Interface Bijection<D,C>

All Superinterfaces:
Function<D,C>, Function<D,C>, Relation<D,C>
All Known Subinterfaces:
Transform<D,C>
All Known Implementing Classes:
DiscreteFourierTransform
public interface Bijection<D,C> extends Function<D,C>
A bijective function (one-to-one and onto mapping).

A bijection is a function f: D → C where:

  • Injective (one-to-one): f(x) = f(y) implies x = y
  • Surjective (onto): For every c ∈ C, there exists d ∈ D such that f(d) = c
Every bijection has an inverse function f⁻¹: C → D.

Examples of bijections:

  • f(x) = 2x (ℝ → ℝ)
  • f(x) = x³ (ℝ → ℝ)
  • exp(x) (ℝ → ℝ⁺), inverse is ln(x)
  • Fourier Transform (time → frequency)

Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Method Details

    • inverse

      Bijection<C,D> inverse()
      Returns the inverse function f⁻¹.

      For a bijection f: D → C, the inverse f⁻¹: C → D satisfies:

      • f⁻¹(f(x)) = x for all x ∈ D
      • f(f⁻¹(y)) = y for all y ∈ C

      Returns:
      the inverse bijection