cc.redberry.rings.poly

Class QuotientRing<Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>>

java.lang.Object

cc.redberry.rings.ARing<Poly>

cc.redberry.rings.poly.QuotientRing<Term,Poly>

All Implemented Interfaces:

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

public class QuotientRing<Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>>
extends ARing<Poly>
implements IPolynomialRing<Poly>

Multivariate quotient ring

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
MultivariateRing<Poly>	baseRing the base ring
Ideal<Term,Poly>	ideal the ideal

Constructor Summary

Constructors

Constructor and Description
QuotientRing(MultivariateRing<Poly> baseRing, Ideal<Term,Poly> ideal)

Method Summary

Modifier and Type	Method and Description
Poly	add(Poly a, Poly 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(Poly o1, Poly o2)
Poly	copy(Poly element) Makes a deep copy of the specified element (for immutable instances the same reference returned).
Poly[]	divideAndRemainder(Poly dividend, Poly divider) Returns quotient and remainder of dividend / divider
Poly	factory() Factory polynomial
Poly	getOne() Returns unit element of this ring (one)
Poly	getZero() Returns zero element of this ring
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)
Poly	mod(Poly el)
Poly	multiply(Poly a, Poly b) Multiplies two elements
Poly	negate(Poly element) Negates the given element
Poly	normalForm(Poly el)
int	nVariables() Number of polynomial variables
Poly	parse(String string) Parse string into ring element
Poly	randomElement(org.apache.commons.math3.random.RandomGenerator rnd) Returns a random element from this ring
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
String	toString()
String	toString(IStringifier<Poly> stringifier) convert this to string with the use of stringifier
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, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

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

mkCoder, parse, signum

Methods inherited from interface cc.redberry.rings.Ring

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

Methods inherited from interface java.util.Comparator

comparing, comparing, comparingDouble, comparingInt, comparingLong, equals, naturalOrder, nullsFirst, nullsLast, reversed, reverseOrder, thenComparing, thenComparing, thenComparing, thenComparingDouble, thenComparingInt, thenComparingLong

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Field Detail

baseRing

public final MultivariateRing<Poly extends AMultivariatePolynomial<Term,Poly>> baseRing

the base ring

ideal

public final Ideal<Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> ideal

the ideal

Constructor Detail

QuotientRing

public QuotientRing(MultivariateRing<Poly> baseRing,
                    Ideal<Term,Poly> ideal)

Method Detail

nVariables

public int nVariables()

Description copied from interface: IPolynomialRing

Number of polynomial variables

Specified by:

nVariables in interface IPolynomialRing<Poly extends AMultivariatePolynomial<Term,Poly>>

factory

public Poly factory()

Description copied from interface: IPolynomialRing

Factory polynomial

Specified by:

factory in interface IPolynomialRing<Poly extends AMultivariatePolynomial<Term,Poly>>

variable

public Poly variable(int variable)

Description copied from interface: IPolynomialRing

Creates poly representing a single specified variable

Specified by:

variable in interface IPolynomialRing<Poly extends AMultivariatePolynomial<Term,Poly>>

isField

public boolean isField()

Description copied from interface: Ring

Returns whether this ring is a field

Specified by:

isField in interface Ring<Poly extends AMultivariatePolynomial<Term,Poly>>

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<Poly extends AMultivariatePolynomial<Term,Poly>>

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<Poly extends AMultivariatePolynomial<Term,Poly>>

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<Poly extends AMultivariatePolynomial<Term,Poly>>

Returns:

characteristic of this ring

mod

public Poly mod(Poly el)

normalForm

public Poly normalForm(Poly el)

add

public Poly add(Poly a,
                Poly b)

Description copied from interface: Ring

Add two elements

Specified by:

add in interface Ring<Poly extends AMultivariatePolynomial<Term,Poly>>

Parameters:

a - the first element

b - the second element

Returns:

a + b

subtract

public Poly subtract(Poly a,
                     Poly b)

