Quelle tails.c Sprache: C

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

#include "nq.h"
#include "glimt.h"

const char *Warning3 = "Warning : This is not a tail in %s( %d, %d, %d )\n";
const char *Warning2 = "Warning : This is not a tail in %s( %d, %d )\n";

static int tail_cba(gen c, gen b, gen a, expvec *ev) {
int     i, l = 0;
expvec  ev1, ev2;

/* (c b) a */
ev1 = ExpVecWord(Generators[c]);
Collect(ev1, Generators[b], (expo)1);
Collect(ev1, Generators[a], (expo)1);

/* c (b a) = c a b^a */
ev2 = ExpVecWord(Generators[c]);
Collect(ev2, Generators[a], (expo)1);
Collect(ev2, Conjugate[b][a], (expo)1);

for (i = 1; i <= NrPcGens; i++) {
  if (ev1[i] != ev2[i]) printf(Warning3, "tail_cba", c, b, a);
  ev1[i] = (expo)0;
}

for (i = NrPcGens + 1; i <= NrPcGens + NrCenGens; i++) {
  ev1[i] -= ev2[i];
  if (ev1[i] != (expo)0 && Exponent[i] != (expo)0) {
   ev1[i] %= Exponent[i];
   if (ev1[i] < (expo)0) ev1[i] += Exponent[i];
  }

  if (ev1[i] != (expo)0) l++;
}

Free(ev2);
*ev = ev1;
return l;
}

#if 0
static int tail_cbn(gen c, gen b, expvec *ev) {
int     i, l = 0;
expvec  ev1, ev2;

/* (c b) b^(n-1) */
ev1 = ExpVecWord(Generators[c]);
Collect(ev1, Generators[b], Exponent[b]);

/* c b^n */
ev2 = ExpVecWord(Generators[c]);
if (Power[b] != (word)0) Collect(ev2, Power[b], (expo)1);

for (i = 1; i <= NrPcGens; i++) {
  if (ev1[i] != ev2[i]) printf(Warning2, "tail_cbn", c, b);
  ev1[i] = (expo)0;
}

for (i = NrPcGens + 1; i <= NrPcGens + NrCenGens; i++) {
  ev1[i] -= ev2[i];
  if (Exponent[i] != (expo)0) {
   ev1[i] %= Exponent[i];
   if (ev1[i] < (expo)0) ev1[i] += Exponent[i];
  }

  if (ev1[i] != 0) l++;
}

Free(ev2);

*ev = ev1;
return l;
}

static int tail_cnb(gen c, gen b, expvec *ev) {
int     i, l = 0;
expvec  ev1, ev2;

/* b (c^b)^n */
ev1 = ExpVecWord(Generators[b]);
Collect(ev1, Conjugate[c][b], Exponent[c]);

/* c^n b */
ev2 = ExpVecWord(Power[c]);
Collect(ev2, Generators[b], (expo)1);

for (i = 1; i <= NrPcGens; i++) {
  if (ev1[i] != ev2[i]) printf(Warning2, "tail_cnb", c, b);
  ev1[i] = (expo)0;
}

for (i = NrPcGens + 1; i <= NrPcGens + NrCenGens; i++) {
  ev1[i] -= ev2[i];
  if (ev1[i] != (expo)0 && Exponent[i] != (expo)0) {
   ev1[i] %= Exponent[i];
   if (ev1[i] < (expo)0) ev1[i] += Exponent[i];
  }

  if (ev1[i] != 0) l++;
}

Free(ev2);

*ev = ev1;
return l;
}
#endif

static int tail_cbb(gen c, gen b, expvec *ev) {
int     i, l = 0;
expvec  ev1;

/* (c b^-1) b */
ev1 = ExpVecWord(Generators[c]);
Collect(ev1, Generators[ b], (expo)1);
Collect(ev1, Generators[-b], (expo)1);
ev1[ c ] -= 1;

for (i = 1; i <= NrPcGens; i++) {
  if (ev1[i] != (expo)0) printf(Warning2, "tail_cnb", c, b);
}

for (i = NrPcGens + 1; i <= NrPcGens + NrCenGens; i++) {
  ev1[i] = -ev1[i];
  if (ev1[i] != (expo)0 && Exponent[i] != (expo)0) {
   ev1[i] %= Exponent[i];
   if (ev1[i] < (expo)0) ev1[i] += Exponent[i];
  }

  if (ev1[i] != 0) l++;
}

*ev = ev1;
return l;
}

static int tail_ccb(gen c, gen b, expvec *ev) {
int     i, l = 0;
expvec  ev1;

