Quelle stabiliser.c Sprache: C

/****************************************************************************
**
*A  stabiliser.c                ANUPQ source                   Eamonn O'Brien
**
*Y  Copyright 1995-2001,  Lehrstuhl D fuer Mathematik,  RWTH Aachen,  Germany
*Y  Copyright 1995-2001,  School of Mathematical Sciences, ANU,     Australia
**
*/

#include "pq_defs.h"
#include "pcp_vars.h"
#include "pga_vars.h"
#include "pq_functions.h"
#include "constants.h"

/*static int ***setup_identity_auts (int nmr_of_generators, int ***auts, struct
* pga_vars *pga);*/
static void evaluate_generators(int pointer,
                                int nmr_of_generators,
                                int ***stabiliser,
                                int ***auts,
                                struct pga_vars *pga,
                                struct pcp_vars *pcp);

/* find the stabiliser of the representative, rep;
   all of the permutations are stored in perms;
   nmr_of_generators is the number of pcp generators in the descendant */

int ***stabiliser_of_rep(int **perms,
                         int rep,
                         int orbit_length,
                         int *a,
                         int *b,
                         char *c,
                         char *d,
                         int ***auts,
                         struct pga_vars *pga,
                         struct pcp_vars *pcp)
{
   register int *y = y_address;

   int ***stabiliser = 0;
   int pointer = pcp->lused + 1;
   Logical soluble_group =
       (pga->soluble || pga->Degree == 1 || pga->nmr_of_perms == 0);
   int nmr_of_generators;
   int restriction;
   int j;
   int *relative;

   nmr_of_generators = pga->final_stage ? y[pcp->clend + pcp->cc - 1] + pga->s
                                        : pcp->lastg + pga->s - pga->q;

   pga->nmr_stabilisers = 0;

   /* if necessary, compute the stabiliser of the representative
      in the insoluble portion using a system call to GAP --
      this is done before setting up the remainder of the automorphisms
      to minimise the size of the workspace created by the system call */

   if (!soluble_group) {

#if defined(GAP_LINK) || defined(GAP_LINK_VIA_FILE)
      insoluble_stab_gens(rep, orbit_length, pga, pcp);
#else
      printf("To compute stabilisers in insoluble automorphism groups, ");
      printf("you must compile pq\nwith the compiler flag GAP_LINK set\n");
      exit(FAILURE);
#endif
   }

   /* determine the generators for the stabiliser if soluble */
   if (soluble_group) {
      stabiliser_generators(perms, rep, a, b, c, d, auts, pga, pcp);

      /* allocate space for stabiliser */
      stabiliser = allocate_array(
          pga->nmr_stabilisers, pga->ndgen, nmr_of_generators, TRUE);

      /* construct the generators of the stabiliser in the soluble group
         as automorphisms */

      if (pga->nmr_stabilisers != 0 && soluble_group) {
         restriction = pga->final_stage ? y[pcp->clend + pcp->cc - 1] + pga->s
                                        : y[pcp->clend + pcp->cc - 1];
         evaluate_generators(pointer, restriction, stabiliser, auts, pga, pcp);
      }
   } else {
/* read in the generators of the stabiliser in the insoluble case --
    these were computed using GAP */

#if defined(GAP_LINK) || defined(GAP_LINK_VIA_FILE)
      stabiliser =
          read_stabiliser_gens(nmr_of_generators, stabiliser, pga, pcp);
#endif
   }

   pcp->lastg = nmr_of_generators;

   if (pga->final_stage) {
      /* include relative orders for central generators */
      relative = allocate_vector(pga->nmr_soluble + pga->nmr_centrals, 1, 0);
      for (j = pga->nmr_soluble; j >= 1; --j)
         relative[pga->nmr_centrals + j] = pga->relative[j];
      for (j = 1; j <= pga->nmr_centrals; ++j)
         relative[j] = pga->p;

