UnivariateRing (rings 2.5.1 API)

java.lang.Object
- cc.redberry.rings.ARing<Poly>
- - cc.redberry.rings.poly.UnivariateRing<Poly>

Type Parameters:

Poly - type of univariate polynomials

All Implemented Interfaces:

IParser<Poly>, Stringifiable<Poly>, IPolynomialRing<Poly>, Ring<Poly>, Serializable, Iterable<Poly>, Comparator<Poly>
```
public final class UnivariateRing<Poly extends IUnivariatePolynomial<Poly>>
extends ARing<Poly>
```
Ring of univariate polynomials.

Since:

1.0

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`static int`	`MAX_DEGREE_OF_RANDOM_POLY` The maximal degree of polynomial generated with `randomElement(RandomGenerator)`
`static int`	`MIN_DEGREE_OF_RANDOM_POLY` The minimal degree of polynomial generated with `randomElement(RandomGenerator)`

Constructor Summary

Constructors
Constructor and Description
`UnivariateRing(Poly factory)` Creates ring of univariate polynomials which support operations over univariate polynomials of the type 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[]`	`divideAndRemainder(Poly a, Poly b)` Returns quotient and remainder of `dividend / divider`
`boolean`	`equals(Object o)`
`Poly[]`	`extendedGCD(Poly a, Poly b)` Returns array of `[gcd(a,b), s, t]` such that `s * a + t * b = gcd(a, b)`
`PolynomialFactorDecomposition<Poly>`	`factor(Poly element)` Factor specified element
`PolynomialFactorDecomposition<Poly>`	`factorSquareFree(Poly element)` Square-free factorization of specified element
`Poly`	`factory()` Factory polynomial
`Poly[]`	`firstBezoutCoefficient(Poly a, Poly b)` Returns array of `[gcd(a,b), s]` such that `s * a + t * b = gcd(a, b)`
`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)
`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
`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 minDegree, int maxDegree, org.apache.commons.math3.random.RandomGenerator rnd)` Gives a random univariate polynomial with the degree randomly picked from `minDegree` (inclusive) to `maxDegree` (exclusive)
`Poly`	`randomElement(int degree, org.apache.commons.math3.random.RandomGenerator rnd)` Gives a random univariate polynomial with the specified degree
`Poly`	`randomElement(org.apache.commons.math3.random.RandomGenerator rnd)` Gives a random univariate polynomial with the degree randomly picked from `MIN_DEGREE_OF_RANDOM_POLY` (inclusive) to `MAX_DEGREE_OF_RANDOM_POLY` (exclusive)
`Poly`	`randomElementTree(int minDegree, int maxDegree, org.apache.commons.math3.random.RandomGenerator rnd)` Gives a random univariate polynomial with the degree randomly picked from `minDegree` (inclusive) to `maxDegree` (exclusive) and coefficients generated via `Ring.randomElementTree(RandomGenerator)` method
`Poly`	`randomElementTree(org.apache.commons.math3.random.RandomGenerator rnd)` Gives a random univariate polynomial with the degree randomly picked from `MIN_DEGREE_OF_RANDOM_POLY` (inclusive) to `MAX_DEGREE_OF_RANDOM_POLY` (exclusive)
`Poly`	`reciprocal(Poly element)` Gives the inverse element `element ^ (-1)`
`Poly`	`remainder(Poly a, Poly b)` Returns the remainder of `dividend / divider`
`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, factorial, fillZeros, gcd, gcd, getNegativeOne, increment, isFinite, isFiniteField, isMinusOne, isPerfectPower, isUnitOrZero, lcm, lcm, lcm, max, min, multiply, multiply, multiply, perfectPowerBase, perfectPowerExponent, pow, pow, quotient, randomElement, randomElementTree, randomNonZeroElement, 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
  - MIN_DEGREE_OF_RANDOM_POLY
```
public static final int MIN_DEGREE_OF_RANDOM_POLY
```
    The minimal degree of polynomial generated with randomElement(RandomGenerator)
    
    See Also:
    
    Constant Field Values
  - MAX_DEGREE_OF_RANDOM_POLY
```
public static final int MAX_DEGREE_OF_RANDOM_POLY
```
    The maximal degree of polynomial generated with randomElement(RandomGenerator)
    
    See Also:
    
    Constant Field Values
- Constructor Detail
  - UnivariateRing
```
public UnivariateRing(Poly factory)
```
    Creates ring of univariate polynomials which support operations over univariate polynomials of the type same as of provided factory polynomial
    
