Package cc.redberry.rings.poly

Class MultivariateRing<Poly extends AMultivariatePolynomial<?,Poly>>

java.lang.Object

cc.redberry.rings.ARing<Poly>

cc.redberry.rings.poly.MultivariateRing<Poly>

Type Parameters:

Poly - type of multivariate polynomials

All Implemented Interfaces:

IParser<Poly>, Stringifiable<Poly>, IPolynomialRing<Poly>, Ring<Poly>, Serializable, Iterable<Poly>, Comparator<Poly>

public final class MultivariateRing<Poly extends AMultivariatePolynomial<?,Poly>>
extends ARing<Poly>

Ring of multivariate polynomials.

Since:

1.0

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
static int	DEGREE_OF_RANDOM_POLY	Default degree of polynomial generated with randomElementTree(RandomGenerator)
static int	SIZE_OF_RANDOM_POLY	Default size of polynomial generated with randomElementTree(RandomGenerator)

Constructor Summary

Constructors

Constructor	Description
MultivariateRing(Poly factory)	Creates ring of multivariate polynomials which support operations over multivariate polynomials of the type and number of variables same as of provided factory polynomial

Method Summary

Modifier and Type	Method	Description
Poly	add(Poly a, Poly b)	Add two elements
Poly	addMutable(Poly a, Poly b)	Adds two elements and destroys the initial content of a.
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(Poly o1, Poly o2)
Poly	copy(Poly element)	Makes a deep copy of the specified element (for immutable instances the same reference returned).
Poly	create(DegreeVector term)	Creates multivariate polynomial over the same ring as this with the single monomial
Poly[]	divideAndRemainder(Poly dividend, Poly divider)	Returns quotient and remainder of dividend / divider
MultivariateRing<Poly>	dropVariable()
boolean	equals(Object o)
PolynomialFactorDecomposition<Poly>	factor(Poly element)	Factor specified element
PolynomialFactorDecomposition<Poly>	factorSquareFree(Poly element)	Square-free factorization of specified element
Poly	factory()	Factory polynomial
Poly	gcd(Iterable<Poly> elements)	Returns greatest common divisor of specified elements
Poly	gcd(Poly[] elements)	Returns greatest common divisor of specified elements
Poly	gcd(Poly a, Poly b)	Returns the greatest common divisor of two elements
Poly	getOne()	Returns unit element of this ring (one)
Poly	getZero()	Returns zero element of this ring
int	hashCode()
boolean	isEuclideanRing()	Returns whether this ring is a Euclidean ring
boolean	isField()	Returns whether this ring is a field
boolean	isOne(Poly element)	Tests whether specified element is one (exactly)
boolean	isUnit(Poly element)	Tests whether specified element is a ring unit
boolean	isZero(Poly element)	Tests whether specified element is zero
Iterator<Poly>	iterator()	Returns iterator over ring elements (for finite rings, otherwise throws exception)
<Term extends AMonomial<Term>> IMonomialAlgebra<Term>	monomialAlgebra()
Poly	multiply(Poly a, Poly b)	Multiplies two elements
Poly	multiplyMutable(Poly a, Poly b)	Multiplies two elements and destroys the initial content of a
Poly	negate(Poly element)	Negates the given element
Poly	negateMutable(Poly element)	Negates the given element and destroys the initial content of element
int	nVariables()	Number of polynomial variables
Comparator<DegreeVector>	ordering()
Poly	parse(String string)	Parse string into ring element
Poly	pow(Poly base, BigInteger exponent)	Returns base in a power of exponent (non negative)
Poly	randomElement(int degree, int size)	Generates random multivariate polynomial
Poly	randomElement(int degree, int size, org.apache.commons.math3.random.RandomGenerator rnd)	Generates random multivariate polynomial
Poly	randomElement(org.apache.commons.math3.random.RandomGenerator rnd)	Gives a random constant polynomial.
Poly	randomElementTree(int degree, int size, org.apache.commons.math3.random.RandomGenerator rnd)	Generates random multivariate polynomial
Poly	randomElementTree(org.apache.commons.math3.random.RandomGenerator rnd)	If this ring has a complicated nested structure, this method guaranties that the resulting random element will reflect ring complicated structure, i.e.
Poly	reciprocal(Poly element)	Gives the inverse element element ^ (-1)
Poly	subtract(Poly a, Poly b)	Subtracts b from a
Poly	subtractMutable(Poly a, Poly b)	Subtracts b from a and destroys the initial content of a
String	toString()
String	toString(IStringifier<Poly> stringifier)	convert this to string with the use of stringifier
String	toString(String... variables)
Poly	valueOf(long val)	Returns ring element associated with specified long
Poly	valueOf(Poly val)	Converts a value from other ring to this ring.
Poly	valueOfBigInteger(BigInteger val)	Returns ring element associated with specified integer
Poly	variable(int variable)	Creates poly representing a single specified variable

