Package dev.nm.analysis.function.polynomial

Class Polynomial

java.lang.Object
dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction
dev.nm.analysis.function.rn2r1.univariate.AbstractUnivariateRealFunction
dev.nm.analysis.function.polynomial.Polynomial
All Implemented Interfaces:
AbelianGroup<Polynomial>, Monoid<Polynomial>, Ring<Polynomial>, VectorSpace<Polynomial,Real>, Function<Vector,Double>, RealScalarFunction, UnivariateRealFunction
Direct Known Subclasses:
CauchyPolynomial, DPolynomial, QuadraticMonomial, ScaledPolynomial
public class Polynomial extends AbstractUnivariateRealFunction implements Ring<Polynomial>, VectorSpace<Polynomial,Real>
A polynomial is a UnivariateRealFunction that represents a finite length expression constructed from variables and constants, using the operations of addition, subtraction, multiplication, and constant non-negative whole number exponents. Specifically, it has the form \[ p(x) = a_0x^n + a_1x^{n-1} + ... + a_{n-1}x + a_n \] This implementation is immutable.
See Also:

  • Field Details

    • ZERO

      public static final Polynomial ZERO
      a polynomial representing 0

    • ONE

      public static final Polynomial ONE
      a polynomial representing 1

  • Constructor Details

    • Polynomial

      public Polynomial(double... coefficients)
      Construct a polynomial from an array of coefficients. The first/0-th entry corresponds to the xn term. The last/n-th entry corresponds to the constant term. The degree of the polynomial is n, the array length minus 1.

      For example,

      new Polynomial(1, -2, 3, 2)
      creates an instance of Polynomial representing x3 - 2x2 + 3x + 2.
      Parameters:
      coefficients - the polynomial coefficients

    • Polynomial

      public Polynomial(Polynomial that)
      Copy constructor.
      Parameters:
      that - a polynomial

  • Method Details

    • degree

      public int degree()
      Get the degree of this polynomial. It is equal to the largest exponent of the variable. For example, x4 + 1 has a degree of 4.
      Returns:
      the polynomial degree

    • getCoefficients

      public double[] getCoefficients()
      Get a copy of the polynomial coefficients. In general, coefficients[i] is the coefficient of xn-i, where n is the polynomial degree. Specifically, coefficients[0] is the leading coefficient and coefficients[n] the constant term.
      Returns:
      a copy of the polynomial coefficients

    • getCoefficient

      public double getCoefficient(int i)
      Get an-i, the coefficient of xn-i.
      Parameters:
      i - the i-th coefficient in this polynomial, counting from 0
      Returns:
      an-i
      See Also:

    • getNormalization

      public Polynomial getNormalization()
      Get the normalized version of this polynomial so the leading coefficient is 1.
      Returns:
      a scaled version of the polynomial that has a leading coefficient 1

    • evaluate

      public Complex evaluate(Number x)
      Evaluate this polynomial at x.
      Parameters:
      x - the argument
      Returns:
      p(x)

    • evaluate

      public double evaluate(double x)
      Evaluate this polynomial at x.
      Specified by:
      evaluate in interface UnivariateRealFunction
      Parameters:
      x - the argument
      Returns:
      p(x)

    • evaluate

      public Complex evaluate(Complex z)
      Evaluate this polynomial at x.
      Parameters:
      z - the argument
      Returns:
      p(x)

    • add

      public Polynomial add(Polynomial that)
      Description copied from interface: AbelianGroup
      + : G × G → G
      Specified by:
      add in interface AbelianGroup<Polynomial>
      Parameters:
      that - the object to be added
      Returns:
      this + that

    • minus

      public Polynomial minus(Polynomial that)
      Description copied from interface: AbelianGroup
      - : G × G → G

      The operation "-" is not in the definition of of an additive group but can be deduced. This function is provided for convenience purpose. It is equivalent to

      this.add(that.opposite())
      .
      Specified by:
      minus in interface AbelianGroup<Polynomial>
      Parameters:
      that - the object to be subtracted (subtrahend)
      Returns:
      this - that

    • multiply

      public Polynomial multiply(Polynomial that)
      Description copied from interface: Monoid
      × : G × G → G
      Specified by:
      multiply in interface Monoid<Polynomial>
      Parameters:
      that - the multiplicand
      Returns:
      this × that

    • pow

      public Polynomial pow(int n)

    • scaled

      public Polynomial scaled(Real c)
      Description copied from interface: VectorSpace
      × : F × V → V

      The result of applying this function to a scalar, c, in F and v in V is denoted cv.

      Specified by:
      scaled in interface VectorSpace<Polynomial,Real>
      Parameters:
      c - a multiplier
      Returns:
      c * this
      See Also:

    • scaled

      public Polynomial scaled(double c)

    • opposite

      public Polynomial opposite()
      Description copied from interface: AbelianGroup
      For each a in G, there exists an element b in G such that a + b = b + a = 0. That is, it is the object such as
      this.add(this.opposite()) == this.ZERO
      Specified by:
      opposite in interface AbelianGroup<Polynomial>
      Returns:
      -this, the additive opposite
      See Also:

    • ZERO

      public Polynomial ZERO()
      Description copied from interface: AbelianGroup
      The additive element 0 in the group, such that for all elements a in the group, the equation 0 + a = a + 0 = a holds.
      Specified by:
      ZERO in interface AbelianGroup<Polynomial>
      Returns:
      0, the additive identity

    • ONE

      public Polynomial ONE()
      Description copied from interface: Monoid
      The multiplicative element 1 in the group such that for any elements a in the group, the equation 1 × a = a × 1 = a holds.
      Specified by:
      ONE in interface Monoid<Polynomial>
      Returns:
      1

    • toString

      public String toString()
      Overrides:
      toString in class Object

    • equals

      public boolean equals(Object obj)
      Overrides:
      equals in class Object

    • hashCode

      public int hashCode()
      Overrides:
      hashCode in class Object