#include <stdio.h>
extern short npt,nb,npt1,exp,prime,pinv[],cp[],power[],wt[],base[],
             ngno[],igno[],*svptr[],*pptr[],d1[];

/* Let the central series for P be P=P(n)>...>P(1)>P(0)=1. The procedures
   in this file express a permutation g in P in in its normal form in the
   PCP generators. Let the Schreier vector generators be g(n),...,g(1) and the
   PCP generators h(n),...,h(1), with g(i),h(i) in P(i)-P(i-1).
   Then we have g(i)=h(i)^x * k, with k in P(i-1), and the exponent x is
   stored as power[i].
*/
firstgen(p,hg,co) short *p,*hg,*co;
/* Let the perm p be  g(i)^t * k with k in H(i-1). This procedure computes i
   and t, and returns them as *hg and *co.
*/
{ short i,j;
  *cp=0;
  for (i=1;i<=nb;i++) addsv(image(p[base[i]]),svptr[i]);
  *co=0; *hg=0;
  for (i=1;i<= *cp;i++)
  { j=igno[cp[i]];
    if (j> *hg) { *hg=j; *co=1; }
    else if (j== *hg) (*co)++;
  }
  (*co) %= prime;
}

express(p,relc,nwt) short *p,*relc,nwt;
/* This computes the full PCP expression for the perm p, and puts as a gen-pow
   string in rel, preceded by its length. If weights are involved, then nwt is
   the weight of p at this point. Otherwise nwt=0.
*/
{ short hgen,h,l,coeff,pow,m,n,*ip,*gp,pt;
  l=0; h=exp; ip=p+npt1;
  while (1)
  { firstgen(p,&hgen,&coeff);
    if (hgen>h) {fprintf(stderr,"Expression error.\n"); return(-1); }
    if (hgen==0) break;
    l++; relc[l]=exp+1-hgen;
    if ((nwt && wt[hgen]<nwt) || (nwt && wt[hgen]==nwt && d1[hgen]==0))
    { power[hgen]=pinv[coeff]; l++; relc[l]=1; *relc=l; return(hgen);}
/* We return at this point, because PCP gen no hgen will be replaced by p */
    pow= (coeff*power[hgen])%prime; l++; relc[l]=pow;
    gp=pptr[ngno[hgen]];
    for (n=1;n<=npt;n++) {pt=ip[n]; for (m=1;m<=pow;m++) pt=gp[pt];p[pt]=n;}
    invert(p,ip); h=hgen-1;
  }
  *relc=l;
  return(0);
}

setpinv()
{ short i,j;
  for (i=0;i<prime;i++) pinv[i]=0;
  for (i=1;i<prime;i++) if (pinv[i]==0) for (j=1;j<prime;j++)
  if (i*j % prime ==1) { pinv[i]=j; pinv[j]=i; break; }
}
