#ifndef BOOST_QVM_GEN_MAT_OPERATIONS3_HPP_INCLUDED
#define BOOST_QVM_GEN_MAT_OPERATIONS3_HPP_INCLUDED

// Copyright 2008-2024 Emil Dotchevski and Reverge Studios, Inc.
// This file was generated by a program. Do not edit manually.
// Distributed under the Boost Software License, Version 1.0. (See accompanying
// file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

#include <b/qvm/assert.hpp>
#include <b/qvm/deduce_mat.hpp>
#include <b/qvm/deduce_vec.hpp>
#include <b/qvm/error.hpp>
#include <b/qvm/gen/mat_assign3.hpp>
#include <b/qvm/quat_traits.hpp>
#include <b/qvm/scalar_traits.hpp>
#include <b/qvm/throw_exception.hpp>

namespace boost { namespace qvm {

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==3,
    deduce_mat2<A,B,3,3> >::type
operator+( A const & a, B const & b )
    {
    typedef typename deduce_mat2<A,B,3,3>::type R;
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::rows==3);
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::cols==3);
    R r;
    write_mat_element<0,0>(r,mat_traits<A>::template read_element<0,0>(a)+mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<0,1>(r,mat_traits<A>::template read_element<0,1>(a)+mat_traits<B>::template read_element<0,1>(b));
    write_mat_element<0,2>(r,mat_traits<A>::template read_element<0,2>(a)+mat_traits<B>::template read_element<0,2>(b));
    write_mat_element<1,0>(r,mat_traits<A>::template read_element<1,0>(a)+mat_traits<B>::template read_element<1,0>(b));
    write_mat_element<1,1>(r,mat_traits<A>::template read_element<1,1>(a)+mat_traits<B>::template read_element<1,1>(b));
    write_mat_element<1,2>(r,mat_traits<A>::template read_element<1,2>(a)+mat_traits<B>::template read_element<1,2>(b));
    write_mat_element<2,0>(r,mat_traits<A>::template read_element<2,0>(a)+mat_traits<B>::template read_element<2,0>(b));
    write_mat_element<2,1>(r,mat_traits<A>::template read_element<2,1>(a)+mat_traits<B>::template read_element<2,1>(b));
    write_mat_element<2,2>(r,mat_traits<A>::template read_element<2,2>(a)+mat_traits<B>::template read_element<2,2>(b));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator+;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct plus_mm_defined;

    template <>
    struct
    plus_mm_defined<3,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==1 && mat_traits<B>::cols==1,
    deduce_mat2<A,B,3,1> >::type
operator+( A const & a, B const & b )
    {
    typedef typename deduce_mat2<A,B,3,1>::type R;
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::rows==3);
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::cols==1);
    R r;
    write_mat_element<0,0>(r,mat_traits<A>::template read_element<0,0>(a)+mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<1,0>(r,mat_traits<A>::template read_element<1,0>(a)+mat_traits<B>::template read_element<1,0>(b));
    write_mat_element<2,0>(r,mat_traits<A>::template read_element<2,0>(a)+mat_traits<B>::template read_element<2,0>(b));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator+;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct plus_mm_defined;

    template <>
    struct
    plus_mm_defined<3,1>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==1 && mat_traits<B>::rows==1 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==3,
    deduce_mat2<A,B,1,3> >::type
operator+( A const & a, B const & b )
    {
    typedef typename deduce_mat2<A,B,1,3>::type R;
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::rows==1);
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::cols==3);
    R r;
    write_mat_element<0,0>(r,mat_traits<A>::template read_element<0,0>(a)+mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<0,1>(r,mat_traits<A>::template read_element<0,1>(a)+mat_traits<B>::template read_element<0,1>(b));
    write_mat_element<0,2>(r,mat_traits<A>::template read_element<0,2>(a)+mat_traits<B>::template read_element<0,2>(b));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator+;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct plus_mm_defined;

    template <>
    struct
    plus_mm_defined<1,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==3,
    deduce_mat2<A,B,3,3> >::type
operator-( A const & a, B const & b )
    {
    typedef typename deduce_mat2<A,B,3,3>::type R;
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::rows==3);
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::cols==3);
    R r;
    write_mat_element<0,0>(r,mat_traits<A>::template read_element<0,0>(a)-mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<0,1>(r,mat_traits<A>::template read_element<0,1>(a)-mat_traits<B>::template read_element<0,1>(b));
    write_mat_element<0,2>(r,mat_traits<A>::template read_element<0,2>(a)-mat_traits<B>::template read_element<0,2>(b));
    write_mat_element<1,0>(r,mat_traits<A>::template read_element<1,0>(a)-mat_traits<B>::template read_element<1,0>(b));
    write_mat_element<1,1>(r,mat_traits<A>::template read_element<1,1>(a)-mat_traits<B>::template read_element<1,1>(b));
    write_mat_element<1,2>(r,mat_traits<A>::template read_element<1,2>(a)-mat_traits<B>::template read_element<1,2>(b));
    write_mat_element<2,0>(r,mat_traits<A>::template read_element<2,0>(a)-mat_traits<B>::template read_element<2,0>(b));
    write_mat_element<2,1>(r,mat_traits<A>::template read_element<2,1>(a)-mat_traits<B>::template read_element<2,1>(b));
    write_mat_element<2,2>(r,mat_traits<A>::template read_element<2,2>(a)-mat_traits<B>::template read_element<2,2>(b));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator-;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct minus_mm_defined;

    template <>
    struct
    minus_mm_defined<3,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==1 && mat_traits<B>::cols==1,
    deduce_mat2<A,B,3,1> >::type
operator-( A const & a, B const & b )
    {
    typedef typename deduce_mat2<A,B,3,1>::type R;
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::rows==3);
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::cols==1);
    R r;
    write_mat_element<0,0>(r,mat_traits<A>::template read_element<0,0>(a)-mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<1,0>(r,mat_traits<A>::template read_element<1,0>(a)-mat_traits<B>::template read_element<1,0>(b));
    write_mat_element<2,0>(r,mat_traits<A>::template read_element<2,0>(a)-mat_traits<B>::template read_element<2,0>(b));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator-;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct minus_mm_defined;