Methods inherited from class cc.redberry.rings.ARing

isPerfectPower, perfectPowerBase, perfectPowerExponent

Methods inherited from class java.lang.Object

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

Methods inherited from interface java.util.Comparator

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

Methods inherited from interface cc.redberry.rings.poly.IPolynomialRing

mkCoder, parse, signum

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Methods inherited from interface cc.redberry.rings.Ring

abs, add, createArray, createArray, createArray, createArray, createArray2d, createArray2d, createZeroesArray, createZeroesArray2d, decrement, divideExact, divideExactMutable, divideOrNull, extendedGCD, factorial, fillZeros, firstBezoutCoefficient, getNegativeOne, increment, isFinite, isFiniteField, isMinusOne, isPerfectPower, isUnitOrZero, lcm, lcm, lcm, max, min, multiply, multiply, multiply, perfectPowerBase, perfectPowerExponent, pow, pow, quotient, randomElement, randomElementTree, randomNonZeroElement, remainder, setToValueOf, valueOf

Field Detail

DEGREE_OF_RANDOM_POLY

public static final int DEGREE_OF_RANDOM_POLY

Default degree of polynomial generated with randomElementTree(RandomGenerator)

See Also:

Constant Field Values

SIZE_OF_RANDOM_POLY

public static final int SIZE_OF_RANDOM_POLY

Default size of polynomial generated with randomElementTree(RandomGenerator)

See Also:

Constant Field Values

Constructor Detail

MultivariateRing

public MultivariateRing(Poly factory)

Creates ring of multivariate polynomials which support operations over multivariate polynomials of the type and number of variables same as of provided factory polynomial

Parameters:

factory - the factory polynomial (the exact value of factory is irrelevant) which fixes the element type of this ring, coefficient ring and the number of variables

Method Detail

monomialAlgebra

public <Term extends AMonomial<Term>> IMonomialAlgebra<Term> monomialAlgebra()

nVariables

public int nVariables()

Description copied from interface: IPolynomialRing

Number of polynomial variables

ordering

public Comparator<DegreeVector> ordering()

dropVariable

public MultivariateRing<Poly> dropVariable()

divideAndRemainder

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

Description copied from interface: Ring

Returns quotient and remainder of dividend / divider

Parameters:

dividend - the dividend

divider - the divider

Returns:

{quotient, remainder}

gcd

public Poly gcd(Poly a,
                Poly b)

Description copied from interface: Ring

Returns the greatest common divisor of two elements

Parameters:

a - the first element

b - the second element

Returns:

gcd

gcd

public Poly gcd(Poly[] elements)

Description copied from interface: Ring

Returns greatest common divisor of specified elements

Parameters:

elements - the elements

Returns:

gcd

gcd

public Poly gcd(Iterable<Poly> elements)

Description copied from interface: Ring

Returns greatest common divisor of specified elements

Parameters:

elements - the elements

Returns:

gcd

factorSquareFree

public PolynomialFactorDecomposition<Poly> factorSquareFree(Poly element)

Description copied from interface: Ring

Square-free factorization of specified element

factor

public PolynomialFactorDecomposition<Poly> factor(Poly element)