/* c^-1 (c b) = c^-1 b c^b */
ev1 = ExpVecWord(Generators[c]);
Collect(ev1, Generators[b], (expo)1);
Collect(ev1, Conjugate[-c][b], (expo)1);
ev1[abs(b)] -= sgn(b);

for (i = 1; i <= NrPcGens; i++) {
  if (ev1[i] != (expo)0) printf(Warning2, "tail_cnb", c, b);
}

for (i = NrPcGens + 1; i <= NrPcGens + NrCenGens; i++) {
  ev1[i] = -ev1[i];
  if (Exponent[i] != (expo)0) {
   ev1[i] %= Exponent[i];
   if (ev1[i] < (expo)0) ev1[i] += Exponent[i];
  }

  if (ev1[i] != 0) l++;
}

*ev = ev1;
return l;
}

static void Tail(gen n, gen m) {
long    lw, lt;
expvec  t;
word    w;

if (n > 0)
  if (m > 0) lt = tail_cba(n, Definition[m].h, Definition[m].g, &t);
  else        lt = tail_cbb(n, m, &t);
else lt = tail_ccb(n,  m, &t);

lw = WordLength(Conjugate[n][m]);
w  = (word)Allocate((lt + lw + 1) * sizeof(gpower));

WordCopy(Conjugate[n][m], w);
WordCopyExpVec(t, w + lw);
free(t);
if (Conjugate[n][m] != Generators[n]) free(Conjugate[n][m]);
Conjugate[n][m] = w;
}

/*
**    The next nilpotency class to be calculated is Class+1. Therefore
**    commutators of weight Class+1, which are currently trivial, will
**    get tails.
*/
void Tails(void) {

int     *Dim = Dimension;
long    b, c, i, j, time = 0;
long    m, M, n, N;

if (Verbose) time = RunTime();

/*
** Precompute exponents of the new generators which are defined
** as a commutator [h,g] with wt(h)=Class.  There is no conclusive
** evidence that is worth the effort.  One probably also has to use
** those power relations that have a non-trivial right hand side.
*/
#if 0
if (0) {
  int     l;
  gen     i, g, h, t;
  expvec  ev;

  for (t = NrPcGens + 1; t <= NrPcGens + NrCenGens; t++) {
   h = Definition[t].h;
   g = Definition[t].g;
   if (h < 0 || Wt(h) < Class) continue;
   if (g != (gen)0 && Exponent[h] != (expo)0) {
    l = tail_cnb(h, g, &ev);
    /* printf( "t: %d, ", t );
   for( i = 1; i <= NrPcGens+NrCenGens; i++ )
     if( ev[i] != (expo)0 ) printf( " %d^"EXP_FORMAT"", i, ev[i] );
   printf( "\n" );*/
    if (l == 1) {
     if (ev[t] == (expo)0)
      printf("Error, exponent zero\n");
     if (Verbose)
      printf("# Setting exponent "EXP_FORMAT" for %d\n", ev[t], t);
     Exponent[t] = ev[t];
     addRow(ev);
    }
   }
   if (g != (gen)0 && Exponent[g] != (expo)0) {
    l = tail_cbn(h, g, &ev);
    /* printf( "t: %d, ", t );
for( i = 1; i <= NrPcGens+NrCenGens; i++ )
  if( ev[i] != (expo)0 ) printf( " %d^"EXP_FORMAT"", i, ev[i] );
  printf( "\n" );*/
    if (l == 1) {
     if (ev[t] == (expo)0)
      printf("Error, exponent zero\n");
     if (Verbose)
      printf("# Setting exponent "EXP_FORMAT" for %d\n", ev[t], t);
     Exponent[t] = ev[t];
     addRow(ev);
    }
   }
  }
}
#endif

N  = NrPcGens;
for (c = Class; c >= 1; c--) {
  n  = N;
  M  = 1;
  for (b = 1; b <= c - b + 1; b++) {
   /* tails for comutators [ <c-b+1>, <b> ] */
   for (j = Dim[c - b + 1]; j >= 1; j--) {
    m = M;
    for (i = 1; n > m && i <= Dim[b]; i++) {
     if (b != 1)
      Tail(n,  m);
     if (Exponent[m] == (expo)0)
      Tail(n, -m);
     if (Exponent[n] == (expo)0)
      Tail(-n,  m);
     if (Exponent[m] + Exponent[n] == (expo)0)
      Tail(-n, -m);
     m++;
    }
    n--;
   }
   M += Dim[b];
  }
  N  -= Dim[c];
}

if (Verbose)
  printf("# Computed tails (%ld msec).\n", RunTime() - time);
}

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