milnor.cpp

#include <fstream>
#include <iostream>
#include "tables.H"
#include "algebras.H"
#include "my_gmp.H"
#include "ftwo.H"
#include <string>
#include "derive.H"
#include "cmdline.H"
using namespace std;


int main(int argc, char** argv)
{
  // initialization   /////////////////////////////

  CommandLine::init(argc, argv);
  string name= CommandLine::parameters[0] + ".final";

  ifstream my_source(name.c_str());
  if(my_source.fail()) {
    cout << "cannot read file" << endl;
    return 2;
  }

  UnstableAlgebra A;
  my_source >> A;

//   Polynomial<F_2> x, y, z, t, u, P;//these commented
//   x=  A.new_variable("X", 1);            //lines correspond
//   y=  A.new_variable("Y", 1);            //to an example
//   z=  A.new_variable("Z", 1);            //written "by hand"
//   // t=  A.new_variable("T", 1);         //rather than loaded
//   //  u=  A.new_variable("D", 4);        //from a file.
//   A.write_trivial_steenrod_operations();
//   P= A.one();
//  //  P.sets_to_zero();
// //   A.steenrod[3][1]= P;
// //   A.steenrod[3][2]= P;
// //   A.steenrod[3][3]= P;

// //   A.add_relation(x*x + x*y + y*y);
//   //A.add_relation(x*y + z*t);
//   A.saturate_and_reduce();
  A.display();
  A.find_grobner_basis();

  MilnorAnalyzer der;
  der.start( &A );
  
  GradedAlgebra<F_2> milnor;
  AffineHomomorphism<F_2> reduction, section, milnor_inclusion;
  // we make a copy of der.ans, which is the
  // answer, and we find a simpler presentation
  milnor= der.ans;
  milnor.fix_alphabets();
  //set the reduction homomorphism
  reduction.source= &der.ans;
  reduction.target= &milnor;
  milnor.split_and_sort_relations();
  reduction.get_data_from( milnor.find_redundancies() );
  //now find a section for it
  section= reduction.simple_section();
  milnor_inclusion= der.ans_inclusion * section;

  cout << "Milnor constants: " << endl
       << milnor << endl
       << "where: " << endl
       << milnor_inclusion
       << endl;
  //now save
  string out_name= CommandLine::parameters[0] + ".milnor";
  ofstream my_out(out_name.c_str());

  milnor.relations.generators.clear();
  my_out << milnor;
  my_out << milnor_inclusion;

  return 0;
}

 

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