit(I element)

Description copied from interface: Ring

Tests whether specified element is a ring unit

Specified by:

isUnit in interface Ring<F>

Parameters:

element - the ring element

Returns:

whether specified element is a ring unit

See Also:

Ring.isOne(Object)

valueOf

public I valueOf(long val)

Description copied from interface: Ring

Returns ring element associated with specified long

Specified by:

valueOf in interface Ring<F>

Parameters:

val - machine integer

Returns:

ring element associated with specified long

valueOfBigInteger

public I valueOfBigInteger(BigInteger val)

Description copied from interface: Ring

Returns ring element associated with specified integer

Specified by:

valueOfBigInteger in interface Ring<F>

Parameters:

val - integer

Returns:

ring element associated with specified integer

valueOf

public I valueOf(I val)

Description copied from interface: Ring

Converts a value from other ring to this ring. The result is not guarantied to be a new instance (i.e. val == valueOf(val) is possible).

Specified by:

valueOf in interface Ring<F>

Parameters:

val - some element from any ring

Returns:

this ring element associated with specified val

iterator

public Iterator<I> iterator()

Description copied from interface: Ring

Returns iterator over ring elements (for finite rings, otherwise throws exception)

Specified by:

iterator in interface Iterable<F>

Specified by:

iterator in interface Ring<F>

gcd

public I gcd(I a,
             I b)

Description copied from interface: Ring

Returns the greatest common divisor of two elements

Specified by:

gcd in interface Ring<F>

Parameters:

a - the first element

b - the second element

Returns:

gcd

extendedGCD

public I[] extendedGCD(I a,
                       I b)

Description copied from interface: Ring

Returns array of [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b)

Specified by:

extendedGCD in interface Ring<F>

lcm

public I lcm(I a,
             I b)

Description copied from interface: Ring

Returns the least common multiple of two elements

Specified by:

lcm in interface Ring<F>

Parameters:

a - the first element

b - the second element

Returns:

lcm

gcd

public I gcd(I... elements)

Description copied from interface: Ring

Returns greatest common divisor of specified elements

Specified by:

gcd in interface Ring<F>

Parameters:

elements - the elements

Returns:

gcd

gcd

public I gcd(Iterable<I> elements)

Description copied from interface: Ring

Returns greatest common divisor of specified elements

Specified by:

gcd in interface Ring<F>

Parameters:

elements - the elements

Returns:

gcd

signum

public int signum(I element)

Description copied from interface: Ring

Returns -1 if element < 0, 0 if element == 0 and 1 if element > 0, where comparison is specified by Comparator.compare(Object, Object)

Specified by:

signum in interface Ring<F>

Parameters:

element - the element

Returns:

-1 if element < 0, 0 if element == 0 and 1 otherwise

factorSquareFree

public FactorDecomposition<I> factorSquareFree(I element)

Description copied from interface: Ring

Square-free factorization of specified element

Specified by:

factorSquareFree in interface Ring<F>

factor

public FactorDecomposition<I> factor(I element)

Description copied from interface: Ring

Factor specified element

Specified by:

factor in interface Ring<F>

parse

public I parse(String string)

Description copied from interface: Ring

Parse string into ring element

Specified by:

parse in interface IParser<F>

Specified by:

parse in interface Ring<F>

Parameters:

string - string

Returns:

ring element

See Also:

Coder

pow

public I pow(I base,
             int exponent)

Description copied from interface: Ring

Returns base in a power of exponent (non negative)

Specified by:

pow in interface Ring<F>

Parameters:

base - base

exponent - exponent (non negative)

Returns:

base in a power of exponent

pow

public I pow(I base,
             long exponent)

Description copied from interface: Ring

Returns base in a power of exponent (non negative)

Specified by:

pow in interface Ring<F>

Parameters:

base - base

exponent - exponent (non negative)

Returns:

base in a power of exponent

pow

public I pow(I base,
             BigInteger exponent)

Description copied from interface: Ring

Returns base in a power of exponent (non negative)

Specified by:

pow in interface Ring<F>

Parameters:

base - base

exponent - exponent (non negative)

Returns:

base in a power of exponent

factorial

public I factorial(long num)

Description copied from interface: Ring

Gives a product of valueOf(1) * valueOf(2) * .... * valueOf(num)

Specified by:

factorial in interface Ring<F>

Parameters:

num - the number

Returns:

valueOf(1) * valueOf(2) * .... * valueOf(num)

randomElement

public I randomElement(org.apache.commons.math3.random.RandomGenerator rnd)

Description copied from interface: Ring

Returns a random element from this ring

Specified by:

randomElement in interface Ring<F>

Parameters:

rnd - the source of randomness

Returns:

random element from this ring

compare

public int compare(I o1,
                   I o2)

Specified by:

compare in interface Comparator<F>

equals

public boolean equals(Object o)

Specified by:

equals in interface Comparator<F>

Overrides:

equals in class Object

hashCode

public int hashCode()

Overrides:

hashCode in class Object