    template <>
    struct
    minus_mm_defined<3,1>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==1 && mat_traits<B>::rows==1 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==3,
    deduce_mat2<A,B,1,3> >::type
operator-( A const & a, B const & b )
    {
    typedef typename deduce_mat2<A,B,1,3>::type R;
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::rows==1);
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::cols==3);
    R r;
    write_mat_element<0,0>(r,mat_traits<A>::template read_element<0,0>(a)-mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<0,1>(r,mat_traits<A>::template read_element<0,1>(a)-mat_traits<B>::template read_element<0,1>(b));
    write_mat_element<0,2>(r,mat_traits<A>::template read_element<0,2>(a)-mat_traits<B>::template read_element<0,2>(b));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator-;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct minus_mm_defined;

    template <>
    struct
    minus_mm_defined<1,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==3,
    A &>::type
operator+=( A & a, B const & b )
    {
    write_mat_element<0,0>(a,mat_traits<A>::template read_element<0,0>(a)+mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<0,1>(a,mat_traits<A>::template read_element<0,1>(a)+mat_traits<B>::template read_element<0,1>(b));
    write_mat_element<0,2>(a,mat_traits<A>::template read_element<0,2>(a)+mat_traits<B>::template read_element<0,2>(b));
    write_mat_element<1,0>(a,mat_traits<A>::template read_element<1,0>(a)+mat_traits<B>::template read_element<1,0>(b));
    write_mat_element<1,1>(a,mat_traits<A>::template read_element<1,1>(a)+mat_traits<B>::template read_element<1,1>(b));
    write_mat_element<1,2>(a,mat_traits<A>::template read_element<1,2>(a)+mat_traits<B>::template read_element<1,2>(b));
    write_mat_element<2,0>(a,mat_traits<A>::template read_element<2,0>(a)+mat_traits<B>::template read_element<2,0>(b));
    write_mat_element<2,1>(a,mat_traits<A>::template read_element<2,1>(a)+mat_traits<B>::template read_element<2,1>(b));
    write_mat_element<2,2>(a,mat_traits<A>::template read_element<2,2>(a)+mat_traits<B>::template read_element<2,2>(b));
    return a;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator+=;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct plus_eq_mm_defined;

    template <>
    struct
    plus_eq_mm_defined<3,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==1 && mat_traits<B>::cols==1,
    A &>::type
operator+=( A & a, B const & b )
    {
    write_mat_element<0,0>(a,mat_traits<A>::template read_element<0,0>(a)+mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<1,0>(a,mat_traits<A>::template read_element<1,0>(a)+mat_traits<B>::template read_element<1,0>(b));
    write_mat_element<2,0>(a,mat_traits<A>::template read_element<2,0>(a)+mat_traits<B>::template read_element<2,0>(b));
    return a;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator+=;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct plus_eq_mm_defined;

    template <>
    struct
    plus_eq_mm_defined<3,1>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==1 && mat_traits<B>::rows==1 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==3,
    A &>::type
operator+=( A & a, B const & b )
    {
    write_mat_element<0,0>(a,mat_traits<A>::template read_element<0,0>(a)+mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<0,1>(a,mat_traits<A>::template read_element<0,1>(a)+mat_traits<B>::template read_element<0,1>(b));
    write_mat_element<0,2>(a,mat_traits<A>::template read_element<0,2>(a)+mat_traits<B>::template read_element<0,2>(b));
    return a;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator+=;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct plus_eq_mm_defined;

    template <>
    struct
    plus_eq_mm_defined<1,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==3,
    A &>::type
operator-=( A & a, B const & b )
    {
    write_mat_element<0,0>(a,mat_traits<A>::template read_element<0,0>(a)-mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<0,1>(a,mat_traits<A>::template read_element<0,1>(a)-mat_traits<B>::template read_element<0,1>(b));
    write_mat_element<0,2>(a,mat_traits<A>::template read_element<0,2>(a)-mat_traits<B>::template read_element<0,2>(b));
    write_mat_element<1,0>(a,mat_traits<A>::template read_element<1,0>(a)-mat_traits<B>::template read_element<1,0>(b));
    write_mat_element<1,1>(a,mat_traits<A>::template read_element<1,1>(a)-mat_traits<B>::template read_element<1,1>(b));
    write_mat_element<1,2>(a,mat_traits<A>::template read_element<1,2>(a)-mat_traits<B>::template read_element<1,2>(b));
    write_mat_element<2,0>(a,mat_traits<A>::template read_element<2,0>(a)-mat_traits<B>::template read_element<2,0>(b));
    write_mat_element<2,1>(a,mat_traits<A>::template read_element<2,1>(a)-mat_traits<B>::template read_element<2,1>(b));
    write_mat_element<2,2>(a,mat_traits<A>::template read_element<2,2>(a)-mat_traits<B>::template read_element<2,2>(b));
    return a;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator-=;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct minus_eq_mm_defined;

    template <>
    struct
    minus_eq_mm_defined<3,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==1 && mat_traits<B>::cols==1,
    A &>::type
operator-=( A & a, B const & b )
    {
    write_mat_element<0,0>(a,mat_traits<A>::template read_element<0,0>(a)-mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<1,0>(a,mat_traits<A>::template read_element<1,0>(a)-mat_traits<B>::template read_element<1,0>(b));
    write_mat_element<2,0>(a,mat_traits<A>::template read_element<2,0>(a)-mat_traits<B>::template read_element<2,0>(b));
    return a;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator-=;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct minus_eq_mm_defined;

    template <>
    struct
    minus_eq_mm_defined<3,1>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==1 && mat_traits<B>::rows==1 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==3,
    A &>::type
operator-=( A & a, B const & b )
    {
    write_mat_element<0,0>(a,mat_traits<A>::template read_element<0,0>(a)-mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<0,1>(a,mat_traits<A>::template read_element<0,1>(a)-mat_traits<B>::template read_element<0,1>(b));
    write_mat_element<0,2>(a,mat_traits<A>::template read_element<0,2>(a)-mat_traits<B>::template read_element<0,2>(b));
    return a;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator-=;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct minus_eq_mm_defined;

