Hamilton's hypercomplex numbers q = a + bi + cj + dk. More...

Public Types
using	scalar_type = R

Public Member Functions
constexpr	Quaternion (R a=R{}, R b=R{}, R c=R{}, R d=R{})
constexpr R	w () const
constexpr R	x () const
constexpr R	y () const
constexpr R	z () const
constexpr Quaternion	operator- () const
	Additive inverse.
constexpr Quaternion	conj () const
	Conjugate q* = a - bi - cj - dk. Satisfies q * conj(q) = \|q\|^2.
constexpr R	norm_squared () const
	Squared Euclidean norm \|q\|^2 = a^2 + b^2 + c^2 + d^2.

Friends
constexpr bool	operator== (const Quaternion &, const Quaternion &)=default
constexpr Quaternion	operator+ (const Quaternion &q, const Quaternion &p)
	q + p component-wise.
constexpr Quaternion	operator- (const Quaternion &q, const Quaternion &p)
	q - p component-wise.
constexpr Quaternion	operator* (const R &s, const Quaternion &q)
	Scalar left-multiplication.
constexpr Quaternion	operator* (const Quaternion &q, const R &s)
	Scalar right-multiplication.
constexpr Quaternion	operator* (const Quaternion &q, const Quaternion &p)
	Quaternion multiplication q * p (non-commutative).

Detailed Description

template<typename R>
requires IsQuaternionScalar<R>
class dedekind::numbers::Quaternion< R >

Hamilton's hypercomplex numbers q = a + bi + cj + dk.

Template Parameters

R	The scalar component type (an exact ring, e.g. `Rational<>`).

Multiplication is non-commutative: ij = k but ji = -k.

◆ operator*

template<typename R>

Quaternion operator*	(	const Quaternion< R > &	q,
		const Quaternion< R > &	p )

friend

Quaternion multiplication q * p (non-commutative).

Using the Hamilton product formula: (a1 + b1 i + c1 j + d1 k)(a2 + b2 i + c2 j + d2 k)

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