      /* free_vector (pga->relative, 1); */
      pga->relative = relative;
      pga->nmr_soluble += pga->nmr_centrals;
   }

   if (pga->print_automorphisms && pga->final_stage) {
      /*
              if (pga->print_automorphisms) {
      */
      printf("Number of stabiliser generators is %d\n", pga->nmr_stabilisers);
      print_auts(pga->nmr_stabilisers, pga->ndgen, stabiliser, pcp);
   }

   pga->m = pga->nmr_centrals + pga->nmr_stabilisers;

   return stabiliser;
}

/* find generators for the stabiliser for orbit representative, rep;
   store each word in y, preceded by its length */

void stabiliser_generators(int **perms,
                           int rep,
                           int *a,
                           int *b,
                           char *c,
                           char *d,
                           int ***auts,
                           struct pga_vars *pga,
                           struct pcp_vars *pcp)
{
   register int *y = y_address;

   register int alpha, k, next;
   register int word_length;
   register int pointer = pcp->lused + 1;
   int index;
   int perm_number;

   /* let k run over the elements of orbit with representative rep;
      if c[k] >= 2, then some permutation did not extend the orbit of k;
      hence, there is some product of subsequent permutations which
      stabilises the representative a[k] */

   k = rep;
   while (k != 0) {
      if (c[k] >= 2) {
         for (alpha = d[k] + 1; alpha <= d[k] + c[k] - 1; ++alpha) {
            ++pga->nmr_stabilisers;
            word_length = 1;
            y[pointer + word_length] = alpha;

            /* does automorphism alpha induce a trivial permutation? */
            if ((perm_number = pga->map[alpha]) == 0)
               next = a[k];
            else {
               next = pga->space_efficient
                          ? find_image(a[k], auts[alpha], pga, pcp)
                          : perms[perm_number][a[k]];
            }

            while (next != a[k]) {
               index = d[next];
               ++word_length;
               y[pointer + word_length] = index;
               if ((perm_number = pga->map[index]) != 0) {
                  next = pga->space_efficient
                             ? find_image(next, auts[index], pga, pcp)
                             : perms[perm_number][next];
               }
            }
            y[pointer] = word_length;
            pointer += word_length + 1;
         }
      }
      k = b[k];
   }

   pcp->lused = pointer;
}

/* evaluate the action of a stabiliser of a representative on the
   defining generators of the group; each stabiliser generator is
   stored as a word in the automorphisms, auts, of the parent, where
   y[pointer] = length of word defining first generator */

static void evaluate_generators(int pointer,
                                int nmr_of_generators,
                                int ***stabiliser,
                                int ***auts,
                                struct pga_vars *pga,
                                struct pcp_vars *pcp)
{
   register int *y = y_address;

   register int i, j;
   register int gamma;
   int cp = pcp->lused;

   for (gamma = 1; gamma <= pga->nmr_stabilisers; ++gamma) {

      for (i = 1; i <= pga->ndgen; ++i) {
         /* compute image of defining generator i
            under generator gamma of stabiliser */
         image_of_generator(i, pointer, auts, pga, pcp);

         /* copy restriction of result into stabiliser array */
         for (j = 1; j <= nmr_of_generators; ++j)
            stabiliser[gamma][i][j] = y[cp + j];
      }
      pointer += y[pointer] + 1;
   }
}

/* compute the image of group generator under a stabiliser generator,
   whose definition as a word in the automorphisms, auts, of the parent
   is stored at y[pointer + 1], .., y[pointer + y[pointer]] */

void image_of_generator(int generator,
                        int pointer,
                        int ***auts,
                        struct pga_vars *pga,
                        struct pcp_vars *pcp)
{
   register int *y = y_address;

   register int i, j, k, l;
   register int alpha, letter;
   register int length, exp;
   int cp = pcp->lused;
   int ptr = cp + pcp->lastg;
   int nmr_of_letters = y[pointer];
   register int bound;

   /* alpha is the last letter in the stabiliser generator word */
   alpha = y[pointer + nmr_of_letters];

   /* set up the image of gen under the action of alpha at cp */
   for (i = 1; i <= pcp->lastg; ++i)
      y[cp + i] = auts[alpha][generator][i];

   /* for each remaining letter in the generator word, set up as a
      word its action on each of the elements of the image under alpha */

   for (letter = nmr_of_letters - 1; letter >= 1; --letter) {

      alpha = y[pointer + letter];

