Class PolynomialFunction<R>

java.lang.Object
org.episteme.core.mathematics.analysis.PolynomialFunction<R>
All Implemented Interfaces:
Function<R,R>, ContinuousFunction<R,R>, DifferentiableFunction<R,R>, Function<R,R>, IntegrableFunction<R,R>, Relation<R,R>
public class PolynomialFunction<R> extends Object implements DifferentiableFunction<R,R>, IntegrableFunction<R,R>
Represents a polynomial function P(x) over a Ring R.
Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Constructor Details

    • PolynomialFunction

      public PolynomialFunction(PolynomialRing.Polynomial<R> polynomial, PolynomialRing<R> ring)
      Creates a polynomial function from a polynomial object.
      Parameters:
      polynomial - the underlying polynomial
      ring - the polynomial ring

  • Method Details

    • evaluate

      public R evaluate(R x)
      Description copied from interface: Function
      Evaluates this function at the given point.
      Specified by:
      evaluate in interface Function<R,R>
      Parameters:
      x - the input point
      Returns:
      the value of the function at x

    • differentiate

      public Function<R,R> differentiate()
      Description copied from interface: DifferentiableFunction
      Returns the derivative of this function.
      Specified by:
      differentiate in interface DifferentiableFunction<R,R>
      Returns:
      f'

    • integrate

      public Function<R,R> integrate()
      Description copied from interface: IntegrableFunction
      Returns the indefinite integral (antiderivative) of this function.
      Specified by:
      integrate in interface IntegrableFunction<R,R>
      Returns:
      F such that F' = f

    • integrate

      public R integrate(R start, R end)
      Description copied from interface: IntegrableFunction
      Calculates the definite integral from start to end.
      Specified by:
      integrate in interface IntegrableFunction<R,R>
      Parameters:
      start - lower bound
      end - upper bound
      Returns:
      integral_{start}^{end} f(x) dx

    • getDomain

      public String getDomain()
      Description copied from interface: Relation
      Returns the domain description.
      Specified by:
      getDomain in interface Relation<R,R>
      Returns:
      domain name (e.g., "ℝ", "ℕ", "ℂ")

    • getCodomain

      public String getCodomain()
      Description copied from interface: Relation
      Returns the codomain description.
      Specified by:
      getCodomain in interface Relation<R,R>
      Returns:
      codomain name

    • toString

      public String toString()
      Overrides:
      toString in class Object