math::VectorSpace< Vector, Scalar > Struct Template Reference

Concept VectorSpace. More...

#include <vector_concepts.hpp>

Inheritance diagram for math::VectorSpace< Vector, Scalar >:

List of all members.

Public Member Functions
axiom	Distributivity (Vector v, Vector w, Scalar a, Scalar b)
	Invariant: Distributivity of scalars and vectors from left and from right.

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Detailed Description

template<typename Vector, typename Scalar = typename Vector::value_type>
struct math::VectorSpace< Vector, Scalar >

Concept VectorSpace.

Parameters:

Vector	The the type of a vector or a collection
Scalar	The scalar over which the vector field is defined

Requires:

• Field < Scalar >;
• Multiplicable <Scalar, Vector>;
• MultiplicableWithAssign <Vector, Scalar>;
• DivisibleWithAssign <Vector, Scalar>;
• std::Assignable <Vector, Multiplicable<Scalar, Vector>::result_type>;
• std::Assignable <Vector, Multiplicable<Vector, Scalar>::result_type>;
• std::Assignable <Vector, Divisible<Vector, Scalar>::result_type>;

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Member Function Documentation

template<typename Vector , typename Scalar = typename Vector::value_type>

axiom math::VectorSpace< Vector, Scalar >::Distributivity	(	Vector	v,
		Vector	w,
		Scalar	a,
		Scalar	b
	)		[inline]

Invariant: Distributivity of scalars and vectors from left and from right.

a * (v + w) == a * v + a * w; // Scalar from left

Vector from right: (a + b) * v == a * v + b * v;

Scalar from right: (v + w) * a == v * a + w * a;

Vector from left: v * (a + b) == v * a + v * b;

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

• vector_concepts.hpp