Package cc.redberry.rings.poly

Interface IPolynomial<Poly extends IPolynomial<Poly>>

Type Parameters:
Poly - the type of polynomial (self type)
All Superinterfaces:
Comparable<Poly>, Serializable, Stringifiable<Poly>
All Known Subinterfaces:
IUnivariatePolynomial<Poly>
All Known Implementing Classes:
AMultivariatePolynomial, MultivariatePolynomial, MultivariatePolynomialZp64, UnivariatePolynomial, UnivariatePolynomialZ64, UnivariatePolynomialZp64
public interface IPolynomial<Poly extends IPolynomial<Poly>>
extends Comparable<Poly>, Stringifiable<Poly>, Serializable
Parent interface for all polynomials. All polynomial instances are mutable, so all structural operations except those where it is stated explicitly will in general modify the instance. All arithmetic operations (add(oth), multiply(oth), monic() etc.) applies to this inplace and return this reference ( so e.g. (poly == poly.add(other))).

Note: modifier operations are not synchronized.

Since:
1.0

  • Method Details

    • sameCoefficientRingWith

      boolean sameCoefficientRingWith​(Poly oth)
      Returns whether oth and this have the same coefficient ring
      Parameters:
      oth - other polynomial
      Returns:
      whether this and oth are over the same coefficient ring

    • assertSameCoefficientRingWith

      default void assertSameCoefficientRingWith​(Poly oth)
      Checks whether oth and this have the same coefficient ring, if not exception will be thrown
      Parameters:
      oth - other polynomial
      Throws:
      IllegalArgumentException - if this and oth have different coefficient ring

    • setCoefficientRingFrom

      Poly setCoefficientRingFrom​(Poly poly)
      Set the coefficient ring from specified poly
      Parameters:
      poly - the polynomial
      Returns:
      a copy of this with the coefficient ring taken from poly

    • setCoefficientRingFromOptional

      default Poly setCoefficientRingFromOptional​(Poly poly)

    • degree

      int degree()
      Returns the degree of this polynomial
      Returns:
      the degree

    • size

      int size()
      Returns the size of this polynomial
      Returns:
      the size

    • isZero

      boolean isZero()
      Returns true if this is zero
      Returns:
      whether this is zero

    • isOne

      boolean isOne()
      Returns true if this is one
      Returns:
      whether this is one

    • isMonic

      boolean isMonic()
      Returns true if this polynomial is monic
      Returns:
      whether this is monic

    • isUnitCC

      boolean isUnitCC()
      Returns true if constant term is equal to one
      Returns:
      whether constant term is 1

    • isZeroCC

      boolean isZeroCC()
      Returns true if constant term is zero
      Returns:
      whether constant term is zero

    • isConstant

      boolean isConstant()
      Returns true if this polynomial has only constant term
      Returns:
      whether this is constant

    • isMonomial

      boolean isMonomial()
      Returns true if this polynomial has only one monomial term
      Returns:
      whether this has only one monomial term

    • isOverField

      boolean isOverField()
      Returns whether the coefficient ring of this polynomial is a field
      Returns:
      whether the coefficient ring of this polynomial is a field

    • isOverZ

      boolean isOverZ()
      Returns whether the coefficient ring of this polynomial is Z
      Returns:
      whether the coefficient ring of this polynomial is Z

    • isOverFiniteField

      boolean isOverFiniteField()
      Returns whether the coefficient ring of this polynomial is a finite field
      Returns:
      whether the coefficient ring of this polynomial is a finite field

    • isLinearOrConstant

      boolean isLinearOrConstant()
      Returns whether this polynomial is linear (i.e. of the form a * X + b)

    • isLinearExactly

      boolean isLinearExactly()
      Returns whether this polynomial is linear (i.e. of the form a * X + b with nonzero a)

    • coefficientRingCardinality

      BigInteger coefficientRingCardinality()
      Returns cardinality of the coefficient ring of this poly
      Returns:
      cardinality of the coefficient ring

    • coefficientRingCharacteristic

      BigInteger coefficientRingCharacteristic()
      Returns characteristic of the coefficient ring of this poly
      Returns:
      characteristic of the coefficient ring

    • isOverPerfectPower

      boolean isOverPerfectPower()
      Returns whether the coefficientRingCardinality() is a perfect power
      Returns:
      whether the coefficientRingCardinality() is a perfect power

    • coefficientRingPerfectPowerBase

      BigInteger coefficientRingPerfectPowerBase()
      Returns base so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite
      Returns:
      base so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite

    • coefficientRingPerfectPowerExponent

      BigInteger coefficientRingPerfectPowerExponent()
      Returns exponent so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite
      Returns:
      exponent so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite

    • monic

      Poly monic()
      Sets this to its monic part (that is this divided by its leading coefficient), or returns null (causing loss of internal data) if some of the elements can't be exactly divided by the lc(). NOTE: if null is returned, the content of this is destroyed.
      Returns:
      monic this or null

    • monicExact

      default Poly monicExact()
      Sets this to its monic part (that is this divided by its leading coefficient), or throws ArithmeticException if some of the elements can't be exactly divided by the l.c.
      Returns:
      monic this or null
      Throws:
      ArithmeticException - if some of the elements can't be exactly divided by the l.c.