      /* set up image under alpha */
      length = 0;
      for (i = 1; i <= pcp->lastg; ++i) {
         if ((exp = y[cp + i]) > 0) {
            /* set up exp copies of the image of generator i under
               action of automorphism alpha */
            for (j = 1; j <= exp; ++j) {
               for (k = 1; k <= pcp->lastg; ++k) {
                  bound = auts[alpha][i][k];
                  for (l = 1; l <= bound; ++l) {
                     ++length;
                     y[ptr + length] = k;
                  }
               }
            }
         }
      }

      /* now zero out previous result */
      for (i = 1; i <= pcp->lastg; ++i)
         y[cp + i] = 0;

      /* now collect the result of the composition of maps so far to cp */
      for (l = 1; l <= length; ++l)
         collect(y[ptr + l], cp, pcp);
   }
}

/* find which automorphism, alpha, induces the permutation with index perm */

int preimage(int perm, struct pga_vars *pga)
{
   int alpha;

   for (alpha = 1; alpha <= pga->m; ++alpha)
      if (pga->map[alpha] == perm)
         return alpha;

   printf("*** Error in function preimage ***\n");
   exit(FAILURE);
}

/* set up those automorphisms which induced the identity on the
   p-multiplicator as the leading elements of the stabiliser */
/*
static int ***setup_identity_auts (int nmr_of_generators, int ***auts, struct
pga_vars *pga)
{
   int alpha, i = 0, j, k;
   int ***stabiliser;

   stabiliser = allocate_array (pga->nmr_stabilisers, pga->ndgen,
                                nmr_of_generators, TRUE);

   for (alpha = 1; alpha <= pga->m; ++alpha) {
      if (pga->map[alpha] == 0) {
         ++i;
         for (j = 1; j <= pga->ndgen; ++j)
            for (k = 1; k <= nmr_of_generators; ++k)
               stabiliser[i][j][k] = auts[alpha][j][k];
      }
   }

   return stabiliser;
}
*/

#if defined(GAP_LINK_VIA_FILE)

/* read the insoluble stabiliser generators from LINK file;
   each list of stabilisers is preceded by a list of integers --
   the first indicates whether the stabiliser is soluble;
   the second is the number of soluble generators for the stabiliser;
   for each soluble generator, its relative order is now listed;
   finally the total number of generators is listed */

int ***read_stabiliser_gens(int nmr_of_generators,
                            int ***soluble_generators,
                            struct pga_vars *pga,
                            struct pcp_vars *pcp)
{
   register int ndgen = pga->ndgen;
   register int gamma, i, j;
   FILE *LINK_output;
   int ***stabiliser;
   int nmr_items;
   int temp;

   LINK_output = OpenFileInput("LINK_output");

   nmr_items = fscanf(LINK_output, "%d", &pga->soluble);
   verify_read(nmr_items, 1);
   nmr_items = fscanf(LINK_output, "%d", &pga->nmr_soluble);
   verify_read(nmr_items, 1);

   pga->relative = allocate_vector(pga->nmr_soluble, 1, 0);
   for (j = 1; j <= pga->nmr_soluble; ++j) {
      nmr_items = fscanf(LINK_output, "%d", &temp);
      verify_read(nmr_items, 1);
      pga->relative[j] = temp;
   }

   nmr_items = fscanf(LINK_output, "%d", &pga->nmr_stabilisers);
   verify_read(nmr_items, 1);

#ifdef DEBUG1
   printf("Nmr of soluble gens for stabiliser is %d\n", pga->nmr_soluble);
   printf("FROM GAP Relative orders are ");
   for (i = 1; i <= pga->nmr_soluble; ++i)
      printf("%d ", pga->relative[i]);
   printf("\n");
   printf("Total Nmr of gens for stabiliser is %d\n", pga->nmr_stabilisers);
#endif

   stabiliser =
       allocate_array(pga->nmr_stabilisers, ndgen, nmr_of_generators, TRUE);

   /* now read in the insoluble generators */
   for (gamma = 1; gamma <= pga->nmr_stabilisers; ++gamma)
      for (i = 1; i <= ndgen; ++i)
         for (j = 1; j <= pcp->ccbeg - 1; ++j) {
            nmr_items = fscanf(LINK_output, "%d", &stabiliser[gamma][i][j]);
            verify_read(nmr_items, 1);
         }

   CloseFile(LINK_output);

   return stabiliser;
}

#endif

quality70%

¤ Dauer der Verarbeitung: 0.13 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.