8{
   11 
   15 
   20 
   24 
   25  
   30 
   31  
   38                "levi_civita(k,l,m)(0,1,2)");
   41                "levi_civita(k,l,m)(0,2,1)");
   46                "levi_civita(k,l,m)(1,0,2)");
   51                "levi_civita(k,l,m)(1,2,0)");
   56                "levi_civita(k,l,m)(2,0,1)");
   59                "levi_civita(k,l,m)(2,1,0)");
   65 
   66  
   68                "levi_civita(n,o,p,q)(0,0,0,0)");
   70                "levi_civita(n,o,p,q)(0,0,0,1)");
   72                "levi_civita(n,o,p,q)(0,0,0,2)");
   74                "levi_civita(n,o,p,q)(0,0,0,3)");
   76                "levi_civita(n,o,p,q)(0,0,1,0)");
   78                "levi_civita(n,o,p,q)(0,0,1,1)");
   80                "levi_civita(n,o,p,q)(0,0,1,2)");
   82                "levi_civita(n,o,p,q)(0,0,1,3)");
   84                "levi_civita(n,o,p,q)(0,0,2,0)");
   86                "levi_civita(n,o,p,q)(0,0,2,1)");
   88                "levi_civita(n,o,p,q)(0,0,2,2)");
   90                "levi_civita(n,o,p,q)(0,0,2,3)");
   92                "levi_civita(n,o,p,q)(0,0,3,0)");
   94                "levi_civita(n,o,p,q)(0,0,3,1)");
   96                "levi_civita(n,o,p,q)(0,0,3,2)");
   98                "levi_civita(n,o,p,q)(0,0,3,3)");
  100                "levi_civita(n,o,p,q)(0,1,0,0)");
  102                "levi_civita(n,o,p,q)(0,1,0,1)");
  104                "levi_civita(n,o,p,q)(0,1,0,2)");
  106                "levi_civita(n,o,p,q)(0,1,0,3)");
  108                "levi_civita(n,o,p,q)(0,1,1,0)");
  110                "levi_civita(n,o,p,q)(0,1,1,1)");
  112                "levi_civita(n,o,p,q)(0,1,1,2)");
  114                "levi_civita(n,o,p,q)(0,1,1,3)");
  116                "levi_civita(n,o,p,q)(0,1,2,0)");
  118                "levi_civita(n,o,p,q)(0,1,2,1)");
  120                "levi_civita(n,o,p,q)(0,1,2,2)");
  122                "levi_civita(n,o,p,q)(0,1,2,3)");
  124                "levi_civita(n,o,p,q)(0,1,3,0)");
  126                "levi_civita(n,o,p,q)(0,1,3,1)");
  128                "levi_civita(n,o,p,q)(0,1,3,2)");
  130                "levi_civita(n,o,p,q)(0,1,3,3)");
  132                "levi_civita(n,o,p,q)(0,2,0,0)");
  134                "levi_civita(n,o,p,q)(0,2,0,1)");
  136                "levi_civita(n,o,p,q)(0,2,0,2)");
  138                "levi_civita(n,o,p,q)(0,2,0,3)");
  140                "levi_civita(n,o,p,q)(0,2,1,0)");
  142                "levi_civita(n,o,p,q)(0,2,1,1)");
  144                "levi_civita(n,o,p,q)(0,2,1,2)");
  146                "levi_civita(n,o,p,q)(0,2,1,3)");
  148                "levi_civita(n,o,p,q)(0,2,2,0)");
  150                "levi_civita(n,o,p,q)(0,2,2,1)");
  152                "levi_civita(n,o,p,q)(0,2,2,2)");
  154                "levi_civita(n,o,p,q)(0,2,2,3)");
  156                "levi_civita(n,o,p,q)(0,2,3,0)");
  158                "levi_civita(n,o,p,q)(0,2,3,1)");
  160                "levi_civita(n,o,p,q)(0,2,3,2)");
  162                "levi_civita(n,o,p,q)(0,2,3,3)");
