dedekind::numbers::Complex< R > Class Template Reference

Collaboration diagram for dedekind::numbers::Complex< R >:

Public Types
using	Domain = Complex
using	scalar_type = R
using	ScalarCarrier = R

Public Member Functions
constexpr	Complex (R re=R{}, R im=R{})
constexpr R	real () const
constexpr R	imag () const

Public Attributes
R	first
R	second

Friends
constexpr bool	operator== (const Complex &, const Complex &)=default
constexpr Complex	operator+ (const Complex &a, const Complex &b)
constexpr Complex	operator- (const Complex &a, const Complex &b)
constexpr Complex	operator- (const Complex &a)
constexpr Complex	operator* (const Complex &a, const Complex &b)
constexpr Complex	operator* (const R &s, const Complex &a)
constexpr Complex	operator* (const Complex &a, const R &s)
constexpr Complex	operator/ (const Complex &a, const Complex &b)
	Division via the conjugate identity: z / w = z · w̄ / |w|².

Friends And Related Symbol Documentation

operator/

template<typename R>

Complex operator/ ( const Complex< R > & a, const Complex< R > & b )

friend

Division via the conjugate identity: z / w = z · w̄ / |w|².

(a + bi) / (c + di) = [(ac + bd) + (bc − ad)i] / (c² + d²).

Requires operator/ on the scalar R. Defined when |w|² ≠ 0; for the zero-division case the behaviour is inherited from R / R (e.g. Rational<Z> throws / asserts).

Lifts Complex<R> from HasRingOperators into HasFieldOperators (the a/b → S clause), which in turn lets Dual<Complex<R>> admit operator/ for holomorphic forward-mode automatic differentiation at compile time.

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The documentation for this class was generated from the following file:

• src/main/modules/dedekind/numbers/complex.cppm