enumerate-balanced-ideals/graph.c

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

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

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 main(int argc, const char *argv[]) {
  semisimple_type_t type;
  unsigned long right_invariance, left_invariance;
  doublequotient_t *dq;
  const char *alphabet = "abcdefghijklmnopqrstuvwxyz";
  char stringbuffer[100];
  char stringbuffer2[100];

  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] > 'G' ||
	  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);

  // color ideals
  int *color = (int*) malloc(dq->count * sizeof(int));
  memset(color, 0, dq->count * sizeof(int));
  for(int i = type.n+3; i < argc; i++) {
    weylgroup_element_t *elem = &dq->group[0]; // identity
    for(int j = 0; j < strlen(argv[i]); j++) {
      int gen = argv[i][j] - 'a';
      elem = elem->right[gen];
    }
    color[elem->coset->index] = 1;
  }

  for(int i = dq->count - 1; i >= 0; i--) {
    if(color[i] > 0) {
      for(doublecoset_list_t *current = dq->cosets[i].bruhat_lower; current; current = current->next) {
	color[current->to->index] = color[i];
      }
    }
  }

  fprintf(stdout, "digraph bruhat {\n");
  for (int i = 0; i < dq->count; i++) {
    fprintf(stdout, "%s [color=\"%s\"];\n",
	    alphabetize(dq->cosets[i].min, stringbuffer),
	    color[i] > 0 ? "red" : "black");

    for (doublecoset_list_t *current = dq->cosets[i].bruhat_lower; current; current = current->next) {
      fprintf(stdout, "%s -> %s [color=\"%s\"];\n",
	      alphabetize(dq->cosets[i].min, stringbuffer),
	      alphabetize(current->to->min, stringbuffer2),
	      color[i] > 0 ? "red" : "black");
    }
  }
  fprintf(stdout, "}\n\n");

  // clean up
  weyl_destroy_bruhat(dq);
  free(color);
  free(type.factors);
}