  164                "levi_civita(n,o,p,q)(0,3,0,0)");
  166                "levi_civita(n,o,p,q)(0,3,0,1)");
  168                "levi_civita(n,o,p,q)(0,3,0,2)");
  170                "levi_civita(n,o,p,q)(0,3,0,3)");
  172                "levi_civita(n,o,p,q)(0,3,1,0)");
  174                "levi_civita(n,o,p,q)(0,3,1,1)");
  176                "levi_civita(n,o,p,q)(0,3,1,2)");
  178                "levi_civita(n,o,p,q)(0,3,1,3)");
  180                "levi_civita(n,o,p,q)(0,3,2,0)");
  182                "levi_civita(n,o,p,q)(0,3,2,1)");
  184                "levi_civita(n,o,p,q)(0,3,2,2)");
  186                "levi_civita(n,o,p,q)(0,3,2,3)");
  188                "levi_civita(n,o,p,q)(0,3,3,0)");
  190                "levi_civita(n,o,p,q)(0,3,3,1)");
  192                "levi_civita(n,o,p,q)(0,3,3,2)");
  194                "levi_civita(n,o,p,q)(0,3,3,3)");
  195 
  197                "levi_civita(n,o,p,q)(1,0,0,0)");
  199                "levi_civita(n,o,p,q)(1,0,0,1)");
  201                "levi_civita(n,o,p,q)(1,0,0,2)");
  203                "levi_civita(n,o,p,q)(1,0,0,3)");
  205                "levi_civita(n,o,p,q)(1,0,1,0)");
  207                "levi_civita(n,o,p,q)(1,0,1,1)");
  209                "levi_civita(n,o,p,q)(1,0,1,2)");
  211                "levi_civita(n,o,p,q)(1,0,1,3)");
  213                "levi_civita(n,o,p,q)(1,0,2,0)");
  215                "levi_civita(n,o,p,q)(1,0,2,1)");
  217                "levi_civita(n,o,p,q)(1,0,2,2)");
  219                "levi_civita(n,o,p,q)(1,0,2,3)");
  221                "levi_civita(n,o,p,q)(1,0,3,0)");
  223                "levi_civita(n,o,p,q)(1,0,3,1)");
  225                "levi_civita(n,o,p,q)(1,0,3,2)");
  227                "levi_civita(n,o,p,q)(1,0,3,3)");
  229                "levi_civita(n,o,p,q)(1,1,0,0)");
  231                "levi_civita(n,o,p,q)(1,1,0,1)");
  233                "levi_civita(n,o,p,q)(1,1,0,2)");
  235                "levi_civita(n,o,p,q)(1,1,0,3)");
  237                "levi_civita(n,o,p,q)(1,1,1,0)");
  239                "levi_civita(n,o,p,q)(1,1,1,1)");
  241                "levi_civita(n,o,p,q)(1,1,1,2)");
  243                "levi_civita(n,o,p,q)(1,1,1,3)");
  245                "levi_civita(n,o,p,q)(1,1,2,0)");
  247                "levi_civita(n,o,p,q)(1,1,2,1)");
  249                "levi_civita(n,o,p,q)(1,1,2,2)");
  251                "levi_civita(n,o,p,q)(1,1,2,3)");
  253                "levi_civita(n,o,p,q)(1,1,3,0)");
  255                "levi_civita(n,o,p,q)(1,1,3,1)");
  257                "levi_civita(n,o,p,q)(1,1,3,2)");
  259                "levi_civita(n,o,p,q)(1,1,3,3)");
  261                "levi_civita(n,o,p,q)(1,2,0,0)");
  263                "levi_civita(n,o,p,q)(1,2,0,1)");
  265                "levi_civita(n,o,p,q)(1,2,0,2)");
  267                "levi_civita(n,o,p,q)(1,2,0,3)");
  269                "levi_civita(n,o,p,q)(1,2,1,0)");
  271                "levi_civita(n,o,p,q)(1,2,1,1)");
