.gitignore pdf files and list length profile

.gitignore

@@ -0,0 +1,7 @@
+*.o
+*.pdf
+enumerate
+idealbounds
+graph
+D2n
+dominant_weights

D2n.c

@@ -0,0 +1,133 @@
+#include "thickenings.h"
+#include "weyl.h"
+#include "queue.h"
+
+#include <strings.h>
+#include <stdio.h>
+#include <inttypes.h>
+
+int main(int argc, const char *argv[])
+{
+	if(argc < 2) {
+		fprintf(stderr, "Rank argument required.\n");
+		return 1;
+	}
+	int rank = atoi(argv[1]);
+	if(rank <= 0 || rank > 1000) {
+		fprintf(stderr, "Rank must be a small positive integer.\n");
+		return 1;
+	}
+	if(rank % 2) {
+		fprintf(stderr, "Rank must be even.\n"); // opposition involution not trivial otherwise
+		return 1;
+	}
+
+	doublequotient_t *dq = (doublequotient_t*)malloc(sizeof(doublequotient_t));
+	simple_type_t type;
+	type.series = 'D';
+	type.rank = rank;
+	dq->type.n = 1;
+	dq->type.factors = &type;
+	dq->left_invariance = (1<<rank) - 2;
+	dq->right_invariance = 0;
+	dq->group = 0;
+	dq->grouplists = 0;
+	dq->groupletters = 0;
+	dq->count = 1 << (rank - 1);
+	dq->cosets = (doublecoset_t*)malloc(dq->count*sizeof(doublecoset_t));
+	dq->lists = (doublecoset_list_t*)malloc(2*dq->count*rank*sizeof(doublecoset_list_t)); // conservative estimate
+	int nlists = 0;
+
+	int *bitmask = malloc((1<<(rank-1)) * sizeof(int));
+	int *bitmask_reverse = malloc((1<<rank) * sizeof(int));
+	int index = 0;
+
+	LOG("Prepare.\n");
+
+	for(int i = 0; i < dq->count; i++) {
+		dq->cosets[i].index = i;
+		dq->cosets[i].bruhat_lower = (doublecoset_list_t*)0;
+		dq->cosets[i].bruhat_higher = (doublecoset_list_t*)0;
+		dq->cosets[i].min = (weylgroup_element_t*)0;
+		dq->cosets[i].max = (weylgroup_element_t*)0;
+	}
+
+	LOG("Create bitmasks.\n");
+
+	for(uint64_t i = 0; i < (1 << rank); i++) {
+		if(__builtin_popcountll(i) % 2 == 1)
+			bitmask_reverse[i] = -1;
+		else {
+			bitmask[index] = i;
+			bitmask_reverse[i] = index++;
+		}
+	}
+
+	LOG("Generate bruhat order.\n");
+
+	for(int i = 0; i < dq->count; i++) {
+		for(int j = 0; j < rank - 1; j++) {
+			if(!(bitmask[i] & BIT(j)) && (bitmask[i] & BIT(j+1))) {
+				int lowerind = bitmask_reverse[bitmask[i] ^ (BIT(j) | BIT(j+1))];
+				dq->lists[nlists].next = dq->cosets[i].bruhat_lower;
+				dq->cosets[i].bruhat_lower = &dq->lists[nlists];
+				dq->cosets[i].bruhat_lower->to = &dq->cosets[lowerind];
+				nlists++;
+			}
+		}
+		if((bitmask[i] & BIT(0)) && (bitmask[i] & BIT(1))) {
+			int lowerind = bitmask_reverse[bitmask[i] & ~(BIT(0) | BIT(1))];
+			dq->lists[nlists].next = dq->cosets[i].bruhat_lower;
+			dq->cosets[i].bruhat_lower = &dq->lists[nlists];
+			dq->cosets[i].bruhat_lower->to = &dq->cosets[lowerind];
+			nlists++;
+		}
+	}
+
+	LOG("Revert bruhat order.\n");
+
+	for(int i = 0; i < dq->count; i++) {
+		for(doublecoset_list_t *cur = dq->cosets[i].bruhat_lower; cur; cur = cur->next) {
+			dq->lists[nlists].next = cur->to->bruhat_higher;
+			cur->to->bruhat_higher = &dq->lists[nlists];
+			cur->to->bruhat_higher->to = &dq->cosets[i];
+			nlists++;
+		}
+	}
+
+	LOG("Find opposites.\n");
+
+	for(int i = 0; i < dq->count; i++) {
+		int oppind = bitmask_reverse[~bitmask[i] & ((1<<rank) - 1)];
+		dq->cosets[i].opposite = &dq->cosets[oppind];
+	}
+
+	/*
+	printf("\n");
+	printf("digraph test123 {\n");
+
+	for(int i = 0; i < dq->count; i++) {
+		for(doublecoset_list_t *cur = dq->cosets[i].bruhat_lower; cur; cur = cur->next) {
+			printf("\"0x%02x\" -> \"0x%02x\";\n", bitmask[i], bitmask[cur->to->index]);
+		}
+	}
+
+	printf("}\n\n");
+
+	printf("Opposites:\n");
+	for(int i = 0; i < dq->count; i++)
+		printf("0x%02x <-> %d 0x%02x\n", bitmask[i], dq->cosets[i].opposite->index, bitmask[dq->cosets[i].opposite->index]);
+	printf("\n");
+	*/
+
+	long count = enumerate_balanced_thickenings(dq, 0, 0);
+	printf("Found %ld balanced ideals.\n", count);
+
+	free(bitmask);
+	free(bitmask_reverse);
+	free(dq->lists);
+	free(dq->cosets);
+	free(dq);
+
+	return 0;
+}

