enumerate-balanced-ideals/enumerate.c
Florian Stecker b823aa7b0b Fixes
2017-03-20 10:46:23 +01:00

362 lines
10 KiB
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, const enumeration_info_t *ei)
{
static long totcount = 0;
if(ei->callback_data) {
info_t *info = (info_t*)ei->callback_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->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);
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) {
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++) {
if(!bv_get_bit(&high, i))
continue;
printf("%s ", alphabetize(info->dq->cosets[size-1-i].min, stringbuffer));
bv_difference(&high, &ei->principal_neg[size-1-i], &high);
bv_difference(&low, &ei->principal_pos[size-1-i], &low);
}
for(int i = size/2 - 1; i >= 0; i--) {
if(!bv_get_bit(&low, i))
continue;
printf("%s ", alphabetize(info->dq->cosets[i].min, stringbuffer));
bv_difference(&low, &ei->principal_pos[i], &low);
}
}
int max_length = 0;
for(int i = 0; i < size/2; i++) {
if(bv_get_bit(pos, i)) {
if(info->dq->cosets[i].max->wordlength > max_length)
max_length = info->dq->cosets[i].max->wordlength;
} else {
if(info->dq->cosets[size-i-1].max->wordlength > max_length)
max_length = info->dq->cosets[size-i-1].max->wordlength;
}
}
// printf(" max length: %d", max_length);
/*
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, const enumeration_info_t *ei)
{
long *count = (long*)ei->callback_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(%d) ", alphabetize(dq->cosets[i].min, stringbuffer), dq->cosets[i].max->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 balanced ideals 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;
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;
if(output_level >= 2) {
fprintf(stdout, "Balanced ideals:\n");
count = enumerate_balanced_thickenings(dq, balanced_thickening_callback, &info);
fprintf(stdout, "\n");
} 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;
}