//***********************************************************
// 
//  NXV4 "Math-on-Paper" software
//
//  package : MTX class _____________________________________
//            
//            supports: move semantix
//                      operators + - * / L,R-val context
//                                += -= *= /=
//                      fabs()
//                      ~  -      unary operators L,R-val
//                      mtx<arithmetic> i.e.     int
//                                               float 
//                                               double
//                                               real
//                                           cpx<int> 
//                                           cpx<float> 
//                                           cpx<double> 
//                                           cpx<real> 
//                      type_casts between the types 
//                      cout << overload 
//
//                      TOTAL = 5084 instantiated op/f's
//                      _____________________________________
//
//
//  authors : Mihai-Tiberiu Dima (1)
//            Maria Dima         (2)
//
//             Meshcheryakov Laboratory of Information Techn.
//             Joint Institute for Nuclear Research
//             Dubna-Russia
//
//            on leave from:
//
//             Hyperion Univ. Bucharest-Romania
//
//
//  date    : MTX4/v1.0.alfa   / Mon Mar 07 12:45:54 CET 2022
//
//***********************************************************
#include <cmath>
#include <iostream>

#include "cpx.hh"
#include "vec.hh"
#include "mtx.hh"

using namespace std                                         ;
using namespace cpx4                                        ;
using namespace vec4                                        ;
using namespace mtx4                                        ;


int main()
{

// vec4::utf8x = true                                         ;
// mtx4::utf8x = true                                         ;

// this is a special math example
//
// In Lie representation group elements
// are exp(gen).
//
//           | 0  1  0 |
//  for Lz = |-1  0  0 |
//           | 0  0  0 |
//
// then rotations around the z-axis are:
//
//   ROT = exp(phi*Lz)
//
// to use this example do the following:
//   rm test.cc
//   ln -s e2.cc test.cc
//   make test
//   make run

  using fltx = float                                        ;
  using dblx = double                                       ;
  using real = long double                                  ;

  double e   = exp(1)                                       ;
  double pi  = 3.14159265853                                ;

  mtx<dblx>     Lz( 0, 1, 0,
                   -1, 0, 0,
                    0, 0, 0 )                               ;

  cout                                             << endl  ;
  cout << noboolalpha                              << endl  ;

  cout                                             << endl  ;
  cout << " _____________________________________" << endl  ;
  cout                                             << endl  ;
  cout                                             << endl  ;
  cout                                             << endl  ;
  cout << "   " << boolalpha
                << "ROT = exp(phi*Lz) = "
                << exp(pi/4*Lz)    << endl << endl << endl  ;
  cout                                             << endl  ;
  cout << "   " << "ROT( |ex> ) = "
                << (exp(-pi/4*Lz)|vec<int>(1,0,0)) << endl  ;
  cout                                             << endl  ;
  cout                                             << endl  ;
  cout                                             << endl  ;
  cout << "   " << "GEN = log(ROT) = "
       <<           log(exp(-pi/4*Lz))*4/pi << endl <<endl  ;
  cout                                             << endl  ;
  cout                                             << endl  ;

}