Makefile

@@ -4,7 +4,7 @@ HEADERS=weyl.h thickenings.h queue.h bitvec.h
 #SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
 SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
 
-OPTIONS=-m64 -march=native -mtune=native -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS)
+OPTIONS=-m64 -march=native -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS)
 NAME=enumerate-balanced-ideals
 
 all: enumerate graph
@@ -21,17 +21,29 @@ enumerate: enumerate.o weyl.o thickenings.o
 graph: graph.o weyl.o
 	gcc $(OPTIONS) -o graph graph.o weyl.o
 
+D2n: D2n.o weyl.o thickenings.o
+	gcc $(OPTIONS) -o D2n D2n.o weyl.o thickenings.o
+
+dominant_weights: dominant_weights.o weyl.o thickenings.o
+	gcc $(OPTIONS) -o dominant_weights dominant_weights.o weyl.o thickenings.o -lcdd
+
 enumerate.o: enumerate.c $(HEADERS)
 	gcc $(OPTIONS) -c enumerate.c
 
 thickenings.o: thickenings.c $(HEADERS)
 	gcc $(OPTIONS) -c thickenings.c
 
+D2n.o: D2n.c $(HEADERS)
+	gcc $(OPTIONS) -c D2n.c
+
 weyl.o: weyl.c $(HEADERS)
 	gcc $(OPTIONS) -c weyl.c
 
 graph.o: graph.c $(HEADERS)
 	gcc $(OPTIONS) -c graph.c
 
+dominant_weights.o: dominant_weights.c $(HEADERS)
+	gcc $(OPTIONS) -c dominant_weights.c
+
 clean:
-	rm -f enumerate graph thickenings.o weyl.o enumerate.o graph.o $(NAME) $(NAME).tar.bz2
+	rm -f enumerate graph D2n dominant_weights thickenings.o weyl.o enumerate.o graph.o D2n.o dominant_weights.o $(NAME) $(NAME).tar.bz2