    template <>
    struct
    minus_eq_mm_defined<1,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<A>::cols==3 && is_scalar<B>::value,
    deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols> >::type
operator*( A const & a, B b )
    {
    typedef typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols>::type R;
    R r;
    write_mat_element<0,0>(r,mat_traits<A>::template read_element<0,0>(a)*b);
    write_mat_element<0,1>(r,mat_traits<A>::template read_element<0,1>(a)*b);
    write_mat_element<0,2>(r,mat_traits<A>::template read_element<0,2>(a)*b);
    write_mat_element<1,0>(r,mat_traits<A>::template read_element<1,0>(a)*b);
    write_mat_element<1,1>(r,mat_traits<A>::template read_element<1,1>(a)*b);
    write_mat_element<1,2>(r,mat_traits<A>::template read_element<1,2>(a)*b);
    write_mat_element<2,0>(r,mat_traits<A>::template read_element<2,0>(a)*b);
    write_mat_element<2,1>(r,mat_traits<A>::template read_element<2,1>(a)*b);
    write_mat_element<2,2>(r,mat_traits<A>::template read_element<2,2>(a)*b);
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator*;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct mul_ms_defined;

    template <>
    struct
    mul_ms_defined<3,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    is_scalar<A>::value && mat_traits<B>::rows==3 && mat_traits<B>::cols==3,
    deduce_mat2<A,B,mat_traits<B>::rows,mat_traits<B>::cols> >::type
operator*( A a, B const & b )
    {
    typedef typename deduce_mat2<A,B,mat_traits<B>::rows,mat_traits<B>::cols>::type R;
    R r;
    write_mat_element<0,0>(r,a*mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<0,1>(r,a*mat_traits<B>::template read_element<0,1>(b));
    write_mat_element<0,2>(r,a*mat_traits<B>::template read_element<0,2>(b));
    write_mat_element<1,0>(r,a*mat_traits<B>::template read_element<1,0>(b));
    write_mat_element<1,1>(r,a*mat_traits<B>::template read_element<1,1>(b));
    write_mat_element<1,2>(r,a*mat_traits<B>::template read_element<1,2>(b));
    write_mat_element<2,0>(r,a*mat_traits<B>::template read_element<2,0>(b));
    write_mat_element<2,1>(r,a*mat_traits<B>::template read_element<2,1>(b));
    write_mat_element<2,2>(r,a*mat_traits<B>::template read_element<2,2>(b));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator*;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct mul_sm_defined;

    template <>
    struct
    mul_sm_defined<3,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<A>::cols==1 && is_scalar<B>::value,
    deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols> >::type
operator*( A const & a, B b )
    {
    typedef typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols>::type R;
    R r;
    write_mat_element<0,0>(r,mat_traits<A>::template read_element<0,0>(a)*b);
    write_mat_element<1,0>(r,mat_traits<A>::template read_element<1,0>(a)*b);
    write_mat_element<2,0>(r,mat_traits<A>::template read_element<2,0>(a)*b);
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator*;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct mul_ms_defined;

    template <>
    struct
    mul_ms_defined<3,1>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    is_scalar<A>::value && mat_traits<B>::rows==3 && mat_traits<B>::cols==1,
    deduce_mat2<A,B,mat_traits<B>::rows,mat_traits<B>::cols> >::type
operator*( A a, B const & b )
    {
    typedef typename deduce_mat2<A,B,mat_traits<B>::rows,mat_traits<B>::cols>::type R;
    R r;
    write_mat_element<0,0>(r,a*mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<1,0>(r,a*mat_traits<B>::template read_element<1,0>(b));
    write_mat_element<2,0>(r,a*mat_traits<B>::template read_element<2,0>(b));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator*;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct mul_sm_defined;

    template <>
    struct
    mul_sm_defined<3,1>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==1 && mat_traits<A>::cols==3 && is_scalar<B>::value,
    deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols> >::type
operator*( A const & a, B b )
    {
    typedef typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols>::type R;
    R r;
    write_mat_element<0,0>(r,mat_traits<A>::template read_element<0,0>(a)*b);
    write_mat_element<0,1>(r,mat_traits<A>::template read_element<0,1>(a)*b);
    write_mat_element<0,2>(r,mat_traits<A>::template read_element<0,2>(a)*b);
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator*;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct mul_ms_defined;

    template <>
    struct
    mul_ms_defined<1,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    is_scalar<A>::value && mat_traits<B>::rows==1 && mat_traits<B>::cols==3,
    deduce_mat2<A,B,mat_traits<B>::rows,mat_traits<B>::cols> >::type
operator*( A a, B const & b )
    {
    typedef typename deduce_mat2<A,B,mat_traits<B>::rows,mat_traits<B>::cols>::type R;
    R r;
    write_mat_element<0,0>(r,a*mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<0,1>(r,a*mat_traits<B>::template read_element<0,1>(b));
    write_mat_element<0,2>(r,a*mat_traits<B>::template read_element<0,2>(b));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator*;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct mul_sm_defined;

    template <>
    struct
    mul_sm_defined<1,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<A>::cols==3 && is_scalar<B>::value,
    A &>::type
operator*=( A & a, B b )
    {
    write_mat_element<0,0>(a,mat_traits<A>::template read_element<0,0>(a)*b);
    write_mat_element<0,1>(a,mat_traits<A>::template read_element<0,1>(a)*b);
    write_mat_element<0,2>(a,mat_traits<A>::template read_element<0,2>(a)*b);
    write_mat_element<1,0>(a,mat_traits<A>::template read_element<1,0>(a)*b);
    write_mat_element<1,1>(a,mat_traits<A>::template read_element<1,1>(a)*b);
    write_mat_element<1,2>(a,mat_traits<A>::template read_element<1,2>(a)*b);
    write_mat_element<2,0>(a,mat_traits<A>::template read_element<2,0>(a)*b);
    write_mat_element<2,1>(a,mat_traits<A>::template read_element<2,1>(a)*b);
    write_mat_element<2,2>(a,mat_traits<A>::template read_element<2,2>(a)*b);
    return a;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator*=;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct mul_eq_ms_defined;

    template <>
    struct
    mul_eq_ms_defined<3,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<A>::cols==1 && is_scalar<B>::value,
    A &>::type
operator*=( A & a, B b )
    {
    write_mat_element<0,0>(a,mat_traits<A>::template read_element<0,0>(a)*b);
    write_mat_element<1,0>(a,mat_traits<A>::template read_element<1,0>(a)*b);
    write_mat_element<2,0>(a,mat_traits<A>::template read_element<2,0>(a)*b);
    return a;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator*=;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct mul_eq_ms_defined;

