/*!
\ingroup PkgKernelDLinAlgConcepts
\cgalConcept

An instance of data type `Vector` is a vector of variables of
number type `NT`. Together with the type `Matrix` it realizes
the basic operations of linear algebra.

*/

class Vector {
public:

/// \name Types
/// @{

/*!
the ring type of the components.
*/
typedef unspecified_type NT;

/*!
the iterator type for accessing components.
*/
typedef unspecified_type iterator;

/*!
the const iterator type for accessing
components.
*/
typedef unspecified_type const_iterator;

/// @}

/// \name Creation
/// @{

/*!
creates an instance `v` of type
`Vector`.
*/
Vector();

/*!
creates an instance `v` of type
`Vector`. `v` is initialized to a vector of dimension \f$ d\f$.

*/
Vector(int d);

/*!
creates an instance `v` of
type `Vector`. `v` is initialized to a vector of dimension
\f$ d\f$ with entries `x`.
*/
Vector(int d, NT x);

/*!
creates an
instance `v` of type `Vector`; `v` is initialized to the
vector with entries `set [first,last)`.
\tparam ForwardIterator has `NT` as value type.
*/
template <class Forward_iterator>
Vector(Forward_iterator first, Forward_iterator last);

/// @}

/// \name Operations
/// @{

/*!
returns the dimension of `v`.
*/
int dimension() ;

/*!
returns true iff `v` is the zero
vector.
*/
bool is_zero() ;

/*!
returns the \f$ i\f$-th component of `v`.

\pre \f$ 0\le i \le v.dimension()-1\f$.
*/
NT& operator[](int i) ;

/*!
iterator to the first component.
*/
iterator begin() ;

/*!
iterator beyond the last component.
*/
iterator end() ;

/*!
iterator to the first component.
*/
const_iterator begin() const;

/*!
iterator beyond the last component.
*/
const_iterator end() const;


/*!
Addition.

\pre `v.dimension() == v1.dimension()`.
*/
Vector operator+(const Vector& v1) ;

/*!
Subtraction.

\pre `v.dimension() == v1.dimension()`.
*/
Vector operator-(const Vector& v1) ;

/*!
Inner Product.

\pre `v.dimension() == v1.dimension()`.
*/
NT operator*(const Vector& v1) ;

/*!
Negation.
*/
Vector operator-() ;

/*!
Addition plus assignment.

\pre `v.dimension() == v1.dimension()`.
*/
Vector& operator+=(const Vector& v1);

/*!
Subtraction plus assignment.

\pre `v.dimension() == v1.dimension()`.
*/
Vector& operator-=(const Vector& v1);

/*!
Scalar multiplication plus
assignment.
*/
Vector& operator*=(const NT& s);

/*!
Scalar division plus assignment.

*/
Vector& operator/=(const NT& s);

/*!
Component-wise multiplication with number \f$ r\f$.
*/
Vector operator*(const NT& r, const Vector& v);

/*!
Component-wise multiplication with number \f$ r\f$.
*/
Vector operator*(const Vector& v, const NT& r);

/// @}

}; /* end Vector */