dominant_weights.c

@@ -0,0 +1,180 @@
+#include <stdio.h>
+#include <string.h>
+#include <malloc.h>
+#include <setoper.h>
+#include <cdd.h>
+
+#include "weyl.h"
+#include "thickenings.h"
+
+doublequotient_t *dq;
+double *vector;
+char buf[1000], buf2[1000];
+
+typedef struct {
+	dd_MatrixPtr M;
+	dd_LPSolutionPtr lps;
+} 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;
+}
+
+static char* print_vector(double *v, int rank, char *buf)
+{
+	int written = 0;
+
+	for(int i = 0; i < rank; i++) {
+		written += sprintf(buf+written, "%.4f", v[i]);
+		if(i != rank -1) {
+			sprintf(buf+written, ", ");
+			written += 2;
+		}
+	}
+
+	return buf;
+}
+
+static char* print_vector_ptr(dd_Arow v, int rank, char *buf)
+{
+	int written = 0;
+
+	for(int i = 0; i < rank; i++) {
+		written += sprintf(buf+written, "%.4f", v[i][0]);
+		if(i != rank -1) {
+			sprintf(buf+written, ", ");
+			written += 2;
+		}
+	}
+
+	return buf;
+}
+
+static void balanced_thickening_callback(const bitvec_t *pos, int size, const enumeration_info_t *ei)
+{
+	int bit, funcbit, sign;
+	dd_rowset ImL, Lbasis;
+	dd_ErrorType err = dd_NoError;
+	info_t *info = (info_t*)ei->callback_data;
+	int rank = weyl_rank(dq->type);
+
+	for(int i = 0; i < size; i++) {
+		bit = i < size/2 ? bv_get_bit(pos, i) : !bv_get_bit(pos, size - 1 - i);
+		sign = bit ? 1 : -1;
+		info->M->matrix[i][0][0] = 0.0;
+		for(int j = 0; j < rank; j++)
+			info->M->matrix[i][j+1][0] = sign*vector[rank*i+j];
+//		printf("0 %.2f %.2f %.2f %d %d\n", sign*vector[3*i], sign*vector[3*i+1], sign*vector[3*i+2], bit, funcbit);
+    }
+
+	for(int i = 0; i < rank; i++) {
+		info->M->matrix[i+size][0][0] = 0.0;
+		for(int j = 0; j < rank; j++) {
+			if(i == j)
+				info->M->matrix[i+size][j+1][0] = 1.0;
+			else
+				info->M->matrix[i+size][j+1][0] = 0.0;
+		}
+	}
+
+//	dd_WriteMatrix(stdout, info->M);
+
+	dd_FindRelativeInterior(info->M, &ImL, &Lbasis, &(info->lps), &err);
+
+	if(set_card(Lbasis) != 0)
+		printf("codim = %ld\n", set_card(Lbasis));
+	else
+		printf("weight = (%s)\n", print_vector_ptr(info->lps->sol, rank + 1, buf));
+
+	dd_FreeLPSolution(info->lps);
+
+//	printf("\n");
+}
+
+static int apply_reflection(double *in, double *out, int rank, int reflection)
+{
+	memcpy(out, in, rank*sizeof(double));
+	/*
+	out[reflection] *= -1;
+	if(reflection != 0)
+		out[reflection-1] += in[reflection];
+	if(reflection != rank-1)
+		out[reflection+1] += in[reflection];
+	*/
+	out[reflection] *= -1;
+	if(reflection != 0)
+		out[reflection] += in[reflection-1];
+	if(reflection != rank-1)
+		out[reflection] += in[reflection+1];
+
+}
+
+int main(int argc, char *argv[])
+{
+	semisimple_type_t type;
+	simple_type_t simple;
+	info_t info;
+
+	type.n = 1;
+	type.factors = &simple;
+	simple.series = 'A';
+	simple.rank = 3;
+
+	dq = weyl_generate_bruhat(type, 0, 0);
+
+	int order = weyl_order(type);
+	int rank = weyl_rank(type);
+	weylgroup_element_t *group = dq->group;
+	vector = malloc(weyl_order(type)*weyl_rank(type)*sizeof(double));
+
+	for(int i = 0; i < rank; i++)
+		vector[i] = 0.0;
+
+	for(int i = 0; 2*i < rank; i++) {
+		for(int j = i; j < rank - i; j++) {
+			vector[j] += rank - 2*i;
+		}
+	}
+
+	/*
+	vector[0] = 4.1;
+	vector[1] = 6.1;
+	vector[2] = 5.9;
+	vector[3] = 3.9;
+	*/
+
+	printf("regular element: (%s)\n", print_vector(vector, rank, buf));
+
+	for(int i = 0; i < order; i++) {
+		printf("%s (%s)\n", alphabetize(&group[i], buf), print_vector(vector + rank*i, rank, buf2));
+
+		for(int j = 0; j < rank; j++)
+			if(group[i].left[j]->wordlength > group[i].wordlength)
+				apply_reflection(&vector[rank*i], &vector[rank*group[i].left[j]->index], rank, j);
+	}
+
+	printf("\n");
+
+	dd_set_global_constants();
+	info.M = dd_CreateMatrix(order+rank, rank+1);
+	info.M->representation = dd_Inequality;
+	info.M->numbtype = dd_Real;
+	info.M->objective = dd_LPmax;
+
+	enumerate_balanced_thickenings(dq, balanced_thickening_callback, &info);
+
+	dd_FreeMatrix(info.M);
+	weyl_destroy_bruhat(dq);
+	free(vector);
+
+	return 0;
+}

enumerate.c

@@ -9,353 +9,367 @@ char stringbuffer[100];
 char stringbuffer2[100];
 
 typedef struct {
-  doublequotient_t *dq;
+	doublequotient_t *dq;
-  int rank;
+	int rank;
-  int order;
+	int order;
-  int positive;
+	int positive;
-  int *buffer;
+	int *buffer;
-  int level;
+	int level;
 } info_t;
 
 static char* alphabetize(weylgroup_element_t *e, char *str)
 {
-  if(e->wordlength == 0)
+	if(e->wordlength == 0)
-    sprintf(str, "1");
+		sprintf(str, "1");
-  else {
+	else {
-    for(int j = 0; j < e->wordlength; j++)
+		for(int j = 0; j < e->wordlength; j++)
-      str[j] = e->word[j] + 'a';
+			str[j] = e->word[j] + 'a';
-    str[e->wordlength] = 0;
+		str[e->wordlength] = 0;
-  }
+	}
 