    template <>
    struct
    mul_eq_ms_defined<3,1>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==1 && mat_traits<A>::cols==3 && is_scalar<B>::value,
    A &>::type
operator*=( A & a, B b )
    {
    write_mat_element<0,0>(a,mat_traits<A>::template read_element<0,0>(a)*b);
    write_mat_element<0,1>(a,mat_traits<A>::template read_element<0,1>(a)*b);
    write_mat_element<0,2>(a,mat_traits<A>::template read_element<0,2>(a)*b);
    return a;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator*=;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct mul_eq_ms_defined;

    template <>
    struct
    mul_eq_ms_defined<1,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<A>::cols==3 && is_scalar<B>::value,
    deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols> >::type
operator/( A const & a, B b )
    {
    typedef typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols>::type R;
    R r;
    write_mat_element<0,0>(r,mat_traits<A>::template read_element<0,0>(a)/b);
    write_mat_element<0,1>(r,mat_traits<A>::template read_element<0,1>(a)/b);
    write_mat_element<0,2>(r,mat_traits<A>::template read_element<0,2>(a)/b);
    write_mat_element<1,0>(r,mat_traits<A>::template read_element<1,0>(a)/b);
    write_mat_element<1,1>(r,mat_traits<A>::template read_element<1,1>(a)/b);
    write_mat_element<1,2>(r,mat_traits<A>::template read_element<1,2>(a)/b);
    write_mat_element<2,0>(r,mat_traits<A>::template read_element<2,0>(a)/b);
    write_mat_element<2,1>(r,mat_traits<A>::template read_element<2,1>(a)/b);
    write_mat_element<2,2>(r,mat_traits<A>::template read_element<2,2>(a)/b);
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator/;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct div_ms_defined;

    template <>
    struct
    div_ms_defined<3,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    is_scalar<A>::value && mat_traits<B>::rows==3 && mat_traits<B>::cols==3,
    deduce_mat2<A,B,mat_traits<B>::rows,mat_traits<B>::cols> >::type
operator/( A a, B const & b )
    {
    typedef typename deduce_mat2<A,B,mat_traits<B>::rows,mat_traits<B>::cols>::type R;
    R r;
    write_mat_element<0,0>(r,a/mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<0,1>(r,a/mat_traits<B>::template read_element<0,1>(b));
    write_mat_element<0,2>(r,a/mat_traits<B>::template read_element<0,2>(b));
    write_mat_element<1,0>(r,a/mat_traits<B>::template read_element<1,0>(b));
    write_mat_element<1,1>(r,a/mat_traits<B>::template read_element<1,1>(b));
    write_mat_element<1,2>(r,a/mat_traits<B>::template read_element<1,2>(b));
    write_mat_element<2,0>(r,a/mat_traits<B>::template read_element<2,0>(b));
    write_mat_element<2,1>(r,a/mat_traits<B>::template read_element<2,1>(b));
    write_mat_element<2,2>(r,a/mat_traits<B>::template read_element<2,2>(b));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator/;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct div_sm_defined;

    template <>
    struct
    div_sm_defined<3,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<A>::cols==1 && is_scalar<B>::value,
    deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols> >::type
operator/( A const & a, B b )
    {
    typedef typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols>::type R;
    R r;
    write_mat_element<0,0>(r,mat_traits<A>::template read_element<0,0>(a)/b);
    write_mat_element<1,0>(r,mat_traits<A>::template read_element<1,0>(a)/b);
    write_mat_element<2,0>(r,mat_traits<A>::template read_element<2,0>(a)/b);
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator/;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct div_ms_defined;

    template <>
    struct
    div_ms_defined<3,1>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    is_scalar<A>::value && mat_traits<B>::rows==3 && mat_traits<B>::cols==1,
    deduce_mat2<A,B,mat_traits<B>::rows,mat_traits<B>::cols> >::type
operator/( A a, B const & b )
    {
    typedef typename deduce_mat2<A,B,mat_traits<B>::rows,mat_traits<B>::cols>::type R;
    R r;
    write_mat_element<0,0>(r,a/mat_traits<B>::template read_element<0,0>(b));
    write_mat_element<1,0>(r,a/mat_traits<B>::template read_element<1,0>(b));
    write_mat_element<2,0>(r,a/mat_traits<B>::template read_element<2,0>(b));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator/;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct div_sm_defined;

    template <>
    struct
    div_sm_defined<3,1>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==1 && mat_traits<A>::cols==3 && is_scalar<B>::value,
    deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols> >::type
operator/( A const & a, B b )
    {
    typedef typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols>::type R;
    R r;
    write_mat_element<0,0>(r,mat_traits<A>::template read_element<0,0>(a)/b);
    write_mat_element<0,1>(r,mat_traits<A>::template read_element<0,1>(a)/b);
    write_mat_element<0,2>(r,mat_traits<A>::template read_element<0,2>(a)/b);
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator/;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct div_ms_defined;

    template <>
    struct
    div_ms_defined<1,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<A>::cols==3 && is_scalar<B>::value,
    A &>::type
operator/=( A & a, B b )
    {
    write_mat_element<0,0>(a,mat_traits<A>::template read_element<0,0>(a)/b);
    write_mat_element<0,1>(a,mat_traits<A>::template read_element<0,1>(a)/b);
    write_mat_element<0,2>(a,mat_traits<A>::template read_element<0,2>(a)/b);
    write_mat_element<1,0>(a,mat_traits<A>::template read_element<1,0>(a)/b);
    write_mat_element<1,1>(a,mat_traits<A>::template read_element<1,1>(a)/b);
    write_mat_element<1,2>(a,mat_traits<A>::template read_element<1,2>(a)/b);
    write_mat_element<2,0>(a,mat_traits<A>::template read_element<2,0>(a)/b);
    write_mat_element<2,1>(a,mat_traits<A>::template read_element<2,1>(a)/b);
    write_mat_element<2,2>(a,mat_traits<A>::template read_element<2,2>(a)/b);
    return a;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator/=;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct div_eq_ms_defined;

    template <>
    struct
    div_eq_ms_defined<3,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<A>::cols==1 && is_scalar<B>::value,
    A &>::type
operator/=( A & a, B b )
    {
    write_mat_element<0,0>(a,mat_traits<A>::template read_element<0,0>(a)/b);
    write_mat_element<1,0>(a,mat_traits<A>::template read_element<1,0>(a)/b);
    write_mat_element<2,0>(a,mat_traits<A>::template read_element<2,0>(a)/b);
    return a;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator/=;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct div_eq_ms_defined;

