multivector.h

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#include <stdarg.h>
#include <vector>

namespace std{
        
template < class T, int N>
class multivector: public vector< multivector<T, N-1> >{
public:
    typedef vector< multivector< T,N-1> > v;
    
    multivector(): v() {}
        multivector(const multivector& m): v(m){}

multivector(const T& value, ...){
                va_list listPointer;
                va_start(listPointer,value);
                int n=va_arg(listPointer,int);
                v::insert(v::begin(),n,multivector<T,N-1>(value,listPointer));
                va_end(listPointer);
                }


multivector(const T& value, va_list & listPointer)
                {
                        int n=va_arg(listPointer,int);
                        v::insert(v::begin(),n,multivector<T,N-1>(value,listPointer));
                        }

};


template< class T >
class multivector<T,1>: public vector<T>{
public:
 typedef vector< T > v;
 multivector(): v() {}
        multivector(const multivector& m): v(m){}

 multivector(const T& value, int x): v(x,value){}

 multivector(const T& value, va_list & listPointer):
                v(va_arg(listPointer,int), value){}
};

class Matrix: public multivector< ex, 2>{
public:

Matrix(): multivector< ex,2>(0,3,3) {}

Matrix(const Matrix& m): multivector< ex,2>(m) {}
Matrix(const char * m[3][3]): multivector< ex,2>(0,3,3){
        for(uint i=0;i<3;i++)
                for(uint j=0;j<3;j++) at(i)[j]=symbol(m[i][j]);
        }
Matrix(const char * name,const char ** index1, const char ** index2): multivector< ex,2>(0,3,3){
        for(uint i=0;i<3;i++)
                for(uint j=0;j<3;j++){
                         string res=string(name)+"_{"+string(index1[i])+" "+string(index2[j])+"}";
                         //cout<<res<<endl;
                         at(i)[j]=symbol(res.c_str());
                         }
        }
Matrix(ex m1, ex m2, ex m3): multivector< ex,2>(0,3,3) {
        at(0)[0]=m1;
        at(1)[1]=m2;
        at(2)[2]=m3;    
}

Matrix(ex m1): multivector< ex,2>(0,3,3){
        Matrix();
        at(0)[0]=m1;
        at(1)[1]=m1;
        at(2)[2]=m1;
        }
Matrix(ex t12, ex t13, ex t23, ex d13): multivector< ex,2>(0,3,3) {
        Matrix();
        ex c12=cos(t12), c13=cos(t13), c23=cos(t23);
        ex s12=sin(t12), s13=sin(t13), s23=sin(t23);
        ex e13=exp(I*d13);
        ex e13t=ex(1)/e13;
        
        ex aux[3][3]={
                        {c12*c13,s12*c13,s13*e13t},
                        {-s12*c23-c12*s23*s13*e13,c12*c23-s12*s23*s13*e13,s23*c13},
                        {s12*s23-c12*c23*s13*e13,-c12*s23-s12*c23*s13*e13,c13*c23}                              
                        };
        for(uint i=0;i<3; i++) at(i).assign(aux[i],aux[i]+3);
        }
ex cs(ex t12){
        return (exp(I*t12)+1/exp(I*t12))/2;
        }
ex sn(ex t12){
        return -I*(exp(I*t12)-1/exp(I*t12))/2;
        }
Matrix conjugate() const {
        Matrix res;
        for(uint i=0;i<3;i++)
                for(uint j=0;j<3;j++)
                        res[i][j]=at(j)[i].conjugate();
        
        return res;
}
};

Matrix operator*(const Matrix & m1,const Matrix & m2){
        Matrix res;
        for(uint i=0;i<3;i++)
                for(uint j=0;j<3;j++)
                        for(uint k=0;k<3;k++)
                                res[i][j]=res[i][j]+m1[i][k]*m2[k][j];
        return res;
}

Matrix operator+(const Matrix & m1,const Matrix & m2){
        Matrix res;
        for(uint i=0;i<3;i++)
                for(uint j=0;j<3;j++)
                                res[i][j]=m1[i][j]+m2[i][j];
        return res;
}



}