Description copied from interface: Ring

Subtracts b from a

Specified by:

subtract in interface Ring<Poly extends AMultivariatePolynomial<Term,Poly>>

Parameters:

a - the first element

b - the second element

Returns:

a - b

multiply

public Poly multiply(Poly a,
                     Poly b)

Description copied from interface: Ring

Multiplies two elements

Specified by:

multiply in interface Ring<Poly extends AMultivariatePolynomial<Term,Poly>>

Parameters:

a - the first element

b - the second element

Returns:

a * b

negate

public Poly negate(Poly element)

Description copied from interface: Ring

Negates the given element

Specified by:

negate in interface Ring<Poly extends AMultivariatePolynomial<Term,Poly>>

Parameters:

element - the ring element

Returns:

-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 AMultivariatePolynomial<Term,Poly>>

Parameters:

element - the element

Returns:

deep copy of specified element

divideAndRemainder

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

Description copied from interface: Ring

Returns quotient and remainder of dividend / divider

Specified by:

divideAndRemainder in interface Ring<Poly extends AMultivariatePolynomial<Term,Poly>>

Parameters:

dividend - the dividend

divider - the divider

Returns:

{quotient, remainder}

reciprocal

public Poly reciprocal(Poly element)

Description copied from interface: Ring

Gives the inverse element element ^ (-1)

Specified by:

reciprocal in interface Ring<Poly extends AMultivariatePolynomial<Term,Poly>>

Parameters:

element - the element

Returns:

element ^ (-1)

getZero

public Poly getZero()

Description copied from interface: Ring

Returns zero element of this ring

Specified by:

getZero in interface Ring<Poly extends AMultivariatePolynomial<Term,Poly>>

Returns:

0

getOne

public Poly getOne()

Description copied from interface: Ring

Returns unit element of this ring (one)

Specified by:

getOne in interface Ring<Poly extends AMultivariatePolynomial<Term,Poly>>

Returns:

1

isZero

public boolean isZero(Poly element)

Description copied from interface: Ring

Tests whether specified element is zero

Specified by:

isZero in interface Ring<Poly extends AMultivariatePolynomial<Term,Poly>>

Parameters:

element - the ring element

Returns:

whether specified element is zero

isOne

public boolean isOne(Poly element)

Description copied from interface: Ring

Tests whether specified element is one (exactly)

Specified by:

isOne in interface Ring<Poly extends AMultivariatePolynomial<Term,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 AMultivariatePolynomial<Term,Poly>>

Parameters:

element - the ring element

Returns:

whether specified element is a ring unit

See Also:

Ring.isOne(Object)

valueOf

public Poly valueOf(long val)

Description copied from interface: Ring

Returns ring element associated with specified long

Specified by:

valueOf in interface Ring<Poly extends AMultivariatePolynomial<Term,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 AMultivariatePolynomial<Term,Poly>>

Parameters:

val - integer

Returns:

ring element associated with specified integer

valueOf

public 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 AMultivariatePolynomial<Term,Poly>>

Parameters:

val - some element from any ring

Returns:

this ring element associated with specified val

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 Ring<Poly extends AMultivariatePolynomial<Term,Poly>>

Specified by:

iterator in interface Iterable<Poly extends AMultivariatePolynomial<Term,Poly>>

compare

public int compare(Poly o1,
                   Poly o2)

Specified by:

compare in interface Comparator<Poly extends AMultivariatePolynomial<Term,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 AMultivariatePolynomial<Term,Poly>>

Specified by:

parse in interface Ring<Poly extends AMultivariatePolynomial<Term,Poly>>

Parameters:

string - string

Returns:

ring element

See Also:

Coder

randomElement

public Poly 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<Poly extends AMultivariatePolynomial<Term,Poly>>

Parameters:

rnd - the source of randomness

Returns:

random element from this ring

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

Specified by:

randomElementTree in interface Ring<Poly extends AMultivariatePolynomial<Term,Poly>>

Returns:

random element from this ring

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 AMultivariatePolynomial<Term,Poly>>

toString

public String toString()

Overrides:

toString in class Object