  273                "levi_civita(n,o,p,q)(1,2,1,2)");
  275                "levi_civita(n,o,p,q)(1,2,1,3)");
  277                "levi_civita(n,o,p,q)(1,2,2,0)");
  279                "levi_civita(n,o,p,q)(1,2,2,1)");
  281                "levi_civita(n,o,p,q)(1,2,2,2)");
  283                "levi_civita(n,o,p,q)(1,2,2,3)");
  285                "levi_civita(n,o,p,q)(1,2,3,0)");
  287                "levi_civita(n,o,p,q)(1,2,3,1)");
  289                "levi_civita(n,o,p,q)(1,2,3,2)");
  291                "levi_civita(n,o,p,q)(1,2,3,3)");
  293                "levi_civita(n,o,p,q)(1,3,0,0)");
  295                "levi_civita(n,o,p,q)(1,3,0,1)");
  297                "levi_civita(n,o,p,q)(1,3,0,2)");
  299                "levi_civita(n,o,p,q)(1,3,0,3)");
  301                "levi_civita(n,o,p,q)(1,3,1,0)");
  303                "levi_civita(n,o,p,q)(1,3,1,1)");
  305                "levi_civita(n,o,p,q)(1,3,1,2)");
  307                "levi_civita(n,o,p,q)(1,3,1,3)");
  309                "levi_civita(n,o,p,q)(1,3,2,0)");
  311                "levi_civita(n,o,p,q)(1,3,2,1)");
  313                "levi_civita(n,o,p,q)(1,3,2,2)");
  315                "levi_civita(n,o,p,q)(1,3,2,3)");
  317                "levi_civita(n,o,p,q)(1,3,3,0)");
  319                "levi_civita(n,o,p,q)(1,3,3,1)");
  321                "levi_civita(n,o,p,q)(1,3,3,2)");
  323                "levi_civita(n,o,p,q)(1,3,3,3)");
  324 
  326                "levi_civita(n,o,p,q)(2,0,0,0)");
  328                "levi_civita(n,o,p,q)(2,0,0,1)");
  330                "levi_civita(n,o,p,q)(2,0,0,2)");
  332                "levi_civita(n,o,p,q)(2,0,0,3)");
  334                "levi_civita(n,o,p,q)(2,0,1,0)");
  336                "levi_civita(n,o,p,q)(2,0,1,1)");
  338                "levi_civita(n,o,p,q)(2,0,1,2)");
  340                "levi_civita(n,o,p,q)(2,0,1,3)");
  342                "levi_civita(n,o,p,q)(2,0,2,0)");
  344                "levi_civita(n,o,p,q)(2,0,2,1)");
  346                "levi_civita(n,o,p,q)(2,0,2,2)");
  348                "levi_civita(n,o,p,q)(2,0,2,3)");
  350                "levi_civita(n,o,p,q)(2,0,3,0)");
  352                "levi_civita(n,o,p,q)(2,0,3,1)");
  354                "levi_civita(n,o,p,q)(2,0,3,2)");
  356                "levi_civita(n,o,p,q)(2,0,3,3)");
  358                "levi_civita(n,o,p,q)(2,1,0,0)");
  360                "levi_civita(n,o,p,q)(2,1,0,1)");
  362                "levi_civita(n,o,p,q)(2,1,0,2)");
  364                "levi_civita(n,o,p,q)(2,1,0,3)");
  366                "levi_civita(n,o,p,q)(2,1,1,0)");
  368                "levi_civita(n,o,p,q)(2,1,1,1)");
  370                "levi_civita(n,o,p,q)(2,1,1,2)");
  372                "levi_civita(n,o,p,q)(2,1,1,3)");
  374                "levi_civita(n,o,p,q)(2,1,2,0)");
  376                "levi_civita(n,o,p,q)(2,1,2,1)");
  378                "levi_civita(n,o,p,q)(2,1,2,2)");
  380                "levi_civita(n,o,p,q)(2,1,2,3)");