    template <>
    struct
    div_eq_ms_defined<3,1>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==1 && mat_traits<A>::cols==3 && is_scalar<B>::value,
    A &>::type
operator/=( A & a, B b )
    {
    write_mat_element<0,0>(a,mat_traits<A>::template read_element<0,0>(a)/b);
    write_mat_element<0,1>(a,mat_traits<A>::template read_element<0,1>(a)/b);
    write_mat_element<0,2>(a,mat_traits<A>::template read_element<0,2>(a)/b);
    return a;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator/=;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct div_eq_ms_defined;

    template <>
    struct
    div_eq_ms_defined<1,3>
        {
        static bool const value=true;
        };
    }

template <class R,class A>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<R>::rows==3 && mat_traits<A>::rows==3 &&
    mat_traits<R>::cols==3 && mat_traits<A>::cols==3,
    R>::type
convert_to( A const & a )
    {
    R r;
    write_mat_element<0,0>(r,mat_traits<A>::template read_element<0,0>(a));
    write_mat_element<0,1>(r,mat_traits<A>::template read_element<0,1>(a));
    write_mat_element<0,2>(r,mat_traits<A>::template read_element<0,2>(a));
    write_mat_element<1,0>(r,mat_traits<A>::template read_element<1,0>(a));
    write_mat_element<1,1>(r,mat_traits<A>::template read_element<1,1>(a));
    write_mat_element<1,2>(r,mat_traits<A>::template read_element<1,2>(a));
    write_mat_element<2,0>(r,mat_traits<A>::template read_element<2,0>(a));
    write_mat_element<2,1>(r,mat_traits<A>::template read_element<2,1>(a));
    write_mat_element<2,2>(r,mat_traits<A>::template read_element<2,2>(a));
    return r;
    }

template <class R,class A>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE
typename enable_if_c<
    is_mat<R>::value && is_quat<A>::value &&
    mat_traits<R>::rows==3 && mat_traits<R>::cols==3,
    R>::type
convert_to( A const & q )
    {
    typedef typename mat_traits<R>::scalar_type T;
    T const a=quat_traits<A>::template read_element<0>(q);
    T const b=quat_traits<A>::template read_element<1>(q);
    T const c=quat_traits<A>::template read_element<2>(q);
    T const d=quat_traits<A>::template read_element<3>(q);
    T const bb = b*b;
    T const cc = c*c;
    T const dd = d*d;
    T const bc = b*c;
    T const bd = b*d;
    T const cd = c*d;
    T const ab = a*b;
    T const ac = a*c;
    T const ad = a*d;
    T const one = scalar_traits<T>::value(1);
    T const two = one+one;
    R r;
    write_mat_element<0,0>(r,one - two*(cc+dd));
    write_mat_element<0,1>(r,two*(bc-ad));
    write_mat_element<0,2>(r,two*(bd+ac));
    write_mat_element<1,0>(r,two*(bc+ad));
    write_mat_element<1,1>(r,one - two*(bb+dd));
    write_mat_element<1,2>(r,two*(cd-ab));
    write_mat_element<2,0>(r,two*(bd-ac));
    write_mat_element<2,1>(r,two*(cd+ab));
    write_mat_element<2,2>(r,one - two*(bb+cc));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::convert_to;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct convert_to_m_defined;

    template <>
    struct
    convert_to_m_defined<3,3>
        {
        static bool const value=true;
        };
    }

template <class R,class A>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<R>::rows==3 && mat_traits<A>::rows==3 &&
    mat_traits<R>::cols==1 && mat_traits<A>::cols==1,
    R>::type
convert_to( A const & a )
    {
    R r;
    write_mat_element<0,0>(r,mat_traits<A>::template read_element<0,0>(a));
    write_mat_element<1,0>(r,mat_traits<A>::template read_element<1,0>(a));
    write_mat_element<2,0>(r,mat_traits<A>::template read_element<2,0>(a));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::convert_to;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct convert_to_m_defined;

    template <>
    struct
    convert_to_m_defined<3,1>
        {
        static bool const value=true;
        };
    }

template <class R,class A>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<R>::rows==1 && mat_traits<A>::rows==1 &&
    mat_traits<R>::cols==3 && mat_traits<A>::cols==3,
    R>::type
convert_to( A const & a )
    {
    R r;
    write_mat_element<0,0>(r,mat_traits<A>::template read_element<0,0>(a));
    write_mat_element<0,1>(r,mat_traits<A>::template read_element<0,1>(a));
    write_mat_element<0,2>(r,mat_traits<A>::template read_element<0,2>(a));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::convert_to;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct convert_to_m_defined;

    template <>
    struct
    convert_to_m_defined<1,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==3,
    bool>::type
operator==( A const & a, B const & b )
    {
    return
        mat_traits<A>::template read_element<0,0>(a)==mat_traits<B>::template read_element<0,0>(b) &&
        mat_traits<A>::template read_element<0,1>(a)==mat_traits<B>::template read_element<0,1>(b) &&
        mat_traits<A>::template read_element<0,2>(a)==mat_traits<B>::template read_element<0,2>(b) &&
        mat_traits<A>::template read_element<1,0>(a)==mat_traits<B>::template read_element<1,0>(b) &&
        mat_traits<A>::template read_element<1,1>(a)==mat_traits<B>::template read_element<1,1>(b) &&
        mat_traits<A>::template read_element<1,2>(a)==mat_traits<B>::template read_element<1,2>(b) &&
        mat_traits<A>::template read_element<2,0>(a)==mat_traits<B>::template read_element<2,0>(b) &&
        mat_traits<A>::template read_element<2,1>(a)==mat_traits<B>::template read_element<2,1>(b) &&
        mat_traits<A>::template read_element<2,2>(a)==mat_traits<B>::template read_element<2,2>(b);
    }

namespace
sfinae
    {
    using ::boost::qvm::operator==;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct eq_mm_defined;

