standalone/progs.d/pkp.c

#include "defs.h"

extern char inf[],outf[],temp[],temp2[],mspace[],*vec[],**mat[],
     cvec[],pinv[],mstr[],full,intop,opt,aut;
extern short svec[],mdim,mv,mm,mpr,msl;
extern int space;
char prime;
short dim,maxnull;

FILE *ip,*op;

int
pkprog (void)
{ char ngens,neg,fac,there,saved,gottm,gotsgn,err,digexp,nc,provn,
       trd,gotfac,heldc,len,**m0,**m1,*m01,irr;
  short nvecs,i,j,rno1,rno2,nlty,fnz,adno,sdim,qdim,tdim;
  int msp;
  irr= opt ? 1 : 0;
  if ((ip=fopen(inf,"r"))==0)
  { fprintf(stderr,"Cannot open %s.\n",inf); return(-1);}
  fscanf(ip,"%hd%hd%hd",&rno1,&dim,&rno2);
  prime=rno1; ngens=rno2;
  if (prime>mpr)
  { fprintf(stderr,"prime too big. Nothing to be done.\n"); return(-1);}
  if (dim>mdim)
  { fprintf(stderr,"dim too big. Increase MDIM.\n"); return(-1);}
  if (ngens>=mm)
  { fprintf(stderr,"Too many generators. Nothing to be done.\n"); return(-1);}
  nvecs=dim*(ngens+1);
  if (nvecs>mv)
  { fprintf(stderr,"Too many vectors. Increase MV.\n"); return(-1);}
  msp=nvecs*dim;
  if (msp>space)
  { fprintf(stderr,"Not enough space. Increase SPACE.\n"); return(-1);}
  seeknln(); setpinv();
/* Set vector and matrix pointers, as usual.
   We take care only to use ngens+1 matrices, thus saving as much storage as
   possible. This means using temporary files to store matrices occasionally.
*/
  for (i=0;i<nvecs;i++) vec[i]= mspace-1+i*dim;
  for (i=0;i<=ngens;i++) mat[i]=vec-1+i*dim;
  for (i=1;i<=ngens;i++) readmat(mat[i]);
  fclose(ip);
  if (aut)
  { printf("Enter maximum value of nullity that should be handled:   ");
    scanf("%hd",&maxnull);
  }
  m0=mat[0]; m1=mat[1]; m01=m0[1];
/* The next section reads in the given expression in the generators, and
   computes the corresponding matrix as m0. A temporary file is used to
   remember the sum so far, whilst a product is being computed.
*/
  while (1)
  { printf("Enter element of group algebra. End expression with $. Example:\n");
    printf("Enter 3a[3]a[3]a[2] + a[2] - a[4]  as  3.3*3*2 + 2 - 4$\n");
    fflush(stdout);
    there=0; saved=0; heldc=0; err=0;
    while (heldc!='$')
    { gotfac=0; gotsgn=0; gottm=0; provn=0; digexp=0; len=0;
      while (gottm==0)
      { if (heldc) { nc=heldc; heldc=0;} else nc=findc();
        if (gotsgn==0)
        { if (nc=='-') { neg=1; gotsgn=1; digexp=1; continue;}
          else if (nc=='+') { neg=0; gotsgn=1; digexp=1; continue;}
          else if (there==0) { neg=0; gotsgn=1; digexp=1;}
        }
        if ((nc=='+' || nc=='-' || nc=='$') && digexp==0 && (len!=0 || provn!=0))
        { heldc=nc; gottm=1;
          if (gotfac==0)
          { if (provn)
            { fac= neg ? prime-1 : 1; len=1; mstr[1]=provn-'0';}
          }
        }
        else if (nc=='.' && digexp==0 && provn!=0 && gotfac==0)
        { gotfac=1; fac=provn-'0'; fac%=prime; provn=0;
          if (neg) fac=prime-fac; digexp=1;
        }
        else if (nc=='*' && digexp==0 && (provn!=0 || len!=0))
        { if (gotfac==0)
          { gotfac=1; fac= neg ? prime-1 : 1; len=1; mstr[1]=provn-'0';}
          digexp=1;
        }
        else if (digit(nc) && digexp)
        { if (gotfac==0) provn=nc;
          else { len++; mstr[len]= nc-'0';}
          digexp=0;
        }
        else
        { fprintf(stderr,"Format error; Try again.\n"); err=1;
          while (getchar()!='\n');
          break;
        }
      }
      if (err) break;
      if (len==1)
      { if (there) sum(fac,mat[mstr[1]],m0); else ncopy(fac,mat[mstr[1]],m0);}
      else
      { if (there)
/* We have a partial sum, and now another product to compute, so we must
   store the partial sum in a temporary file.
*/
        { op=fopen(temp,"w"); printmat(m0); saved=1; fclose(op);}
        ncopy(fac,mat[mstr[1]],m0);
        for (i=2;i<=len;i++) prod(m0,mat[mstr[i]],m0);
        if (saved)
        { ip=fopen(temp,"r");
          for (i=1;i<=dim;i++) rvecsum(1,m0[i]);
          fclose(ip); saved=0;
        }
      }
      there=1;
    }
    if (err) continue;
/* err means the expression input was garbled */
    if (intop) for (i=1;i<=dim;i++)
    { for (j=1;j<=dim;j++) printf("%3d",m0[i][j]); printf("\n"); }
/* Store the matrix m0 in a temporary file temp. Then compute its nullity.
   (nlty writes generators of the null space to another temporary file, temp)
*/
    op=fopen(temp2,"w"); printmat(m0); fclose(op);
    op=fopen(temp,"w"); nlty=null(m0,m1); fclose(op);
    ip=fopen(inf,"r"); seeknln(); readmat(m1); fclose(ip);
    if (nlty==0 || (aut && nlty>maxnull)) continue;
    if (aut) break;
    printf("Shall we use this matrix (y/n)?  ");
    nc=findc();
    if (nc=='y') break;
  }
/* Now we have chosen the matrix that we are going to use for the irreducibility
   test. Next we arrange to consider the one-dimensional subspaces of the
   null-space in order. cvec is used for this purpose.
*/
  for (i=1;i<=nlty;i++) cvec[i]=0;
  fnz=nlty; adno=nlty; trd=0;
  while (fnz!=0)
  { cvec[adno]++;
    for (i=1;i<=dim;i++) m01[i]=0;
/* Compute the current vector in the nullspace by reading from the file temp,
   and store it in m01
*/
    ip=fopen(temp,"r");
    for (i=1;i<=nlty;i++)
    { if ((fac=cvec[i])==0) seeknln(); else {rvecsum(fac,m01); seeknln();}}
    fclose(ip);
    if (intop)
    { for (j=1;j<=dim;j++) printf("%3d",m01[j]); printf("\n");
      if (opt)
      { printf("Shall we skip this one?   "); nc=findc();
        if (nc=='y') goto next;
      }
    }
/* Now compute the subspace it generates */
    sdim=spgen(m0,ngens);
    if (intop)
    { for (i=1;i<=dim;i++) printf("%3d",svec[i]); printf("\n");
      for (i=1;i<=dim;i++)
      { for (j=1;j<=dim;j++) printf("%3d",m0[i][j]); printf("\n");}
    }
    if (sdim<dim)
/* sdim<dim means the module is reducible */
    if (opt==0) break;
    else
    { printf("Shall we compute (y/n)?  ");
      nc=findc();
      if (nc=='y') { opt=0; break;}
      irr=0;
    }
next:
/* The last vector generated the whole space, so go on to the next */
    adno=nlty;
    while (cvec[adno]==prime-1) { cvec[adno]=0; adno--;}
    if (adno<=fnz) { if (adno==fnz) {cvec[adno]=0; adno--;} fnz--;}
  }
  if (opt || sdim==dim)
/* Each vector in the null-space generated the whole space. Finally we have to
   transpose everything, and try just one vector in the null-space.
*/
  { printf("Transforming.\n"); fflush(stdout); trd=1;
    ip=fopen(temp2,"r"); readmat(m0); fclose(ip);
    trans(m0,m1); op=fopen(temp,"w"); null1(m1,m0); fclose(op);
/* That ruined m1 (the first generator), so we must re-read it */
    ip=fopen(inf,"r"); seeknln(); readmat(m1); fclose(ip);
    for (i=1;i<=ngens;i++) {trans(mat[i],m0); copy(m0,mat[i]);}
    ip=fopen(temp,"r");
    for (i=1;i<=dim;i++) {fscanf(ip,"%hd",&rno1); m01[i]=rno1;}
    fclose(ip);
    sdim=spgen(m0,ngens);
    if (opt && sdim<dim)
    { printf("Shall we compute (y/n)?  ");
      nc=findc();
      if (nc=='y') opt=0; else irr=0;
    }
    if (intop)
    { for (i=1;i<=dim;i++) printf("%3d",svec[i]); printf("\n");
      for (i=1;i<=dim;i++)
      { for (j=1;j<=dim;j++) printf("%3d",m0[i][j]); printf("\n");}
    }
  }

