MultivariateRing (rings 2.5.7 API)

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 and 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 and 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

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and 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 cc.redberry.rings.poly.IPolynomialRing
mkCoder, parse, signum

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

Methods inherited from interface java.util.Comparator
comparing, comparing, comparingDouble, comparingInt, comparingLong, naturalOrder, nullsFirst, nullsLast, reversed, reverseOrder, thenComparing, thenComparing, thenComparing, thenComparingDouble, thenComparingInt, thenComparingLong

Methods inherited from interface java.lang.Iterable
forEach, spliterator

- 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 Ring<Poly extends IPolynomial<Poly>>
    
    Specified by:
    
    iterator in interface Iterable<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

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

Field Summary

Constructor Summary

Method Summary

Methods inherited from class cc.redberry.rings.ARing

Methods inherited from class java.lang.Object

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

Methods inherited from interface cc.redberry.rings.Ring

Methods inherited from interface java.util.Comparator

Methods inherited from interface java.lang.Iterable

Field Detail

DEGREE_OF_RANDOM_POLY

SIZE_OF_RANDOM_POLY

Constructor Detail

MultivariateRing

Method Detail

monomialAlgebra

nVariables

ordering

dropVariable

divideAndRemainder

gcd

gcd

gcd

factorSquareFree

factor

variable

create

randomElement

randomElementTree

randomElement

randomElement

randomElementTree

factory

isEuclideanRing

isField

cardinality

characteristic

add

subtract

multiply

negate

pow

addMutable

subtractMutable

multiplyMutable

negateMutable

reciprocal

getZero

getOne

isZero

isOne

isUnit

valueOf

valueOfBigInteger

valueOf

copy

compare

equals

hashCode

iterator

parse

toString

toString

toString