-  return str;
+	return str;
 }
 
 /*
-int shorten(int i, unsigned long left, unsigned long right, doublequotient_t *dq, int rank)
+  int shorten(int i, unsigned long left, unsigned long right, doublequotient_t *dq, int rank)
-{
+  {
   int other, shorter = i;
   do {
-    i = shorter;
+  i = shorter;
-    for(int j = 0; j < rank; j++) {
+  for(int j = 0; j < rank; j++) {
-      other = graph[shorter].left[j];
+  other = graph[shorter].left[j];
-      if(left & (1 << j) &&
+  if(left & (1 << j) &&
-	 graph[other].wordlength < graph[shorter].wordlength)
+  graph[other].wordlength < graph[shorter].wordlength)
-	shorter = other;
+  shorter = other;
-      other = graph[shorter].right[j];
+  other = graph[shorter].right[j];
-      if(right & (1 << j) &&
+  if(right & (1 << j) &&
-	 graph[other].wordlength < graph[shorter].wordlength)
+  graph[other].wordlength < graph[shorter].wordlength)
-	shorter = other;
+  shorter = other;
-    }
+  }
   } while(shorter != i);
 
   return shorter;
-}
+  }
 */
 
 void balanced_thickening_callback(const bitvec_t *pos, int size, const enumeration_info_t *ei)
 {
-  static long totcount = 0;
+	static long totcount = 0;
 
-  if(ei->callback_data) {
+	if(ei->callback_data) {
-    info_t *info = (info_t*)ei->callback_data;
+		info_t *info = (info_t*)ei->callback_data;
 
-    unsigned long right_invariance = FIRSTBITS(info->rank);
+		unsigned long right_invariance = FIRSTBITS(info->rank);
-    unsigned long left_invariance = FIRSTBITS(info->rank);
+		unsigned long left_invariance = FIRSTBITS(info->rank);
 
-    int bit1, bit2left, bit2right, left, right;
+		int bit1, bit2left, bit2right, left, right;
 
-    for(int i = 0; i < size; i++) {
+		for(int i = 0; i < size; i++) {
-      bit1 = i < size/2 ? bv_get_bit(pos, i) : !bv_get_bit(pos, size - 1 - 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++) {
+			for(int j = 0; j < info->rank; j++) {
-	left = info->dq->cosets[i].min->left[j]->coset->index;
+				left = info->dq->cosets[i].min->left[j]->coset->index;
-	right = info->dq->cosets[i].min->right[j]->coset->index;
+				right = info->dq->cosets[i].min->right[j]->coset->index;
-	bit2left = left < size/2 ? bv_get_bit(pos, left) : !bv_get_bit(pos, size - 1 - left);
+				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);
+				bit2right = right < size/2 ? bv_get_bit(pos, right) : !bv_get_bit(pos, size - 1 - right);
-	if(bit1 != bit2left)
+				if(bit1 != bit2left)
-	  left_invariance &= ~BIT(j);
+					left_invariance &= ~BIT(j);
-	if(bit1 != bit2right)
+				if(bit1 != bit2right)
-	  right_invariance &= ~BIT(j);
+					right_invariance &= ~BIT(j);
-      }
+			}
-    }
+		}
 
-    printf("%4d left: ", totcount++);
+		printf("%4d left: ", totcount++);
-    for(int j = 0; j < info->rank; j++)
+		for(int j = 0; j < info->rank; j++)
-      printf("%c", left_invariance & (1 << j) ? j + 'a' : ' ');
+			printf("%c", left_invariance & (1 << j) ? j + 'a' : ' ');
-    printf(" right: ");
+		printf(" right: ");
-    for(int j = 0; j < info->rank; j++)
+		for(int j = 0; j < info->rank; j++)
-      printf("%c", right_invariance & (1 << j) ? j + 'a' : ' ');
+			printf("%c", right_invariance & (1 << j) ? j + 'a' : ' ');
 
-    if(info->buffer) {
+		int length_profile[65]; // can't handle more that 64 positive roots anyway
-      bitvec_t low, high;
-      bv_copy(pos, &low);
-      bv_negate(pos, &high);
 
-      //      printf(" set: ");
+		memset(length_profile, 0, (info->positive+1)*sizeof(int));
-      //      bv_print(stdout, &low, size/2);
-      //      printf(" ");
-      //      bv_print(stdout, &high, size/2);
 
-      printf(" gen: ");
+		for(int i = 0; i < size; i++) {
+			bit1 = i < size/2 ? bv_get_bit(pos, i) : !bv_get_bit(pos, size - 1 - i);
+			if(bit1)
+				length_profile[info->dq->cosets[i].min->wordlength]++;
+		}
+
+		printf(" length profile:");
+		for(int i = 0; i <= info->positive; i++)
+			printf(" %d", length_profile[i]);
+
+		if(info->buffer) {
+			bitvec_t low, high;
+			bv_copy(pos, &low);
+			bv_negate(pos, &high);
+
+			//      printf(" set: ");
+			//      bv_print(stdout, &low, size/2);
+			//      printf(" ");
+			//      bv_print(stdout, &high, size/2);
+
+			printf(" gen: ");
 
 
-      for(int i = 0; i < size/2; i++) {
+			for(int i = 0; i < size/2; i++) {
-	if(!bv_get_bit(&high, i))
+				if(!bv_get_bit(&high, i))
-	  continue;
+					continue;
 
