184 lines
6.0 KiB

#include <stdio.h>
#include <limits.h>
#include <stdlib.h>
#include <malloc.h>
#include <memory.h>
#include "thickenings.h"
#include "weyl.h"
#include "queue.h"
This function enumerates all balanced ideals satisfying certain constraints, given by its arguments pos, neg and next_neg
- info: constant information which just gets passed on to recursive calls, mainly contains the principal ideals
- pos: a set of elements which have to be positive (that is, in the ideal)
- neg: a set of elements which have to be negative (not in the ideal)
- next_neg: this element has to be the first negative one not already contained in neg; if next_neg is info.size/2, then everything not in neg has to be positive
- already_known: not a constraint, but just a hint to speed things up; tells the function that the first already_known elements are set either in neg or in pos; must be less or equal to next_neg
- returns number of balanced ideals found
uses the bitvector functions bv_union, bv_copy, bv_set_range_except, bv_disjoint, bv_next_zero
static long enumerate_tree(const enumeration_info_t *info, const bitvec_t *pos, const bitvec_t *neg, int next_neg, int already_known, int level)
static long totcount = 0;
bitvec_t newpos, newneg, known;
int next_next_neg;
long count = 0;
// the omission of next_neg means inclusion of info->size - 1 - next_neg
// add its principal ideal to pos and the opposite to neg
if(next_neg != info->size/2) {
// if the principal ideal we want to add is not slim by itself, we don't even have to try; but there is not really a performance benefit, it rather makes it slower
// if(!info->principal_is_slim[info->size - 1 - next_neg])
// return 0;
bv_union(&info->principal_pos[info->size - 1 - next_neg], pos, &newpos);
bv_union(&info->principal_neg[info->size - 1 - next_neg], neg, &newneg);
} else { // or, if there is no next_neg, just copy
bv_copy(pos, &newpos);
bv_copy(neg, &newneg);
// everything before next_neg which was unknown should be set to positive; to speed this up, we can start with already_known
bv_set_range_except(&newpos, neg, already_known, next_neg);
#ifdef _DEBUG
bv_print_nice(stderr, &newpos, &newneg, -1, info->size/2);
fprintf(stderr, "\n");
// check if this leads to any conflicts (equivalently, violates slimness)
if(!bv_disjoint(&newpos, &newneg))
return 0;
// what do we know so far?
bv_union(&newpos, &newneg, &known);
next_next_neg = bv_next_zero(&known, next_neg + 1);
if(next_next_neg >= info->size/2) {
// there is no unknown left, so we found a balanced ideal
info->callback(&newpos, info->size, info);
return 1;
do {
count += enumerate_tree(info, &newpos, &newneg, next_next_neg, next_neg + 1, level + 1);
next_next_neg = bv_next_zero(&known, next_next_neg + 1);
} while(next_next_neg <= info->size/2);
return count;
static void generate_principal_ideals(doublequotient_t *dq, bitvec_t *pos, bitvec_t *neg, int *is_slim)
queue_t queue;
int current;
doublecoset_list_t *edge;
int size = dq->count;
// generate principal ideals
int *principal = (int*)malloc(size*sizeof(int));
for(int i = 0; i < size; i++) {
memset(principal, 0, size*sizeof(int));
principal[i] = 1;
queue_put(&queue, i);
while((current = queue_get(&queue)) != -1)
for(edge = dq->cosets[current].bruhat_lower; edge; edge = edge->next)
if(!principal[edge->to->index]) {
principal[edge->to->index] = 1;
queue_put(&queue, edge->to->index);
// copy the first half into bitvectors
is_slim[i] = 1;
for(int j = 0; j < size/2; j++)
bv_set_bit(&pos[i], j);
for(int j = 0; j < size/2; j++)
if(principal[size - 1 - j]) {
bv_set_bit(&neg[i], j);
if(bv_get_bit(&pos[i], j))
is_slim[i] = 0;
#ifdef _DEBUG
if(is_slim[i] && dq->cosets[0].min) { // sometimes we don't want to define min and max
fprintf(stderr, " ids: [0");
for(int j = 1; j < size; j++)
fprintf(stderr, ", %d", dq->cosets[j].min->id);
fprintf(stderr, "]\n");
// output principal ideals
#ifdef _DEBUG
for(int i = 0; i < size; i++) {
fprintf(stderr, "%2d: ", i);
bv_print_nice(stderr, &pos[i], &neg[i], -1, size/2);
fprintf(stderr, "\n");
enumerates all balanced ideals
- graph: hasse diagram of the bruhat order (of double cosets) with opposition pairing
- size: number of nodes in graph
- callback to call when a balanced ideal was found
- arbitrary data for callback function
returns the number of balanced ideals
long enumerate_balanced_thickenings(doublequotient_t *dq, enumeration_callback callback, void *callback_data)
long count = 0;
enumeration_info_t info;
info.size = dq->count;
info.callback = callback;
info.callback_data = callback_data;
info.principal_pos = (bitvec_t*)malloc(info.size*sizeof(bitvec_t));
info.principal_neg = (bitvec_t*)malloc(info.size*sizeof(bitvec_t));
info.principal_is_slim = (int*)malloc(info.size*sizeof(int));
// 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->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
ERROR(info.size > 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);
generate_principal_ideals(dq, info.principal_pos, info.principal_neg, info.principal_is_slim);
// enumerate balanced ideals
bitvec_t pos, neg;
for(int i = 0; i <= info.size/2; i++)
count += enumerate_tree(&info, &pos, &neg, i, 0, 0);
return count;