    • canonical

      default Poly canonical()
      Makes this poly monic if coefficient ring is field, otherwise makes this primitive

    • signumOfLC

      int signumOfLC()
      Gives signum of the leading coefficient
      Returns:
      signum of the leading coefficient

    • toPositiveLC

      default Poly toPositiveLC()
      If signum of leading coefficient is minus one, negate this

    • toZero

      Poly toZero()
      Sets this to zero
      Returns:
      this := zero

    • set

      Poly set​(Poly oth)
      Sets the content of this to oth
      Parameters:
      oth - the polynomial
      Returns:
      this := oth

    • primitivePart

      Poly primitivePart()
      Reduces poly to its primitive part (primitive part will always have positive l.c.)
      Returns:
      primitive part (poly will be modified)

    • primitivePartSameSign

      Poly primitivePartSameSign()
      Reduces poly to its primitive part, so that primitive part will have the same signum as the initial poly
      Returns:
      primitive part (poly will be modified)

    • increment

      Poly increment()
      Adds 1 to this
      Returns:
      this + 1

    • decrement

      Poly decrement()
      Subtracts 1 from this
      Returns:
      this - 1

    • createZero

      Poly createZero()
      Returns the new instance of zero polynomial (with the same coefficient ring)
      Returns:
      new instance of 0

    • createOne

      Poly createOne()
      Returns the new instance of unit polynomial (with the same coefficient ring)
      Returns:
      new instance of 1

    • createConstant

      default Poly createConstant​(long value)
      Creates constant polynomial with specified value
      Parameters:
      value - the value
      Returns:
      constant polynomial

    • add

      Poly add​(Poly oth)
      Adds oth to this.
      Parameters:
      oth - the polynomial
      Returns:
      this + oth

    • add

      default Poly add​(Poly... oth)
      Adds oth to this.
      Parameters:
      oth - the polynomials
      Returns:
      this + oth

    • subtract

      Poly subtract​(Poly oth)
      Subtracts oth from this.
      Parameters:
      oth - the polynomial
      Returns:
      this - oth

    • subtract

      default Poly subtract​(Poly... oth)
      Subtracts oth from this.
      Parameters:
      oth - the polynomial
      Returns:
      this - oth

    • negate

      Poly negate()
      Negates this and returns
      Returns:
      this negated

    • multiply

      Poly multiply​(Poly oth)
      Multiplies this by oth
      Parameters:
      oth - the polynomial
      Returns:
      this * oth

    • multiply

      default Poly multiply​(Poly... oth)
      Multiplies this by oth
      Parameters:
      oth - the polynomials
      Returns:
      this * oth

    • multiply

      default Poly multiply​(Iterable<Poly> oth)
      Multiplies this by oth
      Parameters:
      oth - the polynomials
      Returns:
      this * oth

    • multiply

      Poly multiply​(long factor)
      Multiplies this by factor
      Parameters:
      factor - the factor
      Returns:
      this * factor

    • multiplyByBigInteger

      Poly multiplyByBigInteger​(BigInteger factor)
      Multiplies this by factor
      Parameters:
      factor - the factor
      Returns:
      this * factor

    • square

      Poly square()
      Squares this
      Returns:
      this * this

    • contentAsPoly

      Poly contentAsPoly()
      Returns the content of this (gcd of coefficients) as a constant poly

    • lcAsPoly

      Poly lcAsPoly()
      Returns the leading coefficient as a constant poly

    • ccAsPoly

      Poly ccAsPoly()
      Returns the constant coefficient as a constant poly

    • divideByLC

      Poly divideByLC​(Poly other)
      Divides this polynomial by the leading coefficient of other or returns null (causing loss of internal data) if some of the elements can't be exactly divided by the other.lc(). NOTE: if null is returned, the content of this is destroyed.
      Parameters:
      other - the polynomial
      Returns:
      this divided by the other.lc() or null if exact division is not possible

    • monicWithLC

      Poly monicWithLC​(Poly other)
      Sets this to its monic part multiplied by the leading coefficient of other;
      Parameters:
      other - other polynomial
      Returns:
      monic part multiplied by the leading coefficient of other or null if exact division by the reduced leading coefficient is not possible

    • multiplyByLC

      Poly multiplyByLC​(Poly other)
      Multiply this by the leading coefficient of other
      Parameters:
      other - polynomial
      Returns:
      this * lc(other)

    • clone

      Poly clone()
      Deep copy of this
      Returns:
      deep copy of this

    • copy

      default Poly copy()
      Deep copy of this (alias for clone(), required for scala)
      Returns:
      deep copy of this

    • createArray

      Poly[] createArray​(int length)
      overcome Java generics...

    • createArray2d

      Poly[][] createArray2d​(int length)
      overcome Java generics...

    • createArray2d

      Poly[][] createArray2d​(int length1, int length2)
      overcome Java generics...

    • createArray

      default Poly[] createArray​(Poly a)
      overcome Java generics...

    • createArray

      default Poly[] createArray​(Poly a, Poly b)
      overcome Java generics...

    • createArray

      default Poly[] createArray​(Poly a, Poly b, Poly c)
      overcome Java generics...

    • coefficientRingToString

      String coefficientRingToString​(IStringifier<Poly> stringifier)
      String representation of the coefficient ring of this

    • coefficientRingToString

      default String coefficientRingToString()
      String representation of the coefficient ring of this

    • toString

      default String toString​(String... variables)
      String representation of this polynomial with specified string variables

    • parsePoly

      @Deprecated Poly parsePoly​(String string)
      Deprecated.
      use Coder to parse polynomials