    template <>
    struct
    eq_mm_defined<3,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==1 && mat_traits<B>::cols==1,
    bool>::type
operator==( A const & a, B const & b )
    {
    return
        mat_traits<A>::template read_element<0,0>(a)==mat_traits<B>::template read_element<0,0>(b) &&
        mat_traits<A>::template read_element<1,0>(a)==mat_traits<B>::template read_element<1,0>(b) &&
        mat_traits<A>::template read_element<2,0>(a)==mat_traits<B>::template read_element<2,0>(b);
    }

namespace
sfinae
    {
    using ::boost::qvm::operator==;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct eq_mm_defined;

    template <>
    struct
    eq_mm_defined<3,1>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==1 && mat_traits<B>::rows==1 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==3,
    bool>::type
operator==( A const & a, B const & b )
    {
    return
        mat_traits<A>::template read_element<0,0>(a)==mat_traits<B>::template read_element<0,0>(b) &&
        mat_traits<A>::template read_element<0,1>(a)==mat_traits<B>::template read_element<0,1>(b) &&
        mat_traits<A>::template read_element<0,2>(a)==mat_traits<B>::template read_element<0,2>(b);
    }

namespace
sfinae
    {
    using ::boost::qvm::operator==;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct eq_mm_defined;

    template <>
    struct
    eq_mm_defined<1,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==3,
    bool>::type
operator!=( A const & a, B const & b )
    {
    return
        !(mat_traits<A>::template read_element<0,0>(a)==mat_traits<B>::template read_element<0,0>(b)) ||
        !(mat_traits<A>::template read_element<0,1>(a)==mat_traits<B>::template read_element<0,1>(b)) ||
        !(mat_traits<A>::template read_element<0,2>(a)==mat_traits<B>::template read_element<0,2>(b)) ||
        !(mat_traits<A>::template read_element<1,0>(a)==mat_traits<B>::template read_element<1,0>(b)) ||
        !(mat_traits<A>::template read_element<1,1>(a)==mat_traits<B>::template read_element<1,1>(b)) ||
        !(mat_traits<A>::template read_element<1,2>(a)==mat_traits<B>::template read_element<1,2>(b)) ||
        !(mat_traits<A>::template read_element<2,0>(a)==mat_traits<B>::template read_element<2,0>(b)) ||
        !(mat_traits<A>::template read_element<2,1>(a)==mat_traits<B>::template read_element<2,1>(b)) ||
        !(mat_traits<A>::template read_element<2,2>(a)==mat_traits<B>::template read_element<2,2>(b));
    }

namespace
sfinae
    {
    using ::boost::qvm::operator!=;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct neq_mm_defined;

    template <>
    struct
    neq_mm_defined<3,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==1 && mat_traits<B>::cols==1,
    bool>::type
operator!=( A const & a, B const & b )
    {
    return
        !(mat_traits<A>::template read_element<0,0>(a)==mat_traits<B>::template read_element<0,0>(b)) ||
        !(mat_traits<A>::template read_element<1,0>(a)==mat_traits<B>::template read_element<1,0>(b)) ||
        !(mat_traits<A>::template read_element<2,0>(a)==mat_traits<B>::template read_element<2,0>(b));
    }

namespace
sfinae
    {
    using ::boost::qvm::operator!=;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct neq_mm_defined;

    template <>
    struct
    neq_mm_defined<3,1>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==1 && mat_traits<B>::rows==1 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==3,
    bool>::type
operator!=( A const & a, B const & b )
    {
    return
        !(mat_traits<A>::template read_element<0,0>(a)==mat_traits<B>::template read_element<0,0>(b)) ||
        !(mat_traits<A>::template read_element<0,1>(a)==mat_traits<B>::template read_element<0,1>(b)) ||
        !(mat_traits<A>::template read_element<0,2>(a)==mat_traits<B>::template read_element<0,2>(b));
    }

namespace
sfinae
    {
    using ::boost::qvm::operator!=;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct neq_mm_defined;

    template <>
    struct
    neq_mm_defined<1,3>
        {
        static bool const value=true;
        };
    }

template <class A>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<A>::cols==3,
    deduce_mat<A> >::type
operator-( A const & a )
    {
    typedef typename deduce_mat<A>::type R;
    R r;
    write_mat_element<0,0>(r,-mat_traits<A>::template read_element<0,0>(a));
    write_mat_element<0,1>(r,-mat_traits<A>::template read_element<0,1>(a));
    write_mat_element<0,2>(r,-mat_traits<A>::template read_element<0,2>(a));
    write_mat_element<1,0>(r,-mat_traits<A>::template read_element<1,0>(a));
    write_mat_element<1,1>(r,-mat_traits<A>::template read_element<1,1>(a));
    write_mat_element<1,2>(r,-mat_traits<A>::template read_element<1,2>(a));
    write_mat_element<2,0>(r,-mat_traits<A>::template read_element<2,0>(a));
    write_mat_element<2,1>(r,-mat_traits<A>::template read_element<2,1>(a));
    write_mat_element<2,2>(r,-mat_traits<A>::template read_element<2,2>(a));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator-;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct minus_m_defined;

    template <>
    struct
    minus_m_defined<3,3>
        {
        static bool const value=true;
        };
    }

template <class A>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<A>::cols==1,
    deduce_mat<A> >::type
operator-( A const & a )
    {
    typedef typename deduce_mat<A>::type R;
    R r;
    write_mat_element<0,0>(r,-mat_traits<A>::template read_element<0,0>(a));
    write_mat_element<1,0>(r,-mat_traits<A>::template read_element<1,0>(a));
    write_mat_element<2,0>(r,-mat_traits<A>::template read_element<2,0>(a));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator-;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct minus_m_defined;

    template <>
    struct
    minus_m_defined<3,1>
        {
        static bool const value=true;
        };
    }

template <class A>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==1 && mat_traits<A>::cols==3,
    deduce_mat<A> >::type
operator-( A const & a )
    {
    typedef typename deduce_mat<A>::type R;
    R r;
    write_mat_element<0,0>(r,-mat_traits<A>::template read_element<0,0>(a));
    write_mat_element<0,1>(r,-mat_traits<A>::template read_element<0,1>(a));
    write_mat_element<0,2>(r,-mat_traits<A>::template read_element<0,2>(a));
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator-;
    }

namespace
qvm_detail
    {
    template <int R,int C>
    struct minus_m_defined;

    template <>
    struct
    minus_m_defined<1,3>
        {
        static bool const value=true;
        };
    }