-	printf("%s ", alphabetize(info->dq->cosets[size-1-i].min, stringbuffer));
+				printf("%s ", alphabetize(info->dq->cosets[size-1-i].min, stringbuffer));
 
-	bv_difference(&high, &ei->principal_neg[size-1-i], &high);
+				bv_difference(&high, &ei->principal_neg[size-1-i], &high);
-	bv_difference(&low,  &ei->principal_pos[size-1-i], &low);
+				bv_difference(&low,  &ei->principal_pos[size-1-i], &low);
-      }
+			}
 
-      for(int i = size/2 - 1; i >= 0; i--) {
+			for(int i = size/2 - 1; i >= 0; i--) {
-	if(!bv_get_bit(&low, i))
+				if(!bv_get_bit(&low, i))
-	  continue;
+					continue;
 
-	printf("%s ", alphabetize(info->dq->cosets[i].min, stringbuffer));
+				printf("%s ", alphabetize(info->dq->cosets[i].min, stringbuffer));
 
-	bv_difference(&low, &ei->principal_pos[i], &low);
+				bv_difference(&low, &ei->principal_pos[i], &low);
-      }
+			}
-    }
+		}
 
-    int max_length = 0;
+		int max_length = 0;
-    for(int i = 0; i < size/2; i++) {
+		for(int i = 0; i < size/2; i++) {
-      if(bv_get_bit(pos, i)) {
+			if(bv_get_bit(pos, i)) {
-	if(info->dq->cosets[i].max->wordlength > max_length)
+				if(info->dq->cosets[i].max->wordlength > max_length)
-	  max_length = info->dq->cosets[i].max->wordlength;
+					max_length = info->dq->cosets[i].max->wordlength;
-      } else {
+			} else {
-	if(info->dq->cosets[size-i-1].max->wordlength > max_length)
+				if(info->dq->cosets[size-i-1].max->wordlength > max_length)
-	  max_length = info->dq->cosets[size-i-1].max->wordlength;
+					max_length = info->dq->cosets[size-i-1].max->wordlength;
-      }
+			}
-    }
+		}
-    //    printf(" max length: %d", max_length);
+		//    printf(" max length: %d", max_length);
 
-    /*
+		/*
-    if(info->buffer) {
+		  if(info->buffer) {
-      printf(" generators:");
+		  printf(" generators:");
-      queue_t queue;
+		  queue_t queue;
-      int cur, left, right;
+		  int cur, left, right;
-      int *buffer = info->buffer;
+		  int *buffer = info->buffer;
 
-      for(int i = 0; i < size/2; i++) {
+		  for(int i = 0; i < size/2; i++) {
-	buffer[i] = bv_get_bit(pos, i);
+		  buffer[i] = bv_get_bit(pos, i);
-	buffer[size-1-i] = !buffer[i];
+		  buffer[size-1-i] = !buffer[i];
-      }
+		  }
-      for(int i = size-1; i >= 0; i--) {
+		  for(int i = size-1; i >= 0; i--) {
-	if(buffer[i]) {
+		  if(buffer[i]) {
-	  weylgroup_element_t *shortest = shorten(i, left_invariance, right_invariance, info->dq);
+		  weylgroup_element_t *shortest = shorten(i, left_invariance, right_invariance, info->dq);
-	  printf(" %s", alphabetize(shortest, stringbuffer));
+		  printf(" %s", alphabetize(shortest, stringbuffer));
-	  buffer[i] = 0;
+		  buffer[i] = 0;
-	  queue_init(&queue);
+		  queue_init(&queue);
-	  queue_put(&queue, i);
+		  queue_put(&queue, i);
-	  while((cur = queue_get(&queue)) != -1) {
+		  while((cur = queue_get(&queue)) != -1) {
-	    for(doublecoset_list_t *current = info->dq->coset[cur].bruhat_lower; current; current = current->next) {
+		  for(doublecoset_list_t *current = info->dq->coset[cur].bruhat_lower; current; current = current->next) {
-	      int idx = current->to - info->dq->cosets;
+		  int idx = current->to - info->dq->cosets;
-	      if(buffer[idx]) {
+		  if(buffer[idx]) {
-		buffer[idx] = 0;
+		  buffer[idx] = 0;
-		queue_put(&queue, idx);
+		  queue_put(&queue, idx);
-	      }
+		  }
-	    }
+		  }
-	    for(int j = 0; j < info->rank; j++) {
+		  for(int j = 0; j < info->rank; j++) {
-	      left = info->dq->coset[cur].min.left[j] - info->dq->cosets;
+		  left = info->dq->coset[cur].min.left[j] - info->dq->cosets;
-	      if(left_invariance & (1 << j) &&
+		  if(left_invariance & (1 << j) &&
-		 info->graph[left].wordlength < info->graph[cur].wordlength &&
+		  info->graph[left].wordlength < info->graph[cur].wordlength &&
-		 buffer[left]) {
+		  buffer[left]) {
-		buffer[left] = 0;
+		  buffer[left] = 0;
-		queue_put(&queue, left);
+		  queue_put(&queue, left);
-	      }
+		  }
-	      right = info->graph[cur].left[j];
+		  right = info->graph[cur].left[j];
-	      if(right_invariance & (1 << j) &&
+		  if(right_invariance & (1 << j) &&
-		 info->graph[right].wordlength < info->graph[cur].wordlength &&
+		  info->graph[right].wordlength < info->graph[cur].wordlength &&
-		 buffer[right]) {
+		  buffer[right]) {
-		buffer[right] = 0;
+		  buffer[right] = 0;
-		queue_put(&queue, right);
+		  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");
 	}
-      }
-      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, const enumeration_info_t *ei)
 {
-  long *count = (long*)ei->callback_data;
+	long *count = (long*)ei->callback_data;
 
