Quelle compact_description.c Sprache: C

/****************************************************************************
**
*A  compact_description.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 "pq_functions.h"
#include "constants.h"

/******************************************************************************
**  AUTHOR:     C. Rhodes
**  DATE:       21/1/93
**  REVISION:   1.0   (Release)
**  STATUS:     This code is designed to be an extension to the pq program
**              by E.A. O'Brien. It encodes the pc-presentation into a
**              sequence of integers and then appends that sequence to a
**              file called gps<order>, where <order> is the order of the
**              group. Note that existing files of this name are updated.
****************************************************************************/

#ifdef HAVE_GMP

MP_INT Encode(int p, int length, int *list)
{
   MP_INT powers, code;
   int i;

   mpz_init_set_ui(&code, 0);

   for (i = 1; i <= length; ++i) {
      mpz_init_set_si(&powers, 0);
      if (list[i] != 0)
         mpz_ui_pow_ui(&powers, p, i - 1);
      mpz_add(&code, &code, &powers);
   }
   /*
        if (list[i] != 0) {
           MP_INT factor;
           mpz_init_set_si (&factor, list[i]);
           mpz_ui_pow_ui (&powers, p, i);
           mpz_mul (&powers, &powers, &factor);
           mpz_add (&code, &code, &powers);
        }
     }
   */
   return code;
}
#endif

/* construct a compact description of the group as a sequence;
   if write_to_file TRUE, then write the compact description,
   sequence, to file and also return it */

int *compact_description(Logical write_to_file, struct pcp_vars *pcp)
{
   register int *y = y_address;

   register int p1;
   register int p2;
   int *sequence;
   int nmr_of_exponents;
   int weight_g, weight_h;
   int g, h;
   int generator;
   int offset;
   int index; /* used to count current position in sequence of exponents */
   int n;
#include "access.h"

   n = pcp->lastg;
   nmr_of_exponents = choose(n + 1, 3);
   sequence = allocate_vector(nmr_of_exponents, 1, TRUE);

   offset = 0;
   index = 0;

   if (pcp->cc == 1) {
      /* write the sequence to a file */
      output_information(sequence, nmr_of_exponents, pcp);
      return sequence;
   }

   for (generator = 2; generator <= n; ++generator) {

      /* examine all power relations g^p where g < generator and store
         all exponents of generator which occur in these relations */

      for (g = 1; g < generator; ++g) {
         p1 = y[pcp->ppower + g];

         trace_relation(sequence, &index, p1, generator, pcp);

         /* examine all commutator relations [h, g] where g < h < generator
            and store exponents of generator which occur in such relations */

         weight_g = WT(y[pcp->structure + g]);

         /* is the relation [h, g] stored? */
         for (h = g + 1; h < generator; ++h) {
            weight_h = WT(y[pcp->structure + h]);
            if (weight_g + weight_h <= pcp->cc) {
               p1 = y[pcp->ppcomm + h];
               p2 = y[p1 + g];
               trace_relation(sequence, &index, p2, generator, pcp);
            } else
               ++index;
         }
      }

      offset += (generator - 1) * (generator - 2) / 2 + (generator - 1);
      index = offset;
   }

#if defined(DEBUG)
   print_array(sequence, 1, nmr_of_exponents);
#endif

   /* write the sequence to a file */
   if (write_to_file)
      output_information(sequence, nmr_of_exponents, pcp);

   return sequence;
}

/* find all occurrences of generator in relation with address ptr */

void trace_relation(
    int *sequence, int *index, int ptr, int generator, struct pcp_vars *pcp)
{
   register int *y = y_address;

   int i, gen, exp, count;
#include "access.h"

   ++(*index);
   if (ptr == generator)
      sequence[*index] = 1;
   else if (ptr < 0) {
      ptr = -ptr + 1;
      count = y[ptr];
      for (i = 1; i <= count; i++) {
         gen = FIELD2(y[ptr + i]);
         if (gen == generator) {
            exp = FIELD1(y[ptr + i]);
            sequence[*index] = exp;
         }
      }
   }
}

/* append the sequence of length nmr_of_exponents to file with name
   formed by concatenating "gps" and "p^n" */

void
output_information(int *sequence, int nmr_of_exponents, struct pcp_vars *pcp)
{
   register int *y = y_address;

   FILE *output_file;
   char *file_name;
#ifdef HAVE_GMP
   MP_INT code;
#else
   register int count;
#endif

   file_name = allocate_char_vector(MAXWORD + 1, 0, FALSE);

   sprintf(file_name, "gps%d^%d", pcp->p, pcp->lastg);

   /* open the file in update mode */
   output_file = OpenFile(file_name, "a+");

/* write rank of Frattini quotient, number of pcp generators, prime,
   and exponent-p class to file */

#ifdef HAVE_GMP
   fprintf(
       output_file, "[%d, %d, %d, ", y[pcp->clend + 1], pcp->lastg, pcp->cc);
   code = Encode(pcp->p, nmr_of_exponents, sequence);
   mpz_out_str(output_file, 10, &code);
   fprintf(output_file, "],\n");
#else
   fprintf(output_file,
           "%d %d %d %d ",
           y[pcp->clend + 1],
           pcp->lastg,
           pcp->p,
           pcp->cc);
   /* now write out the sequence of exponents */
   for (count = 1; count <= nmr_of_exponents - 1; count++)
      fprintf(output_file, "%d,", sequence[count]);
   fprintf(output_file, "%d\n", sequence[nmr_of_exponents]);
#endif

   CloseFile(output_file);

   free(file_name);
}

quality95%

¤ Dauer der Verarbeitung: 0.25 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.