  if (opt && irr==0) { unlink(temp); unlink(temp2); return(0);}
  if (sdim==dim)
  { printf("Module is irreducible.\n");
    unlink(temp); unlink(temp2);return(0);
  }
/* Space is reducible. Finally, we compute the generators of the subspace
   and quotient space
*/
  qdim=dim-sdim;
  strcpy(outf,inf);
  if (full) { strcat(outf,"f"); tdim=dim;}
  else { strcat(outf,"s"); tdim=sdim;}
/* if we have transposed, then we first output to the temporary file,
   and then later read it back in and transpose it back again.
*/
  if (trd) op=fopen(temp,"w");
  else { op=fopen(outf,"w"); fprintf(op,"%3d%5d%3d\n",prime,tdim,ngens);}
  opnmat(m0,ngens,tdim,1);
  if (trd==0|| full) fclose(op);
  if (full==0)
  { strcpy(outf,inf); strcat(outf,"q");
    if (trd==0)
    { op=fopen(outf,"w"); fprintf(op,"%3d%5d%3d\n",prime,qdim,ngens);}
    opnmat(m0,ngens,dim,sdim+1);
    fclose(op);
  }
  if (trd)
  { if (full==0) dim=sdim;
/* Retranspose */
    ip=fopen(temp,"r"); op=fopen(outf,"w");
    fprintf(op,"%3d%5d%3d\n",prime,dim,ngens);
    for (i=1;i<=ngens;i++)
    { readmat(m0); trans(m0,m1); printmat(m1);}
    fclose(op);
    if (full==0)
    { dim=qdim; strcpy(outf,inf); strcat(outf,"s");
      op=fopen(outf,"w"); fprintf(op,"%3d%5d%3d\n",prime,dim,ngens);
      for (i=1;i<=ngens;i++)
      { readmat(m0); trans(m0,m1); printmat(m1);}
      fclose(ip); fclose(op);
    }
  }
  unlink(temp); unlink(temp2); return(0);
}

void seeknln (void) { while (getc(ip)!='\n');}

void setpinv (void)
{ int 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; }
}

int findc (void)
{ char c; while ((c=getchar())==' ' || c=='\n'); return(c); }

int digit (int c)
{ if (c>='1' && c<='9') return(1); else return(0);}