-  if((++(*count)) % 100000000 == 0) {
+	if((++(*count)) % 100000000 == 0) {
-    bv_print(stderr, pos, size/2);
+		bv_print(stderr, pos, size/2);
-    fprintf(stderr, "\n");
+		fprintf(stderr, "\n");
-  }
+	}
 }
 
 int main(int argc, const char *argv[])
 {
-  semisimple_type_t type;
+	semisimple_type_t type;
-  unsigned long right_invariance, left_invariance;
+	unsigned long right_invariance, left_invariance;
-  int rank, order, positive;
+	int rank, order, positive;
-  int fixpoints;
+	int fixpoints;
 
-  doublequotient_t *dq;
+	doublequotient_t *dq;
 
-  const char *alphabet = "abcdefghijklmnopqrstuvwxyz";
+	const char *alphabet = "abcdefghijklmnopqrstuvwxyz";
 
-  // read arguments
+	// read arguments
 
-  ERROR(argc < 2, "Too few arguments!\n");
+	ERROR(argc < 2, "Too few arguments!\n");
 
-  type.n = 0;
+	type.n = 0;
-  for(int i = 0; i < argc - 1; i++) {
+	for(int i = 0; i < argc - 1; i++) {
-    if(argv[i+1][0] < 'A' || argv[i+1][0] > 'G')
+		if(argv[i+1][0] < 'A' || argv[i+1][0] > 'G')
-      break;
+			break;
-    type.n++;
+		type.n++;
-  }
+	}
 
-  type.factors = (simple_type_t*)malloc(type.n*sizeof(simple_type_t));
+	type.factors = (simple_type_t*)malloc(type.n*sizeof(simple_type_t));
-  for(int i = 0; i < type.n; i++) {
+	for(int i = 0; i < type.n; i++) {
-    type.factors[i].series = argv[i+1][0];
+		type.factors[i].series = argv[i+1][0];
-    type.factors[i].rank = argv[i+1][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");
+		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;
+	left_invariance = right_invariance = 0;
 
-  if(argc - type.n >= 3) {
+	if(argc - type.n >= 3) {
-    if(strcmp(argv[type.n + 1], "-") != 0)
+		if(strcmp(argv[type.n + 1], "-") != 0)
-      for(int i = 0; i < strlen(argv[type.n + 1]); i++)
+			for(int i = 0; i < strlen(argv[type.n + 1]); i++)
-	left_invariance |= (1 << (argv[type.n + 1][i] - 'a'));
+				left_invariance |= (1 << (argv[type.n + 1][i] - 'a'));
-    if(strcmp(argv[type.n + 2], "-") != 0)
+		if(strcmp(argv[type.n + 2], "-") != 0)
-      for(int i = 0; i < strlen(argv[type.n + 2]); i++)
+			for(int i = 0; i < strlen(argv[type.n + 2]); i++)
-	right_invariance |= (1 << (argv[type.n + 2][i] - 'a'));
+				right_invariance |= (1 << (argv[type.n + 2][i] - 'a'));
-  }
+	}
 
-  // generate graph
+	// generate graph
 
-  dq = weyl_generate_bruhat(type, left_invariance, right_invariance);
+	dq = weyl_generate_bruhat(type, left_invariance, right_invariance);
 
-  // print stuff
+	// print stuff
 
-  int output_level = 2;
+	int output_level = 2;
-  if(getenv("OUTPUT_LEVEL"))
+	if(getenv("OUTPUT_LEVEL"))
-    output_level = atoi(getenv("OUTPUT_LEVEL"));
+		output_level = atoi(getenv("OUTPUT_LEVEL"));
 
-  rank = weyl_rank(type);                // number of simple roots
+	rank = weyl_rank(type);                // number of simple roots
-  order = weyl_order(type);              // number of Weyl group elements
+	order = weyl_order(type);              // number of Weyl group elements
-  positive = weyl_positive(type);        // number of positive roots
+	positive = weyl_positive(type);        // number of positive roots
 
