Quelle eliminate.c Sprache: C

/*****************************************************************************
**
**    eliminate.c                     NQ                       Werner Nickel
**                                         nickel@mathematik.tu-darmstadt.de
*/

#include <assert.h>

#include "nq.h"
#include "glimt.h"
#include "relations.h" /* for ElimAllEpim */

long appendExpVector(gen k, expvec ev, word w, gen *renumber) {
long    l = 0;

/* Copy the negative of the exponent vector ev[] into w. */
for (; k <= NrCenGens; k++) {
  if (ev[k] > (expo)0) {
   if (Exponent[renumber[k]] != (expo)0)
    printf("Warning: Positive entry in matrix.");
   else {
    w[l].g = -renumber[k];
    w[l].e = ev[k];
   }
  } else if (ev[k] < (expo)0) {
   w[l].g = renumber[k];
   w[l].e = -ev[k];
  } else
   continue;
  if (Exponent[abs(w[l].g)] != (expo)0) {
   if (w[l].g < 0)
    printf("Negative exponent for torsion generator.\n");
   if (w[l].e >= Exponent[w[l].g])
    printf("Unreduced exponent for torsion generators.\n");
  }
  l++;
}
w[l].g = EOW;
w[l].e = (expo)0;
l++;
return l;
}

static word elimRHS(word v, long *eRow, gen *renumber, expvec ev, expvec *M) {
word    w;
gen     cg;
long    j, k, l;
expo    s;

w = (word)malloc((NrPcGens + NrCenGens + 1) * sizeof(gpower));
if (w == (word)0) {
  perror("elimRHS(), w");
  exit(2);
}

/* copy the first NrPcGens generators into w. */
l = 0;
while (v->g != EOW && abs(v->g) <= NrPcGens) { w[l] = *v++; l++; }

/* copy the eliminating rows into ev[]. */
while (v->g != EOW) {
  cg = abs(v->g) - NrPcGens;
  if (cg <= 0)
   printf("Warning : non-central generator in elimRHS()\n");
  if (eRow[ cg ] == -1 || M[eRow[cg]][cg] != (expo)1)
   /* generator cg survives. */
   ev[ cg ] += sgn(v->g) * v->e;
  else
   for (k = cg + 1; k <= NrCenGens; k++)
    ev[k] -= sgn(v->g) * v->e * M[eRow[cg]][k];
  v++;
}
/* Reduce all entries modulo the exponents. */
for (k = 1; k <= NrCenGens; k++)
  if (renumber[k] > 0 && Exponent[renumber[k]] > (expo)0)
   if ((s = ev[k] / Exponent[renumber[k]]) != (expo)0
           || ev[k] < (expo)0) {
    if (ev[k] - s * M[eRow[k]][k] < (expo)0)  s--;
    for (j = k; j <= NrCenGens; j++)
     ev[j] -= s * M[eRow[k]][j];
   }
/* Now copy the exponent vector back into the word. */
for (k = 1; k <= NrCenGens; k++) {
  if (ev[k] > (expo)0) {
   w[l].g = renumber[k];
   w[l].e = ev[k];
  } else if (ev[k] < (expo)0) {
   w[l].g = -renumber[k];
   w[l].e = -ev[k];
  } else continue;
  if (Exponent[abs(w[l].g)] != (expo)0) {
   if (w[l].g < 0)
    printf("Negative exponent for torsion generator.\n");
   if (w[l].e >= Exponent[w[l].g])
    printf("Unreduced exponent for torsion generators.\n");
  }
  l++;
}
w[l].g = EOW;
w[l].e = (expo)0;
l++;

for (k = 1; k <= NrCenGens; k++) ev[k] = (expo)0;

return (word)realloc(w, l * sizeof(gpower));
}

void ElimGenerators(void) {

long    i, j, k, l, n = 0, *eRow, t = 0;
expvec  ev, *M = 0;
gen     *renumber;
word    v, w;

if (Verbose) t = RunTime();

M = MatrixToExpVecs();

/* first assign a new number to each central generator which is
   not to be eliminated. */
renumber = (gen*) calloc(NrCenGens + 1, sizeof(gen));
if (renumber == (gen*)0) {
  perror("elimGenerators(), renumber");
  exit(2);
}
for (k = 1, i = 0; k <= NrCenGens; k++)
  if (i >= NrRows || k != Heads[i])
   renumber[ k ] = NrPcGens + k - n;
  else if (M[i][k] != 1) {  /* k will become a torsion element */
   renumber[ k ] = NrPcGens + k - n;
   Exponent[ renumber[k] ] = M[i][k];
   i++;
  } else {                  /* k will be eliminated. */
   n++;
   i++;
  }