    Parameters:
    
    factory - factory polynomial (the exact value of factory is irrelevant)
- Method Detail
  - nVariables
```
public int nVariables()
```
    Description copied from interface: IPolynomialRing
    
    Number of polynomial variables
  - remainder
```
public Poly remainder(Poly a,
                      Poly b)
```
    Description copied from interface: Ring
    
    Returns the remainder of dividend / divider
    
    Parameters:
    
    a - the dividend
    
    b - the divider
    
    Returns:
    
    the remainder of dividend / divider
  - divideAndRemainder
```
public Poly[] divideAndRemainder(Poly a,
                                 Poly b)
```
    Description copied from interface: Ring
    
    Returns quotient and remainder of dividend / divider
    
    Parameters:
    
    a - the dividend
    
    b - 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
  - extendedGCD
```
public Poly[] extendedGCD(Poly a,
                          Poly b)
```
    Description copied from interface: Ring
    
    Returns array of [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b)
  - firstBezoutCoefficient
```
public Poly[] firstBezoutCoefficient(Poly a,
                                     Poly b)
```
    Description copied from interface: Ring
    
    Returns array of [gcd(a,b), s] such that s * a + t * b = gcd(a, b)
    
    Parameters:
    
    a - the first ring element (for which the Bezout coefficient is computed)
    
    b - the second ring element
    
    Returns:
    
    array of [gcd(a,b), s] such that s * a + t * b = gcd(a, b)
  - 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
  - randomElement
```
public Poly randomElement(int minDegree,
                          int maxDegree,
                          org.apache.commons.math3.random.RandomGenerator rnd)
```
    Gives a random univariate polynomial with the degree randomly picked from minDegree (inclusive) to maxDegree (exclusive)
    
    Parameters:
    
    minDegree - the minimal degree of the result
    
    maxDegree - the maximal degree of the result
    
    rnd - the source of randomness
    
    Returns:
    
    random univariate polynomial with the degree randomly picked from minDegree (inclusive) to maxDegree (exclusive)
    
    See Also:
    
    RandomUnivariatePolynomials
  - randomElement
```
public Poly randomElement(int degree,
                          org.apache.commons.math3.random.RandomGenerator rnd)
```
    Gives a random univariate polynomial with the specified degree
    
    Parameters:
    
    degree - the degree of the result
    
    rnd - the source of randomness
    
    Returns:
    
    random univariate polynomial with the specified degree
  - randomElement
```
public Poly randomElement(org.apache.commons.math3.random.RandomGenerator rnd)
```
    Gives a random univariate polynomial with the degree randomly picked from MIN_DEGREE_OF_RANDOM_POLY (inclusive) to MAX_DEGREE_OF_RANDOM_POLY (exclusive)
    
    Parameters:
    
    rnd - the source of randomness
    
    Returns:
    
    random univariate polynomial
  - randomElementTree
```
public Poly randomElementTree(int minDegree,
                              int maxDegree,
                              org.apache.commons.math3.random.RandomGenerator rnd)
```
    Gives a random univariate polynomial with the degree randomly picked from minDegree (inclusive) to maxDegree (exclusive) and coefficients generated via Ring.randomElementTree(RandomGenerator) method
    
    Parameters:
    
    minDegree - the minimal degree of the result
    
    maxDegree - the maximal degree of the result
    
    rnd - the source of randomness
    
    Returns:
    
    random univariate polynomial with the degree randomly picked from minDegree (inclusive) to maxDegree (exclusive)
    
    See Also:
    
    RandomUnivariatePolynomials
  - randomElementTree
```
public Poly randomElementTree(org.apache.commons.math3.random.RandomGenerator rnd)
```
    Gives a random univariate polynomial with the degree randomly picked from MIN_DEGREE_OF_RANDOM_POLY (inclusive) to MAX_DEGREE_OF_RANDOM_POLY (exclusive)
    
    Parameters:
    
    rnd - the source of randomness
    
    Returns:
    
    random univariate polynomial
  - 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 UnivariateRing<Poly extends IUnivariatePolynomial<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

MIN_DEGREE_OF_RANDOM_POLY

MAX_DEGREE_OF_RANDOM_POLY

Constructor Detail

UnivariateRing

Method Detail

nVariables

remainder

divideAndRemainder

gcd

extendedGCD

firstBezoutCoefficient

factorSquareFree

factor

variable

randomElement

randomElement

randomElement

randomElementTree

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