  382                "levi_civita(n,o,p,q)(2,1,3,0)");
  384                "levi_civita(n,o,p,q)(2,1,3,1)");
  386                "levi_civita(n,o,p,q)(2,1,3,2)");
  388                "levi_civita(n,o,p,q)(2,1,3,3)");
  390                "levi_civita(n,o,p,q)(2,2,0,0)");
  392                "levi_civita(n,o,p,q)(2,2,0,1)");
  394                "levi_civita(n,o,p,q)(2,2,0,2)");
  396                "levi_civita(n,o,p,q)(2,2,0,3)");
  398                "levi_civita(n,o,p,q)(2,2,1,0)");
  400                "levi_civita(n,o,p,q)(2,2,1,1)");
  402                "levi_civita(n,o,p,q)(2,2,1,2)");
  404                "levi_civita(n,o,p,q)(2,2,1,3)");
  406                "levi_civita(n,o,p,q)(2,2,2,0)");
  408                "levi_civita(n,o,p,q)(2,2,2,1)");
  410                "levi_civita(n,o,p,q)(2,2,2,2)");
  412                "levi_civita(n,o,p,q)(2,2,2,3)");
  414                "levi_civita(n,o,p,q)(2,2,3,0)");
  416                "levi_civita(n,o,p,q)(2,2,3,1)");
  418                "levi_civita(n,o,p,q)(2,2,3,2)");
  420                "levi_civita(n,o,p,q)(2,2,3,3)");
  422                "levi_civita(n,o,p,q)(2,3,0,0)");
  424                "levi_civita(n,o,p,q)(2,3,0,1)");
  426                "levi_civita(n,o,p,q)(2,3,0,2)");
  428                "levi_civita(n,o,p,q)(2,3,0,3)");
  430                "levi_civita(n,o,p,q)(2,3,1,0)");
  432                "levi_civita(n,o,p,q)(2,3,1,1)");
  434                "levi_civita(n,o,p,q)(2,3,1,2)");
  436                "levi_civita(n,o,p,q)(2,3,1,3)");
  438                "levi_civita(n,o,p,q)(2,3,2,0)");
  440                "levi_civita(n,o,p,q)(2,3,2,1)");
  442                "levi_civita(n,o,p,q)(2,3,2,2)");
  444                "levi_civita(n,o,p,q)(2,3,2,3)");
  446                "levi_civita(n,o,p,q)(2,3,3,0)");
  448                "levi_civita(n,o,p,q)(2,3,3,1)");
  450                "levi_civita(n,o,p,q)(2,3,3,2)");
  452                "levi_civita(n,o,p,q)(2,3,3,3)");
  453 
  455                "levi_civita(n,o,p,q)(3,0,0,0)");
  457                "levi_civita(n,o,p,q)(3,0,0,1)");
  459                "levi_civita(n,o,p,q)(3,0,0,2)");
  461                "levi_civita(n,o,p,q)(3,0,0,3)");
  463                "levi_civita(n,o,p,q)(3,0,1,0)");
  465                "levi_civita(n,o,p,q)(3,0,1,1)");
  467                "levi_civita(n,o,p,q)(3,0,1,2)");
  469                "levi_civita(n,o,p,q)(3,0,1,3)");
  471                "levi_civita(n,o,p,q)(3,0,2,0)");
  473                "levi_civita(n,o,p,q)(3,0,2,1)");
  475                "levi_civita(n,o,p,q)(3,0,2,2)");
  477                "levi_civita(n,o,p,q)(3,0,2,3)");
  479                "levi_civita(n,o,p,q)(3,0,3,0)");
  481                "levi_civita(n,o,p,q)(3,0,3,1)");
  483                "levi_civita(n,o,p,q)(3,0,3,2)");
  485                "levi_civita(n,o,p,q)(3,0,3,3)");
  487                "levi_civita(n,o,p,q)(3,1,0,0)");
  489                "levi_civita(n,o,p,q)(3,1,0,1)");
