/*  This file constructs a PC presentation for a generalised
Nottingham group in Gap format.
*/

#include "global.h"

#include <stdio.h>

/* Prototypes */

void GAPfprintvec(vector v, FILE *fp);
void GAPfpowers(FILE *fp);
void GAPfcommutators(FILE *fp);
void GapPres(void);

extern int prime, rank, total;

void GAPfprintvec(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, " a1^0 ");
}

void GAPfpowers(FILE *fp)
{
  int i, j, k, t = 1;
  vector v;
  group_elt g, h;
  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);
      groupinv(g,h);
      normalform(h, v);
      fprintf(fp, "a%d^%d * ",t++ , prime);
      GAPfprintvec(v, fp);
      fprintf(fp, ",\n");
    }
}

void GAPfcommutators(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(g, h, c);
           fprintf(fp, "Comm(a%d,a%d)*",t,s);          
           normalform(c, vec);
           GAPfprintvec(vec, fp);
           if (t != rank * (total - rank - 1) || s != t-1) fprintf(fp,",");
           fprintf(fp,"\n");
         }
        }
    }
}       
      
void GapPres(void)
{
  int complength, i;
  FILE *fp;
  set_file(&fp);
  complength = rank * (total - rank - 1);
  for(i = 0; i < complength; i++)
  {
    fprintf(fp, "a%d:=AbstractGenerator(\"a%d\");\n", i+1, i+1);
  }
  fprintf(fp, "generators:=[");
  for (i = 0; i < complength; i++)
  {
    fprintf(fp, "a%d", i+1);
    if (i < complength -1) fprintf(fp, ",");
  }
  fprintf(fp, "];");
  fprintf(fp,"\n relators:=[");
  GAPfpowers(fp);
  GAPfcommutators(fp);
  fprintf(fp, "];\n");
  fprintf(fp, "G := AgGroupFpGroup(rec(generators:=generators, relators:=relators));");
}