template <class A>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<A>::cols==3,
    typename mat_traits<A>::scalar_type>::type
determinant( A const & a )
    {
    typedef typename mat_traits<A>::scalar_type T;
    T const a00=mat_traits<A>::template read_element<0,0>(a);
    T const a01=mat_traits<A>::template read_element<0,1>(a);
    T const a02=mat_traits<A>::template read_element<0,2>(a);
    T const a10=mat_traits<A>::template read_element<1,0>(a);
    T const a11=mat_traits<A>::template read_element<1,1>(a);
    T const a12=mat_traits<A>::template read_element<1,2>(a);
    T const a20=mat_traits<A>::template read_element<2,0>(a);
    T const a21=mat_traits<A>::template read_element<2,1>(a);
    T const a22=mat_traits<A>::template read_element<2,2>(a);
    T det=(a00*(a11*a22-a12*a21)-a01*(a10*a22-a12*a20)+a02*(a10*a21-a11*a20));
    return det;
    }

namespace
sfinae
    {
    using ::boost::qvm::determinant;
    }

namespace
qvm_detail
    {
    template <int D>
    struct determinant_defined;

    template <>
    struct
    determinant_defined<3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<A>::cols==3 && is_scalar<B>::value,
    deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols> >::type
inverse( A const & a, B det )
    {
    typedef typename mat_traits<A>::scalar_type T;
    BOOST_QVM_ASSERT(det!=scalar_traits<B>::value(0));
    T const a00=mat_traits<A>::template read_element<0,0>(a);
    T const a01=mat_traits<A>::template read_element<0,1>(a);
    T const a02=mat_traits<A>::template read_element<0,2>(a);
    T const a10=mat_traits<A>::template read_element<1,0>(a);
    T const a11=mat_traits<A>::template read_element<1,1>(a);
    T const a12=mat_traits<A>::template read_element<1,2>(a);
    T const a20=mat_traits<A>::template read_element<2,0>(a);
    T const a21=mat_traits<A>::template read_element<2,1>(a);
    T const a22=mat_traits<A>::template read_element<2,2>(a);
    T const f=scalar_traits<T>::value(1)/det;
    typedef typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols>::type R;
    R r;
    write_mat_element<0,0>(r, f*(a11*a22-a12*a21));
    write_mat_element<0,1>(r,-f*(a01*a22-a02*a21));
    write_mat_element<0,2>(r, f*(a01*a12-a02*a11));
    write_mat_element<1,0>(r,-f*(a10*a22-a12*a20));
    write_mat_element<1,1>(r, f*(a00*a22-a02*a20));
    write_mat_element<1,2>(r,-f*(a00*a12-a02*a10));
    write_mat_element<2,0>(r, f*(a10*a21-a11*a20));
    write_mat_element<2,1>(r,-f*(a00*a21-a01*a20));
    write_mat_element<2,2>(r, f*(a00*a11-a01*a10));
    return r;
    }

template <class A>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<A>::cols==3,
    deduce_mat<A> >::type
inverse( A const & a )
    {
    typedef typename mat_traits<A>::scalar_type T;
    T det=determinant(a);
    if( det==scalar_traits<T>::value(0) )
        BOOST_QVM_THROW_EXCEPTION(zero_determinant_error());
    return inverse(a,det);
    }

namespace
sfinae
    {
    using ::boost::qvm::inverse;
    }

namespace
qvm_detail
    {
    template <int D>
    struct inverse_m_defined;

    template <>
    struct
    inverse_m_defined<3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==3,
    deduce_mat2<A,B,3,3> >::type
operator*( A const & a, B const & b )
    {
    typedef typename mat_traits<A>::scalar_type Ta;
    typedef typename mat_traits<B>::scalar_type Tb;
    Ta const a00 = mat_traits<A>::template read_element<0,0>(a);
    Ta const a01 = mat_traits<A>::template read_element<0,1>(a);
    Ta const a02 = mat_traits<A>::template read_element<0,2>(a);
    Ta const a10 = mat_traits<A>::template read_element<1,0>(a);
    Ta const a11 = mat_traits<A>::template read_element<1,1>(a);
    Ta const a12 = mat_traits<A>::template read_element<1,2>(a);
    Ta const a20 = mat_traits<A>::template read_element<2,0>(a);
    Ta const a21 = mat_traits<A>::template read_element<2,1>(a);
    Ta const a22 = mat_traits<A>::template read_element<2,2>(a);
    Tb const b00 = mat_traits<B>::template read_element<0,0>(b);
    Tb const b01 = mat_traits<B>::template read_element<0,1>(b);
    Tb const b02 = mat_traits<B>::template read_element<0,2>(b);
    Tb const b10 = mat_traits<B>::template read_element<1,0>(b);
    Tb const b11 = mat_traits<B>::template read_element<1,1>(b);
    Tb const b12 = mat_traits<B>::template read_element<1,2>(b);
    Tb const b20 = mat_traits<B>::template read_element<2,0>(b);
    Tb const b21 = mat_traits<B>::template read_element<2,1>(b);
    Tb const b22 = mat_traits<B>::template read_element<2,2>(b);
    typedef typename deduce_mat2<A,B,3,3>::type R;
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::rows==3);
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::cols==3);
    R r;
    write_mat_element<0,0>(r,a00*b00+a01*b10+a02*b20);
    write_mat_element<0,1>(r,a00*b01+a01*b11+a02*b21);
    write_mat_element<0,2>(r,a00*b02+a01*b12+a02*b22);
    write_mat_element<1,0>(r,a10*b00+a11*b10+a12*b20);
    write_mat_element<1,1>(r,a10*b01+a11*b11+a12*b21);
    write_mat_element<1,2>(r,a10*b02+a11*b12+a12*b22);
    write_mat_element<2,0>(r,a20*b00+a21*b10+a22*b20);
    write_mat_element<2,1>(r,a20*b01+a21*b11+a22*b21);
    write_mat_element<2,2>(r,a20*b02+a21*b12+a22*b22);
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator*;
    }

namespace
qvm_detail
    {
    template <int R,int /*CR*/,int C>
    struct mul_mm_defined;