-  if(output_level >= 1) {
+	if(output_level >= 1) {
-    if(left_invariance) {
+		if(left_invariance) {
-      printf("<");
+			printf("<");
-      for(int j = 0; j < rank; j++)
+			for(int j = 0; j < rank; j++)
-	if(left_invariance & BIT(j))
+				if(left_invariance & BIT(j))
-	  fputc(alphabet[j], stdout);
+					fputc(alphabet[j], stdout);
-      printf("> \\ ");
+			printf("> \\ ");
-    }
+		}
 
-    for(int i = 0; i < type.n; i++)
+		for(int i = 0; i < type.n; i++)
-      printf("%s%c%d", i == 0 ? "" : " x ", type.factors[i].series, type.factors[i].rank);
+			printf("%s%c%d", i == 0 ? "" : " x ", type.factors[i].series, type.factors[i].rank);
 
-    if(right_invariance) {
+		if(right_invariance) {
-      printf(" / <");
+			printf(" / <");
-      for(int j = 0; j < rank; j++)
+			for(int j = 0; j < rank; j++)
-	if(right_invariance & BIT(j))
+				if(right_invariance & BIT(j))
-	  fputc(alphabet[j], stdout);
+					fputc(alphabet[j], stdout);
-      printf(">");
+			printf(">");
-    }
+		}
-    fprintf(stdout, "\n");
+		fprintf(stdout, "\n");
 
-    fprintf(stdout, "Rank: %d\tOrder: %d\tPositive Roots: %d\tCosets: %d\n\n", rank, order, positive, dq->count);
+		fprintf(stdout, "Rank: %d\tOrder: %d\tPositive Roots: %d\tCosets: %d\n\n", rank, order, positive, dq->count);
-  }
+	}
 
-  if(output_level >= 3) {
+	if(output_level >= 3) {
-    fprintf(stdout, "Shortest coset representatives: \n");
+		fprintf(stdout, "Shortest coset representatives: \n");
-    for(int i = 0, wl = 0; i < dq->count; i++) {
+		for(int i = 0, wl = 0; i < dq->count; i++) {
-      if(dq->cosets[i].min->wordlength > wl) {
+			if(dq->cosets[i].min->wordlength > wl) {
-	printf("\n");
+				printf("\n");
-	wl = dq->cosets[i].min->wordlength;
+				wl = dq->cosets[i].min->wordlength;
-      }
+			}
-      //      fprintf(stdout, "%s(%d) ", alphabetize(dq->cosets[i].min, stringbuffer), dq->cosets[i].max->wordlength);
+			//      fprintf(stdout, "%s(%d) ", alphabetize(dq->cosets[i].min, stringbuffer), dq->cosets[i].max->wordlength);
-      fprintf(stdout, "%s ", alphabetize(dq->cosets[i].min, stringbuffer));
+			fprintf(stdout, "%s ", alphabetize(dq->cosets[i].min, stringbuffer));
-    }
+		}
-    fprintf(stdout, "\n\n");
+		fprintf(stdout, "\n\n");
-  }
+	}
 
-  if(output_level >= 4) {
+	if(output_level >= 4) {
-    fprintf(stdout, "Bruhat order in graphviz format:\n");
+		fprintf(stdout, "Bruhat order in graphviz format:\n");
-    fprintf(stdout, "digraph test123 {\n");
+		fprintf(stdout, "digraph test123 {\n");
-    for(int i = 0; i < dq->count; i++)
+		for(int i = 0; i < dq->count; i++)
-      for(doublecoset_list_t *current = dq->cosets[i].bruhat_lower; current; current = current->next)
+			for(doublecoset_list_t *current = dq->cosets[i].bruhat_lower; current; current = current->next)
-	fprintf(stdout, "%s -> %s;\n",
+				fprintf(stdout, "%s -> %s;\n",
-		alphabetize(dq->cosets[i].min, stringbuffer),
+				        alphabetize(dq->cosets[i].min, stringbuffer),
-		alphabetize(current->to->min, stringbuffer2));
+				        alphabetize(current->to->min, stringbuffer2));
-    fprintf(stdout, "}\n\n");
+		fprintf(stdout, "}\n\n");
-  }
+	}
 
-  if(output_level >= 4) {
+	if(output_level >= 4) {
-    fprintf(stdout, "Opposites:\n");
+		fprintf(stdout, "Opposites:\n");
-    for(int i = 0; i < dq->count; i++)
+		for(int i = 0; i < dq->count; i++)
-      fprintf(stdout, "%s <-> %s\n",
+			fprintf(stdout, "%s <-> %s\n",
-	      alphabetize(dq->cosets[i].min, stringbuffer),
+			        alphabetize(dq->cosets[i].min, stringbuffer),
-	      alphabetize(dq->cosets[i].opposite->min, stringbuffer2));
+			        alphabetize(dq->cosets[i].opposite->min, stringbuffer2));
-    fprintf(stdout, "\n");
+		fprintf(stdout, "\n");
-  }
+	}
 
