algebra.h

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#ifndef ALGEBRA_INCLUDED
#define ALGEBRA_INCLUDED
 
#include <cmath>
 
namespace Util
{
    template< class Element >
    class AdditiveGroup
    {
    public:
        friend Element operator - ( const Element &e ){ return e.additiveInverse(); }
 
        friend Element operator - ( const Element &e1 , const Element &e2 ){ return e1 + (-e2); }
 
        friend Element& operator += ( Element &e1 , const Element &e2 ){ e1 = e1 + e2 ; return e1; }
 
        friend Element& operator -= ( Element &e1 , const Element &e2 ){ e1 = e1 - e2 ; return e1; }
    };
 
    template< class Element >
    class MultiplicativeGroup
    {
    public:
        friend Element operator / ( const Element &e1 , const Element &e2 ){ return e1 * e2.multiplicativeInverse(); }
 
        friend Element& operator *= ( Element &e1 , const Element &e2 ){ e1 = e1 * e2 ; return e1; }
 
        friend Element& operator /= ( Element &e1 , const Element &e2 ){ e1 = e1 / e2 ; return e1; }
    };
 
    template< class Element >
    class Field : public AdditiveGroup< Element > , public MultiplicativeGroup< Element >{};
 
    template< class Element >
    class VectorSpace
    {
    public:
        friend Element operator - ( const Element &e1 , const Element &e2 ){ return e1 + (-e2); }
 
        friend Element operator / ( const Element &e , double s ){ return e * (1./s); }
 
        friend Element& operator += ( Element & e1 , const Element &e2 ){ e1 = e1 + e2 ; return e1; }
 
        friend Element& operator -= ( Element &e1 , const Element &e2 ){ return e1 += (-e2); }
 
        friend Element& operator *= ( Element &e , double s ){ e = e*s ; return e; }
 
        friend Element& operator /= ( Element &e , double s ){ return e *= (1./s); }
 
        friend Element  operator - ( const Element &e ){ return e * (-1.); }
 
        friend Element  operator * ( double s , const Element &e ){ return e*s; }
    };
 
    template< class Element >
    class _InnerProductSpace
    {
    public:
        static double Dot( const Element &e1 , const Element &e2 ){ return e1.dot(e2); }
 
        static double SquareNorm( const Element &e ){ return e.dot(e); }
 
        static double Length( const Element &e ){ return sqrt( e.dot(e) ); }
 
        static double SquareDistance( const Element &e1 , const Element &e2 ){ return SquareNorm(e1-e2); }
 
        static double Distance( const Element &e1 , const Element &e2 ){ return sqrt( SquareDistance(e1,e2) ); }
 
        double squareNorm( void ) const { return SquareNorm( *( Element * )this ); }
 
        double length( void ) const { return sqrt( squareNorm() ); }
 
        Element unit( void ) const { return *( Element * )this / _InnerProductSpace< Element >::length(); }
    };
 
    template< class Element >
    class InnerProductSpace : public VectorSpace< Element > , public _InnerProductSpace< Element >{};
 
    template< class Element >
    class Algebra : public VectorSpace< Element >
    {
    public:
        friend Element& operator *= ( Element &e1 , const Element &e2 ){ e1 = e1 * e2 ; return e1; }
    };
}
#endif // ALGEBRA_INCLUDED