  491                "levi_civita(n,o,p,q)(3,1,0,2)");
  493                "levi_civita(n,o,p,q)(3,1,0,3)");
  495                "levi_civita(n,o,p,q)(3,1,1,0)");
  497                "levi_civita(n,o,p,q)(3,1,1,1)");
  499                "levi_civita(n,o,p,q)(3,1,1,2)");
  501                "levi_civita(n,o,p,q)(3,1,1,3)");
  503                "levi_civita(n,o,p,q)(3,1,2,0)");
  505                "levi_civita(n,o,p,q)(3,1,2,1)");
  507                "levi_civita(n,o,p,q)(3,1,2,2)");
  509                "levi_civita(n,o,p,q)(3,1,2,3)");
  511                "levi_civita(n,o,p,q)(3,1,3,0)");
  513                "levi_civita(n,o,p,q)(3,1,3,1)");
  515                "levi_civita(n,o,p,q)(3,1,3,2)");
  517                "levi_civita(n,o,p,q)(3,1,3,3)");
  519                "levi_civita(n,o,p,q)(3,2,0,0)");
  521                "levi_civita(n,o,p,q)(3,2,0,1)");
  523                "levi_civita(n,o,p,q)(3,2,0,2)");
  525                "levi_civita(n,o,p,q)(3,2,0,3)");
  527                "levi_civita(n,o,p,q)(3,2,1,0)");
  529                "levi_civita(n,o,p,q)(3,2,1,1)");
  531                "levi_civita(n,o,p,q)(3,2,1,2)");
  533                "levi_civita(n,o,p,q)(3,2,1,3)");
  535                "levi_civita(n,o,p,q)(3,2,2,0)");
  537                "levi_civita(n,o,p,q)(3,2,2,1)");
  539                "levi_civita(n,o,p,q)(3,2,2,2)");
  541                "levi_civita(n,o,p,q)(3,2,2,3)");
  543                "levi_civita(n,o,p,q)(3,2,3,0)");
  545                "levi_civita(n,o,p,q)(3,2,3,1)");
  547                "levi_civita(n,o,p,q)(3,2,3,2)");
  549                "levi_civita(n,o,p,q)(3,2,3,3)");
  551                "levi_civita(n,o,p,q)(3,3,0,0)");
  553                "levi_civita(n,o,p,q)(3,3,0,1)");
  555                "levi_civita(n,o,p,q)(3,3,0,2)");
  557                "levi_civita(n,o,p,q)(3,3,0,3)");
  559                "levi_civita(n,o,p,q)(3,3,1,0)");
  561                "levi_civita(n,o,p,q)(3,3,1,1)");
  563                "levi_civita(n,o,p,q)(3,3,1,2)");
  565                "levi_civita(n,o,p,q)(3,3,1,3)");
  567                "levi_civita(n,o,p,q)(3,3,2,0)");
  569                "levi_civita(n,o,p,q)(3,3,2,1)");
  571                "levi_civita(n,o,p,q)(3,3,2,2)");
  573                "levi_civita(n,o,p,q)(3,3,2,3)");
  575                "levi_civita(n,o,p,q)(3,3,3,0)");
  577                "levi_civita(n,o,p,q)(3,3,3,1)");
  579                "levi_civita(n,o,p,q)(3,3,3,2)");
  581                "levi_civita(n,o,p,q)(3,3,3,3)");
  582}
FTensor::Index< 'i', SPACE_DIM > i
const double n
refractive index of diffusive medium
FTensor::Index< 'l', 3 > l
FTensor::Index< 'j', 3 > j
FTensor::Index< 'k', 3 > k
constexpr std::enable_if<(Dim0<=2 &&Dim1<=2), Tensor2_Expr< Levi_Civita< T >, T, Dim0, Dim1, i, j > >::type levi_civita(const Index< i, Dim0 > &, const Index< j, Dim1 > &)
levi_civita functions to make for easy adhoc use
FTensor::Index< 'm', 3 > m
void test_for_zero(const T &t, const std::string &s)