Description copied from interface: Ring

Factor specified element

variable

public Poly variable(int variable)

Description copied from interface: IPolynomialRing

Creates poly representing a single specified variable

create

public Poly create(DegreeVector term)

Creates multivariate polynomial over the same ring as this with the single monomial

Parameters:

term - the monomial

Returns:

multivariate polynomial

randomElement

public Poly randomElement(int degree,
                          int size,
                          org.apache.commons.math3.random.RandomGenerator rnd)

Generates random multivariate polynomial

Parameters:

degree - maximal degree of the result

size - number of elements in the result

rnd - random source

Returns:

random polynomial

randomElementTree

public Poly randomElementTree(int degree,
                              int size,
                              org.apache.commons.math3.random.RandomGenerator rnd)

Generates random multivariate polynomial

Parameters:

degree - maximal degree of the result

size - number of elements in the result

rnd - random source

Returns:

random polynomial

randomElement

public Poly randomElement(int degree,
                          int size)

Generates random multivariate polynomial

Parameters:

degree - maximal degree of the result

size - number of elements in the result

Returns:

random polynomial

randomElement

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

Gives a random constant polynomial. For generating non-constant random polynomials see RandomMultivariatePolynomials

Parameters:

rnd - the source of randomness

Returns:

random constant polynomial

See Also:

RandomMultivariatePolynomials

randomElementTree

public Poly randomElementTree(org.apache.commons.math3.random.RandomGenerator rnd)

Description copied from interface: Ring

If this ring has a complicated nested structure, this method guaranties that the resulting random element will reflect ring complicated structure, i.e. the result will be roughly as complicated as the ring is

Returns:

random element from this ring

factory

public Poly factory()

Description copied from interface: IPolynomialRing

Factory polynomial

Specified by:

factory in interface IPolynomialRing<Poly extends IPolynomial<Poly>>

isEuclideanRing

public boolean isEuclideanRing()

Description copied from interface: Ring

Returns whether this ring is a Euclidean ring

Specified by:

isEuclideanRing in interface Ring<Poly extends IPolynomial<Poly>>

Returns:

whether this ring is a Euclidean ring

isField

public final boolean isField()

Description copied from interface: Ring

Returns whether this ring is a field

Specified by:

isField in interface Ring<Poly extends IPolynomial<Poly>>

Returns:

whether this ring is a field

cardinality

public final 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<Poly extends IPolynomial<Poly>>

Returns:

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

characteristic

public final BigInteger characteristic()

Description copied from interface: Ring

Returns characteristic of this ring

Specified by:

characteristic in interface Ring<Poly extends IPolynomial<Poly>>

Returns:

characteristic of this ring

add

public final Poly add(Poly a,
                      Poly b)

Description copied from interface: Ring

Add two elements

Specified by:

add in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

a - the first element

b - the second element

Returns:

a + b

subtract

public final Poly subtract(Poly a,
                           Poly b)

Description copied from interface: Ring

Subtracts b from a

Specified by:

subtract in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

a - the first element

b - the second element

Returns:

a - b

multiply

public final Poly multiply(Poly a,
                           Poly b)

Description copied from interface: Ring

Multiplies two elements

Specified by:

multiply in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

a - the first element

b - the second element

Returns:

a * b

negate

public final Poly negate(Poly element)

Description copied from interface: Ring

Negates the given element

Specified by:

negate in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

element - the ring element

Returns:

-val

pow

public Poly pow(Poly base,
                BigInteger exponent)

Description copied from interface: Ring

Returns base in a power of exponent (non negative)

Specified by:

pow in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

base - base

exponent - exponent (non negative)

Returns:

base in a power of exponent

addMutable

public Poly addMutable(Poly a,
                       Poly b)

Description copied from interface: Ring

Adds two elements and destroys the initial content of a.

