/*  This file constructs a PC presentation for a generalised
Nottingham group in MAGMA format.
It exports Mpres to interpret.c.
*/

#include "global.h"

#include <stdio.h>

extern int prime, rank, total;

/* Imports from group_elt.c */

void initgroupelt(group_elt g);
void gpower(group_elt g, int n);
void commutator(group_elt f, group_elt g, group_elt h);

/* Imports from presentation.c */

void normalform(group_elt g, vector v);

/* Prototypes */

void set_file(FILE **fp_ptr);
void fprintvec(vector v, FILE *fp);
void fpowers(FILE *fp);
void fcommutators(FILE *fp);
void Mpres(void);

void set_file(FILE **fp_ptr)
{
  char s[2], fname[20];
  printf("Do you want to direct the presentation to a file? y/n.\n");
  scanf("%1s", s);
  if (s[0] == 'y')
  {
    printf("Enter filename:\n");
    scanf("%s", fname);
    *fp_ptr = fopen(fname, "w");
  }
  else *fp_ptr = stdout;
}

void fprintvec(vector v, FILE *fp)
{
  int i, id = 1;
  for(i = 0; i < (total - rank - 1) * rank; i++)
    if (v[i])
      { if (!id) fprintf(fp, "* ");
        fprintf(fp, "a%d^%d ", i + 1,  v[i]); id = 0;
      }
  if (id) fprintf(fp, " 1 ");
}

void fpowers(FILE *fp)
{
  int i, j, k, t = 1;
  vector v;
  group_elt g;
  for(i = rank + 1; i < total; i++)
    for(j = 0; j < rank; j++)   
    {
      initgroupelt(g);
      for(k = 0; k < rank; k++)
        g[k][rank - k] = 1;
      g[j][i] = 1;
      gpower(g, prime);
      normalform(g, v);
      fprintf(fp, "a%d^%d = ",t++ , prime);
      fprintvec(v, fp);
      fprintf(fp, ",\n");
    }
}

void fcommutators(FILE *fp)
{
  vector vec;
  group_elt g, h, c;
  int i, j, u, v, k, t, s = 0;
  for(i = rank + 1; i < total; i++)
    for(j = 0; j < rank; j++)
    {
      initgroupelt(g);
      for(k = 0; k < rank; k++)
        g[k][rank - k] = 1;
      g[j][i] = 1;
      s++;
      t = 0;
      for(u = rank + 1; u < total; u++)
        for(v = 0; v < rank; v++)
        {
         t++;
         if (t>s)
         {
           initgroupelt(h);
           for(k = 0; k < rank; k++)
             h[k][rank - k] = 1;
           h[v][u] = 1;
           commutator(h, g, c);
           fprintf(fp, "(a%d,a%d)=",t,s);          
           normalform(c, vec);
           fprintvec(vec, fp);
           if (t != rank * (total - rank - 1) || s != t-1) fprintf(fp,",");
           fprintf(fp,"\n");
         }
        }
    }
}       
      
void Mpres(void)
{
  int complength, i;
  FILE *fp;
  set_file(&fp);
  complength = rank * (total - rank - 1);
  fprintf(fp, "G<");
  for (i = 0; i < complength; i++)
  {
    fprintf(fp, "a%d", i+1);
    if (i < complength - 1) fprintf(fp, ",");
  }  
  fprintf(fp, "> := PolycyclicGroup<");
  for (i = 0; i < complength; i++)
  {
    fprintf(fp, "a%d", i+1);
    if (i < complength - 1) fprintf(fp, ",");
  }
  fprintf(fp, "|\n");
  fpowers(fp);
  fcommutators(fp);
  fprintf(fp, ">;\n");
}