-  fixpoints = 0;
+	fixpoints = 0;
-  for(int i = 0; i < dq->count; i++)
+	for(int i = 0; i < dq->count; i++)
-    if(dq->cosets[i].opposite == &dq->cosets[i]) {
+		if(dq->cosets[i].opposite == &dq->cosets[i]) {
-      if(output_level >= 1) {
+			if(output_level >= 1) {
-	if(fixpoints == 0)
+				if(fixpoints == 0)
-	  fprintf(stdout, "No balanced ideals since the longest element fixes the following cosets:");
+					fprintf(stdout, "No balanced ideals since the longest element fixes the following cosets:");
-	fprintf(stdout, " %s", alphabetize(dq->cosets[i].min, stringbuffer));
+				fprintf(stdout, " %s", alphabetize(dq->cosets[i].min, stringbuffer));
-      }
+			}
-      fixpoints++;
+			fixpoints++;
-    }
+		}
-  if(output_level >= 1 && fixpoints)
+	if(output_level >= 1 && fixpoints)
-    fprintf(stdout, "\n\n");
+		fprintf(stdout, "\n\n");
 
 
-  if(!fixpoints) {
+	if(!fixpoints) {
-    int *buffer = (int*)malloc(dq->count*sizeof(int));
+		int *buffer = (int*)malloc(dq->count*sizeof(int));
 
-    info_t info;
+		info_t info;
-    info.dq = dq;
+		info.dq = dq;
-    info.rank = weyl_rank(type);
+		info.rank = weyl_rank(type);
-    info.order = weyl_order(type);
+		info.order = weyl_order(type);
-    info.positive = weyl_positive(type);
+		info.positive = weyl_positive(type);
-    info.buffer = buffer;
+		info.buffer = buffer;
-    info.level = output_level;
+		info.level = output_level;
 
-    ERROR(dq->count > 2*BV_BLOCKSIZE*BV_RANK, "We can handle at most %d cosets. Increase BV_RANK if more is needed.\n", 2*BV_BLOCKSIZE*BV_RANK);
+		ERROR(dq->count > 2*BV_BLOCKSIZE*BV_RANK, "We can handle at most %d cosets. Increase BV_RANK if more is needed.\n", 2*BV_BLOCKSIZE*BV_RANK);
 
-    long count;
+		long count;
-    if(output_level >= 2) {
+		if(output_level >= 2) {
-      fprintf(stdout, "Balanced ideals:\n");
+			fprintf(stdout, "Balanced ideals:\n");
-      count = enumerate_balanced_thickenings(dq, balanced_thickening_callback, &info);
+			count = enumerate_balanced_thickenings(dq, balanced_thickening_callback, &info);
-      fprintf(stdout, "\n");
+			fprintf(stdout, "\n");
-    } else {
+		} else {
-      long outputcount = 0;
+			long outputcount = 0;
-      count = enumerate_balanced_thickenings(dq, balanced_thickening_simple_callback, &outputcount);
+			count = enumerate_balanced_thickenings(dq, balanced_thickening_simple_callback, &outputcount);
-    }
+		}
 
-    if(output_level >= 1)
+		if(output_level >= 1)
-      fprintf(stdout, "Found %ld balanced ideal%s\n", count, count == 1 ? "" : "s");
+			fprintf(stdout, "Found %ld balanced ideal%s\n", count, count == 1 ? "" : "s");
-  }
+	}
 
-  weyl_destroy_bruhat(dq);
+	weyl_destroy_bruhat(dq);
-  free(type.factors);
+	free(type.factors);
 
-  return 0;
+	return 0;
 }

thickenings.c

@@ -110,12 +110,12 @@ static void generate_principal_ideals(doublequotient_t *dq, bitvec_t *pos, bitve
       }
 
 #ifdef _DEBUG
-    if(is_slim[i]) {
+    if(is_slim[i] && dq->cosets[0].min) { // sometimes we don't want to define min and max
-      fprintf(stderr, " ids: [0");
+	    fprintf(stderr, " ids: [0");
-      for(int j = 1; j < size; j++)
+	    for(int j = 1; j < size; j++)
-	if(principal[j])
+		    if(principal[j])
-	  fprintf(stderr, ", %d", dq->cosets[j].min->id);
+			    fprintf(stderr, ", %d", dq->cosets[j].min->id);
-      fprintf(stderr, "]\n");
+	    fprintf(stderr, "]\n");
     }
 #endif
 
@@ -160,7 +160,7 @@ long enumerate_balanced_thickenings(doublequotient_t *dq, enumeration_callback c
   // the algorithm only works if the opposition pairing does not stabilize any element
   // if this happens, there can be no balanced thickenings
   for(int i = 0; i < dq->count; i++)
-    if(dq->cosets[i].opposite->min->id == dq->cosets[i].min->id)
+	  if(dq->cosets[i].opposite->index == i)
       return 0;
 
   // we can only handle bitvectors up to BV_BLOCKSIZE*BV_RANK bits, but we only store half of the weyl group