Package 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 Details

  • Constructor Details

  • Method Details

    • nVariables

      public int nVariables()
      Description copied from interface: IPolynomialRing
      Number of polynomial variables
      Specified by:
      nVariables in interface IPolynomialRing<Term extends AMonomial<Term>>

    • factory

      public Poly factory()
      Description copied from interface: IPolynomialRing
      Factory polynomial
      Specified by:
      factory in interface IPolynomialRing<Term extends AMonomial<Term>>

    • variable

      public Poly variable​(int variable)
      Description copied from interface: IPolynomialRing
      Creates poly representing a single specified variable
      Specified by:
      variable in interface IPolynomialRing<Term extends AMonomial<Term>>

    • isField

      public boolean isField()
      Description copied from interface: Ring
      Returns whether this ring is a field
      Specified by:
      isField in interface Ring<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      Returns:
      0

    • getOne

      public Poly getOne()
      Description copied from interface: Ring
      Returns unit element of this ring (one)
      Specified by:
      getOne in interface Ring<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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 Iterable<Term extends AMonomial<Term>>
      Specified by:
      iterator in interface Ring<Term extends AMonomial<Term>>

    • compare

      public int compare​(Poly o1, Poly o2)
      Specified by:
      compare in interface Comparator<Term extends AMonomial<Term>>

    • parse

      public Poly parse​(String string)
      Description copied from interface: Ring
      Parse string into ring element
      Specified by:
      parse in interface IParser<Term extends AMonomial<Term>>
      Specified by:
      parse in interface Ring<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>
      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<Term extends AMonomial<Term>>

    • toString

      public String toString()
      Overrides:
      toString in class Object