Package cc.redberry.rings.poly

Class UnivariateRing<Poly extends IUnivariatePolynomial<Poly>>

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 Details

  • Constructor Details

    • 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 Details

    • 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 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