enumerate-balanced-ideals/enumerate.c

#include "thickenings.h"
#include "weyl.h"
#include "queue.h"

#include <strings.h>
#include <stdio.h>

char stringbuffer[100];
char stringbuffer2[100];

typedef struct {
  doublequotient_t *dq;
  int rank;
  int order;
  int positive;
  int *buffer;
  int level;
} info_t;

static char* alphabetize(weylgroup_element_t *e, char *str)
{
  if(e->wordlength == 0)
    sprintf(str, "1");
  else {
    for(int j = 0; j < e->wordlength; j++)
      str[j] = e->word[j] + 'a';
    str[e->wordlength] = 0;
  }

  return str;
}

/*
int shorten(int i, unsigned long left, unsigned long right, doublequotient_t *dq, int rank)
{
  int other, shorter = i;
  do {
    i = shorter;
    for(int j = 0; j < rank; j++) {
      other = graph[shorter].left[j];
      if(left & (1 << j) &&
	 graph[other].wordlength < graph[shorter].wordlength)
	shorter = other;
      other = graph[shorter].right[j];
      if(right & (1 << j) &&
	 graph[other].wordlength < graph[shorter].wordlength)
	shorter = other;
    }
  } while(shorter != i);

  return shorter;
}
*/

void balanced_thickening_callback(const bitvec_t *pos, int size, void *data)
{
  static long totcount = 0;

  if(data) {
    info_t *info = (info_t*)data;

    unsigned long right_invariance = FIRSTBITS(info->rank);
    unsigned long left_invariance = FIRSTBITS(info->rank);

    int bit1, bit2left, bit2right, left, right;

    for(int i = 0; i < size; i++) {
      bit1 = i < size/2 ? bv_get_bit(pos, i) : !bv_get_bit(pos, size - 1 - i);
      for(int j = 0; j < info->rank; j++) {
	left = info->dq->cosets[i].min->left[j]->coset - info->dq->cosets;
	right = info->dq->cosets[i].min->right[j]->coset - info->dq->cosets;
	bit2left = left < size/2 ? bv_get_bit(pos, left) : !bv_get_bit(pos, size - 1 - left);
	bit2right = right < size/2 ? bv_get_bit(pos, right) : !bv_get_bit(pos, size - 1 - right);
	if(bit1 != bit2left)
	  left_invariance &= ~BIT(j);
	if(bit1 != bit2right)
	  right_invariance &= ~BIT(j);
      }
    }

    printf("%4d left: ", totcount++);
    for(int j = 0; j < info->rank; j++)
      printf("%c", left_invariance & (1 << j) ? j + 'a' : ' ');
    printf(" right: ");
    for(int j = 0; j < info->rank; j++)
      printf("%c", right_invariance & (1 << j) ? j + 'a' : ' ');

    /*
    if(info->buffer) {
      printf(" generators:");
      queue_t queue;
      int cur, left, right;
      int *buffer = info->buffer;

      for(int i = 0; i < size/2; i++) {
	buffer[i] = bv_get_bit(pos, i);
	buffer[size-1-i] = !buffer[i];
      }
      for(int i = size-1; i >= 0; i--) {
	if(buffer[i]) {
	  weylgroup_element_t *shortest = shorten(i, left_invariance, right_invariance, info->dq);
	  printf(" %s", alphabetize(shortest, stringbuffer));
	  buffer[i] = 0;
	  queue_init(&queue);
	  queue_put(&queue, i);
	  while((cur = queue_get(&queue)) != -1) {
	    for(doublecoset_list_t *current = info->dq->coset[cur].bruhat_lower; current; current = current->next) {
	      int idx = current->to - info->dq->cosets;
	      if(buffer[idx]) {
		buffer[idx] = 0;
		queue_put(&queue, idx);
	      }
	    }
	    for(int j = 0; j < info->rank; j++) {
	      left = info->dq->coset[cur].min.left[j] - info->dq->cosets;
	      if(left_invariance & (1 << j) &&
		 info->graph[left].wordlength < info->graph[cur].wordlength &&
		 buffer[left]) {
		buffer[left] = 0;
		queue_put(&queue, left);
	      }
	      right = info->graph[cur].left[j];
	      if(right_invariance & (1 << j) &&
		 info->graph[right].wordlength < info->graph[cur].wordlength &&
		 buffer[right]) {
		buffer[right] = 0;
		queue_put(&queue, right);
	      }
	    }
	  }
	}
      }
      if(info->level >= 5) {
	printf(" ids: [0");
	for(int i = 1; i < size/2; i++)
	  if(bv_get_bit(pos, i))
	    printf(", %d", info->graph[i].id);
	for(int i = 0; i < size/2; i++)
	  if(!bv_get_bit(pos, i))
	    printf(", %d", info->graph[size-1-i].id);
	printf("]");
      }
    }
    */

    printf("\n");
  }
}

void balanced_thickening_simple_callback(const bitvec_t *pos, int size, void *data)
{
  long *count = (long*)data;

  if((++(*count)) % 100000000 == 0) {
    bv_print(stderr, pos, size/2);
    fprintf(stderr, "\n");
  }
}

int main(int argc, const char *argv[])
{
  semisimple_type_t type;
  unsigned long right_invariance, left_invariance;
  int rank, order, positive;
  int fixpoints;

  doublequotient_t *dq;

  const char *alphabet = "abcdefghijklmnopqrstuvwxyz";