    template <>
    struct
    mul_mm_defined<3,3,3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==3,
    A &>::type
operator*=( A & a, B const & b )
    {
    typedef typename mat_traits<A>::scalar_type Ta;
    typedef typename mat_traits<B>::scalar_type Tb;
    Ta const a00 = mat_traits<A>::template read_element<0,0>(a);
    Ta const a01 = mat_traits<A>::template read_element<0,1>(a);
    Ta const a02 = mat_traits<A>::template read_element<0,2>(a);
    Ta const a10 = mat_traits<A>::template read_element<1,0>(a);
    Ta const a11 = mat_traits<A>::template read_element<1,1>(a);
    Ta const a12 = mat_traits<A>::template read_element<1,2>(a);
    Ta const a20 = mat_traits<A>::template read_element<2,0>(a);
    Ta const a21 = mat_traits<A>::template read_element<2,1>(a);
    Ta const a22 = mat_traits<A>::template read_element<2,2>(a);
    Tb const b00 = mat_traits<B>::template read_element<0,0>(b);
    Tb const b01 = mat_traits<B>::template read_element<0,1>(b);
    Tb const b02 = mat_traits<B>::template read_element<0,2>(b);
    Tb const b10 = mat_traits<B>::template read_element<1,0>(b);
    Tb const b11 = mat_traits<B>::template read_element<1,1>(b);
    Tb const b12 = mat_traits<B>::template read_element<1,2>(b);
    Tb const b20 = mat_traits<B>::template read_element<2,0>(b);
    Tb const b21 = mat_traits<B>::template read_element<2,1>(b);
    Tb const b22 = mat_traits<B>::template read_element<2,2>(b);
    write_mat_element<0,0>(a,a00*b00+a01*b10+a02*b20);
    write_mat_element<0,1>(a,a00*b01+a01*b11+a02*b21);
    write_mat_element<0,2>(a,a00*b02+a01*b12+a02*b22);
    write_mat_element<1,0>(a,a10*b00+a11*b10+a12*b20);
    write_mat_element<1,1>(a,a10*b01+a11*b11+a12*b21);
    write_mat_element<1,2>(a,a10*b02+a11*b12+a12*b22);
    write_mat_element<2,0>(a,a20*b00+a21*b10+a22*b20);
    write_mat_element<2,1>(a,a20*b01+a21*b11+a22*b21);
    write_mat_element<2,2>(a,a20*b02+a21*b12+a22*b22);
    return a;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator*=;
    }

namespace
qvm_detail
    {
    template <int D>
    struct mul_eq_mm_defined;

    template <>
    struct
    mul_eq_mm_defined<3>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==3 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==1,
    deduce_mat2<A,B,3,1> >::type
operator*( A const & a, B const & b )
    {
    typedef typename mat_traits<A>::scalar_type Ta;
    typedef typename mat_traits<B>::scalar_type Tb;
    Ta const a00 = mat_traits<A>::template read_element<0,0>(a);
    Ta const a01 = mat_traits<A>::template read_element<0,1>(a);
    Ta const a02 = mat_traits<A>::template read_element<0,2>(a);
    Ta const a10 = mat_traits<A>::template read_element<1,0>(a);
    Ta const a11 = mat_traits<A>::template read_element<1,1>(a);
    Ta const a12 = mat_traits<A>::template read_element<1,2>(a);
    Ta const a20 = mat_traits<A>::template read_element<2,0>(a);
    Ta const a21 = mat_traits<A>::template read_element<2,1>(a);
    Ta const a22 = mat_traits<A>::template read_element<2,2>(a);
    Tb const b00 = mat_traits<B>::template read_element<0,0>(b);
    Tb const b10 = mat_traits<B>::template read_element<1,0>(b);
    Tb const b20 = mat_traits<B>::template read_element<2,0>(b);
    typedef typename deduce_mat2<A,B,3,1>::type R;
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::rows==3);
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::cols==1);
    R r;
    write_mat_element<0,0>(r,a00*b00+a01*b10+a02*b20);
    write_mat_element<1,0>(r,a10*b00+a11*b10+a12*b20);
    write_mat_element<2,0>(r,a20*b00+a21*b10+a22*b20);
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator*;
    }

namespace
qvm_detail
    {
    template <int R,int /*CR*/,int C>
    struct mul_mm_defined;

    template <>
    struct
    mul_mm_defined<3,3,1>
        {
        static bool const value=true;
        };
    }

template <class A,class B>
BOOST_QVM_CONSTEXPR BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
    mat_traits<A>::rows==1 && mat_traits<B>::rows==3 &&
    mat_traits<A>::cols==3 && mat_traits<B>::cols==3,
    deduce_mat2<A,B,1,3> >::type
operator*( A const & a, B const & b )
    {
    typedef typename mat_traits<A>::scalar_type Ta;
    typedef typename mat_traits<B>::scalar_type Tb;
    Ta const a00 = mat_traits<A>::template read_element<0,0>(a);
    Ta const a01 = mat_traits<A>::template read_element<0,1>(a);
    Ta const a02 = mat_traits<A>::template read_element<0,2>(a);
    Tb const b00 = mat_traits<B>::template read_element<0,0>(b);
    Tb const b01 = mat_traits<B>::template read_element<0,1>(b);
    Tb const b02 = mat_traits<B>::template read_element<0,2>(b);
    Tb const b10 = mat_traits<B>::template read_element<1,0>(b);
    Tb const b11 = mat_traits<B>::template read_element<1,1>(b);
    Tb const b12 = mat_traits<B>::template read_element<1,2>(b);
    Tb const b20 = mat_traits<B>::template read_element<2,0>(b);
    Tb const b21 = mat_traits<B>::template read_element<2,1>(b);
    Tb const b22 = mat_traits<B>::template read_element<2,2>(b);
    typedef typename deduce_mat2<A,B,1,3>::type R;
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::rows==1);
    BOOST_QVM_STATIC_ASSERT(mat_traits<R>::cols==3);
    R r;
    write_mat_element<0,0>(r,a00*b00+a01*b10+a02*b20);
    write_mat_element<0,1>(r,a00*b01+a01*b11+a02*b21);
    write_mat_element<0,2>(r,a00*b02+a01*b12+a02*b22);
    return r;
    }

namespace
sfinae
    {
    using ::boost::qvm::operator*;
    }

namespace
qvm_detail
    {
    template <int R,int /*CR*/,int C>
    struct mul_mm_defined;

    template <>
    struct
    mul_mm_defined<1,3,3>
        {
        static bool const value=true;
        };
    }

} }

#endif
