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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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#include "polymake_tropical.h"

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Obj REAL_TROPICAL_HYPERSURFACE_BY_MONOMS_AND_COEFFICIENTS( Polymake_Data* data, Obj monomials, Obj coefficients ){

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#ifdef MORE_TESTS

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  if( ! IS_PLIST( monomials ) ){

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    ErrorMayQuit( "not a plain list", 0, 0);

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    return NULL;

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  }

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#endif

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  int len = LEN_PLIST( monomials );

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  Obj akt = ELM_PLIST( monomials, 1 );

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  Obj elem;

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#ifdef MORE_TESTS

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  if( !IS_PLIST( akt ) ){

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    ErrorMayQuit( "not a plain list", 0, 0);

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    return NULL;

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  }

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#endif

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#ifdef MORE_TESTS

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  if( !IS_PLIST( coefficients ) ){

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     ErrorMayQuit( "coefficients not a plain list", 0, 0);

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    return NULL;

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  }

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#endif

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  int len_elem = LEN_PLIST( akt );

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  data->main_polymake_session->set_application("tropical");

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  pm::Integer* ratarray;

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  ratarray = new pm::Integer[(len)*(len_elem)];

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  pm::Integer* coeffarray;

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  coeffarray = new pm::Integer[len];

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  for(int i=1;i<=len;i++){

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      akt = ELM_PLIST( monomials, i );

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#ifdef MORE_TESTS

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      if( !IS_PLIST( akt ) ){

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        delete [] ratarray;

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        delete [] coeffarray;

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        ErrorMayQuit( "not a plain list", 0, 0);

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        return NULL;

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      }

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      if( LEN_PLIST( akt ) != len_elem ){

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        delete [] ratarray;

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        delete [] coeffarray;

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        ErrorMayQuit( "monomials are not of the same lenght", 0, 0);

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        return NULL;

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      }

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#endif

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      for(int j = 1; j <= len_elem; j++){

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        elem = ELM_PLIST( akt, j);

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#ifdef MORE_TESTS

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        if( ! IS_INTOBJ( elem ) ){

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          delete [] ratarray;

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          delete [] coeffarray;

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          ErrorMayQuit( "some entries are not integers", 0, 0);

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          return NULL;

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        }

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#endif

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        ratarray[(i-1)*(len_elem)+j-1] = INT_INTOBJ( elem );

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      }

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      elem = ELM_PLIST( coefficients, i );

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#ifdef MORE_TESTS

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        if( ! IS_INTOBJ( elem ) ){

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          delete [] ratarray;

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          delete [] coeffarray;

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          ErrorMayQuit( "some entries are not integers", 0, 0);

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          return NULL;

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        }

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#endif

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      coeffarray[ i - 1 ] = INT_INTOBJ( elem );

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  }

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  pm::Matrix<pm::Integer>* matr = new pm::Matrix<pm::Integer>(len,len_elem,ratarray);

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  delete [] ratarray;

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  pm::Vector<pm::Integer>* coeff = new pm::Vector<pm::Integer>(len,coeffarray);

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  delete [] coeffarray;

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  perlobj* p = new perlobj("TropicalHypersurface");

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  p->take("MONOMIALS") << *matr;

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  p->take("COEFFICIENTS") << *coeff;

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  delete matr;

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  delete coeff;

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  elem = NewPolymakeExternalObject( T_POLYMAKE_EXTERNAL_TROPICAL_HYPERSURFACE );

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  POLYMAKEOBJ_SET_PERLOBJ( elem, p );

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  return elem;

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}

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Obj REAL_MONOMIALS_OF_HYPERSURFACE( Polymake_Data* data, Obj hypersurf){

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#ifdef MORE_TESTS

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  if(! IS_POLYMAKE_TROPICAL_HYPERSURFACE(hypersurf) ){

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    ErrorMayQuit(" parameter is not a hypersurface.",0,0);

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    return NULL;

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  }

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#endif

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  perlobj* polyobj = PERLOBJ_POLYMAKEOBJ( hypersurf );

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  data->main_polymake_session->set_application_of(*polyobj);

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  pm::Matrix<pm::Rational> matr;

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  try{

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      pm::Matrix<pm::Rational> matr_temp = polyobj->give("MONOMIALS");

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      matr = matr_temp;

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  }

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  POLYMAKE_GAP_CATCH

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  UInt l = 10;

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  Obj RETLI = NEW_PLIST( T_PLIST , l );

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  SET_LEN_PLIST(RETLI, l );

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  UInt k = 0;

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  Obj LIZeil;

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  UInt matr_cols = matr.cols();

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  for(int i = 0;i<matr.rows();i++){

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      if( ++k > l){

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        GROW_PLIST(RETLI,l*=2);

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        SET_LEN_PLIST(RETLI, l );

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      }

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      LIZeil = NEW_PLIST( T_PLIST, matr.cols());

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      SET_LEN_PLIST( LIZeil , matr_cols );

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      for(int j = 0;j<matr.cols();j++){

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        SET_ELM_PLIST(LIZeil,j+1,INTOBJ_INT((matr(i,j)).to_int()));

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      }

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      SET_ELM_PLIST(RETLI,k,LIZeil);

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      CHANGED_BAG(RETLI);

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  }

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  SHRINK_PLIST(RETLI,k);

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  SET_LEN_PLIST(RETLI, k );

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  return RETLI;

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}

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Obj REAL_TROPICAL_POLYTOPE_BY_POINTS( Polymake_Data* data, Obj points ){

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    if( ! IS_PLIST( points ) ){

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    ErrorMayQuit( "not a plain list", 0, 0);

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    return NULL;

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  }

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  int len = LEN_PLIST( points );

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  Obj akt = ELM_PLIST( points, 1 );

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  Obj elem;

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#ifdef MORE_TESTS

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  if( !IS_PLIST( akt ) ){

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    ErrorMayQuit( "first ray is not a plain list", 0, 0);

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    return NULL;

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  }

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#endif

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  int len_elem = LEN_PLIST( akt );

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  data->main_polymake_session->set_application("tropical");

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  pm::Integer* ratarray;

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  ratarray = new pm::Integer[(len)*(len_elem)];

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  for(int i=0;i<len;i++){

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      akt = ELM_PLIST( points, i+1 );

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#ifdef MORE_TESTS

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      if( !IS_PLIST( akt ) ){

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        delete [] ratarray;

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        ErrorMayQuit( "one point is not a plain list", 0, 0);

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        return NULL;

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      }

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      if( LEN_PLIST( akt ) != len_elem ){

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        delete [] ratarray;

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        ErrorMayQuit( "points are not of the same lenght", 0, 0);

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        return NULL;

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      }

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#endif

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      for(int j = 0; j < len_elem; j++){

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        elem = ELM_PLIST( akt, j+1);

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#ifdef MORE_TESTS

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        if( ! IS_INTOBJ( elem) ){

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          delete [] ratarray;

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          ErrorMayQuit( "some entries are not integers", 0, 0);

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          return NULL;

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        }

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#endif

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        ratarray[ ( i * len_elem ) + j] = INT_INTOBJ( elem );

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      }

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  }

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  pm::Matrix<pm::Integer>* matr = new pm::Matrix<pm::Integer>(len,len_elem,ratarray);

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  delete [] ratarray;

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  perlobj* p = new perlobj("TropicalPolytope");

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  p->take("POINTS") << *matr;

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  delete matr;

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  elem = NewPolymakeExternalObject(T_POLYMAKE_EXTERNAL_POLYTOPE);

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  POLYMAKEOBJ_SET_PERLOBJ(elem, p);

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  return elem;

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}

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