  // read arguments

  ERROR(argc < 2, "Too few arguments!\n");

  type.n = 0;
  for(int i = 0; i < argc - 1; i++) {
    if(argv[i+1][0] < 'A' || argv[i+1][0] > 'G')
      break;
    type.n++;
  }

  type.factors = (simple_type_t*)malloc(type.n*sizeof(simple_type_t));
  for(int i = 0; i < type.n; i++) {
    type.factors[i].series = argv[i+1][0];
    type.factors[i].rank = argv[i+1][1] - '0';
    ERROR(argv[i+1][0] < 'A' || argv[i+1][0] > 'I' || argv[i+1][1] < '1' || argv[i+1][1] > '9', "Arguments must be Xn with X out of A-G and n out of 1-9\n");
  }

  left_invariance = right_invariance = 0;

  if(argc - type.n >= 3) {
    if(strcmp(argv[type.n + 1], "-") != 0)
      for(int i = 0; i < strlen(argv[type.n + 1]); i++)
	left_invariance |= (1 << (argv[type.n + 1][i] - 'a'));
    if(strcmp(argv[type.n + 2], "-") != 0)
      for(int i = 0; i < strlen(argv[type.n + 2]); i++)
	right_invariance |= (1 << (argv[type.n + 2][i] - 'a'));
  }

  // generate graph

  dq = weyl_generate_bruhat(type, left_invariance, right_invariance);

  // print stuff

  int output_level = 2;
  if(getenv("OUTPUT_LEVEL"))
    output_level = atoi(getenv("OUTPUT_LEVEL"));

  rank = weyl_rank(type);                // number of simple roots
  order = weyl_order(type);              // number of Weyl group elements
  positive = weyl_positive(type);        // number of positive roots

  if(output_level >= 1) {
    if(left_invariance) {
      printf("<");
      for(int j = 0; j < rank; j++)
	if(left_invariance & BIT(j))
	  fputc(alphabet[j], stdout);
      printf("> \\ ");
    }

    for(int i = 0; i < type.n; i++)
      printf("%s%c%d", i == 0 ? "" : " x ", type.factors[i].series, type.factors[i].rank);

    if(right_invariance) {
      printf(" / <");
      for(int j = 0; j < rank; j++)
	if(right_invariance & BIT(j))
	  fputc(alphabet[j], stdout);
      printf(">");
    }
    fprintf(stdout, "\n");

    fprintf(stdout, "Rank: %d\tOrder: %d\tPositive Roots: %d\tCosets: %d\n\n", rank, order, positive, dq->count);
  }

  if(output_level >= 3) {
    fprintf(stdout, "Shortest coset representatives: \n");
    for(int i = 0, wl = 0; i < dq->count; i++) {
      if(dq->cosets[i].min->wordlength > wl) {
	printf("\n");
	wl = dq->cosets[i].min->wordlength;
      }
      fprintf(stdout, "%s ", alphabetize(dq->cosets[i].min, stringbuffer));
    }
    fprintf(stdout, "\n\n");
  }

  if(output_level >= 4) {
    fprintf(stdout, "Bruhat order in graphviz format:\n");
    fprintf(stdout, "digraph test123 {\n");
    for(int i = 0; i < dq->count; i++)
      for(doublecoset_list_t *current = dq->cosets[i].bruhat_lower; current; current = current->next)
	fprintf(stdout, "%s -> %s;\n",
		alphabetize(dq->cosets[i].min, stringbuffer),
		alphabetize(current->to->min, stringbuffer2));
    fprintf(stdout, "}\n\n");
  }

  if(output_level >= 4) {
    fprintf(stdout, "Opposites:\n");
    for(int i = 0; i < dq->count; i++)
      fprintf(stdout, "%s <-> %s\n",
	      alphabetize(dq->cosets[i].min, stringbuffer),
	      alphabetize(dq->cosets[i].opposite->min, stringbuffer2));
    fprintf(stdout, "\n");
  }

  fixpoints = 0;
  for(int i = 0; i < dq->count; i++)
    if(dq->cosets[i].opposite == &dq->cosets[i]) {
      if(output_level >= 1) {
	if(fixpoints == 0)
	  fprintf(stdout, "No thickenings since the longest element fixes the following cosets:");
	fprintf(stdout, " %s", alphabetize(dq->cosets[i].min, stringbuffer));
      }
      fixpoints++;
    }
  if(output_level >= 1 && fixpoints)
    fprintf(stdout, "\n\n");


  if(!fixpoints) {
    int *buffer = (int*)malloc(dq->count*sizeof(int));

    info_t info;
    info.dq = dq;
    info.rank = weyl_rank(type);
    info.order = weyl_order(type);
    info.positive = weyl_positive(type);
    info.buffer = buffer;
    info.level = output_level;

    long count;
    if(output_level >= 2) {
      fprintf(stdout, "Balanced ideals:\n", count);
      count = enumerate_balanced_thickenings(dq, balanced_thickening_callback, &info);
      fprintf(stdout, "\n", count);
    } else {
      long outputcount = 0;
      count = enumerate_balanced_thickenings(dq, balanced_thickening_simple_callback, &outputcount);
    }

    if(output_level >= 1)
      fprintf(stdout, "Found %ld balanced ideal%s\n", count, count == 1 ? "" : "s");
  }

  weyl_destroy_bruhat(dq);
  free(type.factors);

  return 0;
}