octonion.hpp

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                e(requested_e),
                f(requested_f),
                g(requested_g),
                h(requested_h)
            {
                // nothing to do!
            }
            
            
            // constructor for H seen as C^4
                
            explicit                octonion(   ::std::complex<T> const & z0,
                                                ::std::complex<T> const & z1 = ::std::complex<T>(),
                                                ::std::complex<T> const & z2 = ::std::complex<T>(),
                                                ::std::complex<T> const & z3 = ::std::complex<T>())
            :   a(z0.real()),
                b(z0.imag()),
                c(z1.real()),
                d(z1.imag()),
                e(z2.real()),
                f(z2.imag()),
                g(z3.real()),
                h(z3.imag())
            {
                // nothing to do!
            }
            
            
            // constructor for O seen as H^2
                
            explicit                octonion(   ::boost::math::quaternion<T> const & q0,
                                                ::boost::math::quaternion<T> const & q1 = ::boost::math::quaternion<T>())
            :   a(q0.R_component_1()),
                b(q0.R_component_2()),
                c(q0.R_component_3()),
                d(q0.R_component_4()),
                e(q1.R_component_1()),
                f(q1.R_component_2()),
                g(q1.R_component_3()),
                h(q1.R_component_4())
            {
                // nothing to do!
            }
            
            
            // UNtemplated copy constructor
            // (this is taken care of by the compiler itself)
            
            
            // templated copy constructor
            
            template<typename X>
            explicit                octonion(octonion<X> const & a_recopier)
            :   a(static_cast<T>(a_recopier.R_component_1())),
                b(static_cast<T>(a_recopier.R_component_2())),
                c(static_cast<T>(a_recopier.R_component_3())),
                d(static_cast<T>(a_recopier.R_component_4())),
                e(static_cast<T>(a_recopier.R_component_5())),
                f(static_cast<T>(a_recopier.R_component_6())),
                g(static_cast<T>(a_recopier.R_component_7())),
                h(static_cast<T>(a_recopier.R_component_8()))
            {
                // nothing to do!
            }
            
            
            // destructor
            // (this is taken care of by the compiler itself)
            
            
            // accessors
            //
            // Note:    Like complex number, octonions do have a meaningful notion of "real part",
            //            but unlike them there is no meaningful notion of "imaginary part".
            //            Instead there is an "unreal part" which itself is an octonion, and usually
            //            nothing simpler (as opposed to the complex number case).
            //            However, for practicallity, there are accessors for the other components
            //            (these are necessary for the templated copy constructor, for instance).
            
            BOOST_OCTONION_ACCESSOR_GENERATOR(T)
            
            // assignment operators
            
            BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(T)
            
            // other assignment-related operators
            //
            // NOTE:    Octonion multiplication is *NOT* commutative;
            //            symbolically, "q *= rhs;" means "q = q * rhs;"
            //            and "q /= rhs;" means "q = q * inverse_of(rhs);";
            //            octonion multiplication is also *NOT* associative
            
            octonion<T> &            operator += (T const & rhs)
            {
                T    at = a + rhs;    // exception guard
                
                a = at;
                
                return(*this);
            }
            
            
            octonion<T> &            operator += (::std::complex<T> const & rhs)
            {
                T    at = a + rhs.real();    // exception guard
                T    bt = b + rhs.imag();    // exception guard
                
                a = at; 
                b = bt;
                
                return(*this);
            }
            
            
            octonion<T> &            operator += (::boost::math::quaternion<T> const & rhs)
            {
                T    at = a + rhs.R_component_1();    // exception guard
                T    bt = b + rhs.R_component_2();    // exception guard
                T    ct = c + rhs.R_component_3();    // exception guard
                T    dt = d + rhs.R_component_4();    // exception guard
                
                a = at; 
                b = bt;
                c = ct;
                d = dt;
                
                return(*this);
            }
            
            
            template<typename X>
            octonion<T> &            operator += (octonion<X> const & rhs)
            {
                T    at = a + static_cast<T>(rhs.R_component_1());    // exception guard
                T    bt = b + static_cast<T>(rhs.R_component_2());    // exception guard
                T    ct = c + static_cast<T>(rhs.R_component_3());    // exception guard
                T    dt = d + static_cast<T>(rhs.R_component_4());    // exception guard
                T    et = e + static_cast<T>(rhs.R_component_5());    // exception guard
                T    ft = f + static_cast<T>(rhs.R_component_6());    // exception guard
                T    gt = g + static_cast<T>(rhs.R_component_7());    // exception guard
                T    ht = h + static_cast<T>(rhs.R_component_8());    // exception guard
                
                a = at;
                b = bt;
                c = ct;
                d = dt;
                e = et;
                f = ft;
                g = gt;
                h = ht;
                
                return(*this);
            }
            
            
            
            octonion<T> &            operator -= (T const & rhs)
            {
                T    at = a - rhs;    // exception guard
                
                a = at;
                
                return(*this);
            }
            
            
            octonion<T> &            operator -= (::std::complex<T> const & rhs)
            {
                T    at = a - rhs.real();    // exception guard
                T    bt = b - rhs.imag();    // exception guard
                
                a = at; 
                b = bt;
                
                return(*this);
            }
            
            
            octonion<T> &            operator -= (::boost::math::quaternion<T> const & rhs)
            {
                T    at = a - rhs.R_component_1();    // exception guard
                T    bt = b - rhs.R_component_2();    // exception guard
                T    ct = c - rhs.R_component_3();    // exception guard
                T    dt = d - rhs.R_component_4();    // exception guard
                
                a = at; 
                b = bt;
                c = ct;
                d = dt;
                
                return(*this);
            }
            
            
            template<typename X>
            octonion<T> &            operator -= (octonion<X> const & rhs)
            {
                T    at = a - static_cast<T>(rhs.R_component_1());    // exception guard
                T    bt = b - static_cast<T>(rhs.R_component_2());    // exception guard
                T    ct = c - static_cast<T>(rhs.R_component_3());    // exception guard
                T    dt = d - static_cast<T>(rhs.R_component_4());    // exception guard
                T    et = e - static_cast<T>(rhs.R_component_5());    // exception guard
                T    ft = f - static_cast<T>(rhs.R_component_6());    // exception guard
                T    gt = g - static_cast<T>(rhs.R_component_7());    // exception guard
                T    ht = h - static_cast<T>(rhs.R_component_8());    // exception guard
                
                a = at;
                b = bt;
                c = ct;
                d = dt;
                e = et;
                f = ft;
                g = gt;
                h = ht;