Quelle pcarith.c Sprache: C

/****************************************************************************
**
**    pcarith.c                       NQ                       Werner Nickel
**                                         nickel@mathematik.tu-darmstadt.de
**
**    This file contains an arithmetic for elements of a group that is
**    given by a polycyclic presentation. The elements are in generator
**    exponent form. Multiplication is performed by a collection process.
**    There are the following functions :
**
**
**    int  WordCmp( u, w )  ......... Compare the two words u and w and
**                                    return 0, if the words are equal and
**                                    1 otherwise.
**    void WordCopy( u, w ) ......... Copy the word u to the word w. It is
**                                    assumed that storage for w has already
**                                    been allocated.
**    int  WordLength( u )  ......... Return the length of the word u, i.e.,
**                                    the number of powers of generators in u.
**    word WordGen( g )     ......... Return the image under the epimorphism
**                                    of the generator number g.
**    word WordMult( u, w ) ......... Return the product of the word u and
**                                    the word w and free u and w.
**    word WordPow( u, pn ) ......... Return the word u raised to the power
**                                    of (*pn). Free u.
**    word WordConj( u, w ) ......... Return the conjugate of the word u by
**                                    the word w and free u and w.
**    word WordComm( u, w ) ......... Return the commutator [u,w] of the
**                                    words u and w. Free u and w.
**    word WordEngel( u, w, n ) ..... Return the Engel-n commutator [u, n w]\
**                                    of the words u and w.  Free u and w.
**                                    the word w and free u and w.
**    word WordRel( u, w )  ......... Return the quotient u^-1 * w of the
**                                    words u and w. Free u and w.
**    void WordInit( f )    ......... Initialize the evaluator with this
**                                    arithmetic module. f is the function
**                                    used by this module to obtain a
**                                    generator through its number.
**    void WordPrint( u )   ......... Print the word u. The word u is not
**                                    freed.
**
*/

#include "config.h"

#include "presentation.h"
#include "pc.h"
#include "pcarith.h"
#include "collect.h"
#include "engel.h"

static WordGenerator PcGenerator;

void    WordCopyExpVec(expvec ev, word w) {
long    l;
gen     g;

for (l = 0, g = 1; g <= NrPcGensList[Class > 0 ? Class + 1 : 1]; g++)
  if (ev[g] != (expo)0) {
   if (ev[g] > (expo)0) { w[l].g =  g; w[l].e =  ev[g]; }
   else                 { w[l].g = -g; w[l].e = -ev[g]; }
   l++;
  }

w[l].g = EOW;
w[l].e = (expo)0;
}

word    WordExpVec(expvec ev) {
long    l;
gen     g;
word    w;

for (l = 0, g = 1; g <= NrPcGensList[Class > 0 ? Class + 1 : 1]; g++)
  if (ev[g] != (expo)0) l++;

w = (word)Allocate((l + 1) * sizeof(gpower));

WordCopyExpVec(ev, w);
return w;
}

expvec  ExpVecWord(word w) {
expvec  ev;

ev = (expvec)Allocate((NrPcGens + NrCenGens + 1) * sizeof(expo));

if (w != (word)0)
  while (w->g != EOW) {
   if (w->g > 0) ev[ w->g ] = w->e;
   else           ev[ -w->g ] = -w->e;
   w++;
  }
return ev;
}

int     WordCmp(word u, word w) {
if (u == w) return 0;
while (u->g == w->g && u->e == w->e) {
  if (u->g == EOW) return 0;
  u++;
  w++;
}
return 1;
}

void    WordCopy(word u, word w) {
while (u->g != EOW) *w++ = *u++;
*w = *u;
}

int     WordLength(word w) {
int     l = 0;

while (w->g != EOW) { w++; l++; }
return l;
}

word WordGen(gen g) {
word    w;
int     l;

if (g == 0) {
  w = (word)Allocate(sizeof(gpower));
  w[0].g = EOW;
} else {
  if ((*PcGenerator)(g) == 0)
   return (word)0;

  l = WordLength((*PcGenerator)(g));
  w = (word)Allocate((l + 1) * sizeof(gpower));
  WordCopy((*PcGenerator)(g), w);
}

return w;
}

static word WordMult(word u, word w) {
expvec  ev;

ev = ExpVecWord(u);
Free((void *)u);
if (Collect(ev, w, (expo)1)) {
  Free((void *)w);
  Free((void *)ev);
  return (word)0;
}

Free((void *)w);
w = WordExpVec(ev);
Free((void *)ev);
return w;
}

static word WordPow(word w, int * pn) {
expvec  ev;
word    ww;
int     n;

n = *pn;
if (n == 0) {
  Free((void *)w);
  return WordGen(0);
}
if (n < 0) {
  ww = Invert(w);
  Free((void *)w);
  w = ww;
  n = -n;
}

if (n == 1) return w;

ev = ExpVecWord(w);
if (Collect(ev, w, (expo)(n - 1))) {
  Free((void *)w);
  Free((void *)ev);
  return (word) 0;
}

Free((void *)w);
w = WordExpVec(ev);
Free((void *)ev);
return w;
}

static word WordConj(word u, word w) {
word    uw, x;
expvec  ev;

/* x = u^w = w^-1 * u * w   <===>   w * x = u * w. */
ev = ExpVecWord(u);
Free((void *)u);

if (Collect(ev, w, (expo)1)) {
  Free((void *)ev);
  Free((void *)w);
  return (word)0;
}
uw = WordExpVec(ev);
Free((void *)ev);

x = Solve(w, uw);
Free((void *)w);
Free((void *)uw);

return x;
}

word WordComm(word u, word w) {
word    x;

x = Commutator(u, w);

Free(u);
Free(w);
return  x;
}

word WordEngel(word u, word w, int *e) {
word    x;

x = EngelCommutator(u, w, *e);

Free(u);
Free(w);
return  x;
}

static word WordRel(word u, word w) {
word    x;

/* The relation u = w is interpreted as
**          x = u^-1 * w, which is equivalent to
**      u * x = w.
*/
x = Solve(u, w);
Free((void *)u);
Free((void *)w);

return x;
}

void    WordInit(WordGenerator generator) {
PcGenerator = generator;

/* SetEvalFunc(TGEN, (EvalFunc)WordGen);*/
SetEvalFunc(TMULT, (EvalFunc)WordMult);
SetEvalFunc(TPOW, (EvalFunc)WordPow);
SetEvalFunc(TCONJ, (EvalFunc)WordConj);
SetEvalFunc(TCOMM, (EvalFunc)WordComm);
SetEvalFunc(TREL, (EvalFunc)WordRel);
SetEvalFunc(TDRELL, (EvalFunc)WordRel);
SetEvalFunc(TDRELR, (EvalFunc)WordRel);
/* SetEvalFunc(TENGEL, (EvalFunc)WordEngel);*/
}

void    WordPrint(word gs) {
if (gs->g != EOW)
  if (gs->g > 0) {
   PrintGen(gs->g);
   if (gs->e > (expo)1)
    printf("^"EXP_FORMAT, gs->e);
  } else {
   PrintGen(-gs->g);
   printf("^-"EXP_FORMAT, gs->e);
  }
else {
  printf("1");
  return;
}
gs++;

while (gs->g != EOW) {
  putchar('*');
  if (gs->g > 0) {
   PrintGen(gs->g);
   if (gs->e > (expo)1)
    printf("^"EXP_FORMAT, gs->e);
  } else {
   PrintGen(-gs->g);
   printf("^-"EXP_FORMAT, gs->e);
  }
  gs++;
}
}

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