/* extend the memory for Power[], note that n is the number of
   generators to be eliminated. */
Power = (word*)realloc(Power, (NrPcGens + NrCenGens + 1 - n) * sizeof(word));
if (Power == (word*)0) {
  perror("elimGenerators(), Power");
  exit(2);
}

/* extend the memory for Definition[]. */
Definition =
     (def*)realloc(Definition, (NrPcGens + NrCenGens + 1 - n) * sizeof(def));
if (Definition == (def*)0) {
  perror("elimGenerators(), Definition");
  exit(2);
}

/* first we eliminate ALL central generators that occur in the
** epimorphism. */
i = ElimAllEpim(n, M, renumber);

/* secondly we eliminate ALL generators from right hand sides of
** power relations. */
for (j = 1; j <= NrPcGens; j++)
  if (Exponent[j] != (expo)0) {
   l = WordLength(Power[ j ]);
   w = (word)malloc((l + NrCenGens + 1 - n) * sizeof(gpower));
   WordCopy(Power[ j ], w);
   l--;
   l += appendExpVector(w[l].g + 1 - NrPcGens, M[i], w + l, renumber);

   if (Power[j] != (word)0) free(Power[j]);
   if (l == 1) {
    Power[j] = (word)0;
    free(w);
   } else
    Power[j] = (word)realloc(w, l * sizeof(gpower));
   i++;
  }

/* Thirdly we eliminate the generators from the right hand
** side of conjugates, but before that we fix the definitions
** of surviving generators. */

/* set up an array that specifies the row which eliminates a
** generator. */
eRow = (long*)malloc((NrCenGens + 1) * sizeof(long));
if (eRow == (long*)0) {
  perror("elimGenerators(), eRow");
  exit(2);
}
for (k = 0; k <= NrCenGens; k++) eRow[ k ] = -1;
for (k = 0; k <  NrRows;    k++) eRow[ Heads[k] ] = k;

ev = (expvec)calloc((NrCenGens + 1), sizeof(expo));
if (ev == (expvec)0) {
  perror("elimGenerators(), ev");
  exit(2);
}
for (j = 1; j <= NrPcGens; j++)
  for (i = 1; i < j; i++) {
   if (Wt(j) + Wt(i) > Class + 1) continue;

   k = Conjugate[j][i][1].g - NrPcGens;
   if (k > 0 &&
           i <= Dimension[1] && j > NrPcGens - Dimension[Class] &&
           (eRow[ k ] == -1 || M[eRow[k]][k] != (expo)1)) {
    /* Fix the definitions of surviving generators and
** their power relations. */
    Conjugate[j][i][1].g = renumber[k];
    Definition[ renumber[k] ].h  = j;
    Definition[ renumber[k] ].g  = i;
    if (eRow[ k ] != -1) {
     w = (word)malloc((NrCenGens + 1 - n) * sizeof(gpower));
     if (w == (word)0) {
      perror("elimGenerators(), w");
      exit(2);
     }
     l = appendExpVector(k + 1, M[eRow[k]], w, renumber);
     w = (word)realloc(w, l * sizeof(gpower));
     Power[ renumber[k] ] = w;
    }
   } else {
    v = elimRHS(Conjugate[j][i], eRow, renumber, ev, M);
    if (Conjugate[j][i] != Generators[j])
     free(Conjugate[j][i]);
    Conjugate[j][i] = v;
   }

   if (Exponent[i] == (expo)0) {
    v = elimRHS(Conjugate[j][-i], eRow, renumber, ev, M);
    if (Conjugate[j][-i] != Generators[j])
     free(Conjugate[j][-i]);
    Conjugate[j][-i] = v;
   }
   if (Exponent[j] == (expo)0) {
    v = elimRHS(Conjugate[-j][i], eRow, renumber, ev, M);
    if (Conjugate[-j][i] != Generators[-j])
     free(Conjugate[-j][i]);
    Conjugate[-j][i] = v;
   }
   if (Exponent[j] + Exponent[i] == (expo)0) {
    v = elimRHS(Conjugate[-j][-i], eRow, renumber, ev, M);
    if (Conjugate[-j][-i] != Generators[-j])
     free(Conjugate[-j][-i]);
    Conjugate[-j][-i] = v;
   }
  }

/* Now adjust the sizes of the arrays */
assert(Commute == CommuteList[ Class + 1 ]);
Commute   = (gen*)realloc(Commute,
                           (NrPcGens + NrCenGens + 1 - n) * sizeof(gen));
CommuteList[ Class + 1 ] = Commute;
Exponent = (expo*)realloc(Exponent,
                          (NrPcGens + NrCenGens + 1 - n) * sizeof(expo));

free(renumber);
free(ev);
free(eRow);

if (M != (expvec*)0) freeExpVecs(M);
NrCenGens -= n;

if (Verbose)
  printf("# Eliminated generators (%ld msec).\n", RunTime() - t);
}

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