Specified by:

addMutable in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

a - the first element (may be destroyed)

b - the second element

Returns:

a + b

subtractMutable

public Poly subtractMutable(Poly a,
                            Poly b)

Description copied from interface: Ring

Subtracts b from a and destroys the initial content of a

Specified by:

subtractMutable in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

a - the first element (may be destroyed)

b - the second element

Returns:

a - b

multiplyMutable

public Poly multiplyMutable(Poly a,
                            Poly b)

Description copied from interface: Ring

Multiplies two elements and destroys the initial content of a

Specified by:

multiplyMutable in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

a - the first element (may be destroyed)

b - the second element

Returns:

a * b

negateMutable

public Poly negateMutable(Poly element)

Description copied from interface: Ring

Negates the given element and destroys the initial content of element

Specified by:

negateMutable in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

element - the ring element (may be destroyed)

Returns:

-element

reciprocal

public final Poly reciprocal(Poly element)

Description copied from interface: Ring

Gives the inverse element element ^ (-1)

Specified by:

reciprocal in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

element - the element

Returns:

element ^ (-1)

getZero

public final Poly getZero()

Description copied from interface: Ring

Returns zero element of this ring

Specified by:

getZero in interface Ring<Poly extends IPolynomial<Poly>>

Returns:

0

getOne

public final Poly getOne()

Description copied from interface: Ring

Returns unit element of this ring (one)

Specified by:

getOne in interface Ring<Poly extends IPolynomial<Poly>>

Returns:

1

isZero

public final boolean isZero(Poly element)

Description copied from interface: Ring

Tests whether specified element is zero

Specified by:

isZero in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

element - the ring element

Returns:

whether specified element is zero

isOne

public final boolean isOne(Poly element)

Description copied from interface: Ring

Tests whether specified element is one (exactly)

Specified by:

isOne in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

element - the ring element

Returns:

whether specified element is exactly one

See Also:

Ring.isUnit(Object)

isUnit

public boolean isUnit(Poly element)

Description copied from interface: Ring

Tests whether specified element is a ring unit

Specified by:

isUnit in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

element - the ring element

Returns:

whether specified element is a ring unit

See Also:

Ring.isOne(Object)

valueOf

public final Poly valueOf(long val)

Description copied from interface: Ring

Returns ring element associated with specified long

Specified by:

valueOf in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

val - machine integer

Returns:

ring element associated with specified long

valueOfBigInteger

public Poly valueOfBigInteger(BigInteger val)

Description copied from interface: Ring

Returns ring element associated with specified integer

Specified by:

valueOfBigInteger in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

val - integer

Returns:

ring element associated with specified integer

valueOf

public final Poly valueOf(Poly 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<Poly extends IPolynomial<Poly>>

Parameters:

val - some element from any ring

Returns:

this ring element associated with specified val

copy

public Poly copy(Poly 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<Poly extends IPolynomial<Poly>>

Parameters:

element - the element

Returns:

deep copy of specified element

compare

public final int compare(Poly o1,
                         Poly o2)

Specified by:

compare in interface Comparator<Poly extends IPolynomial<Poly>>

equals

public final boolean equals(Object o)

Specified by:

equals in interface Comparator<Poly extends IPolynomial<Poly>>

Overrides:

equals in class Object

hashCode

public final int hashCode()

Overrides:

hashCode in class Object

iterator

public Iterator<Poly> iterator()

Description copied from interface: Ring

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

Specified by:

iterator in interface Iterable<Poly extends IPolynomial<Poly>>

Specified by:

iterator in interface Ring<Poly extends IPolynomial<Poly>>

parse

public Poly parse(String string)

Description copied from interface: Ring

Parse string into ring element

Specified by:

parse in interface IParser<Poly extends IPolynomial<Poly>>

Specified by:

parse in interface Ring<Poly extends IPolynomial<Poly>>

Parameters:

string - string

Returns:

ring element

See Also:

Coder

toString

public String toString(IStringifier<Poly> stringifier)

Description copied from interface: Stringifiable

convert this to string with the use of stringifier

Specified by:

toString in interface Stringifiable<Poly extends IPolynomial<Poly>>

toString

public String toString(String... variables)

toString

public String toString()

Overrides:

toString in class Object