314 lines
8.5 KiB
C
314 lines
8.5 KiB
C
#include "thickenings.h"
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#include "weyl.h"
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#include "queue.h"
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#include <strings.h>
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#include <stdio.h>
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char stringbuffer[100];
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char stringbuffer2[100];
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typedef struct {
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doublequotient_t *dq;
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int rank;
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int order;
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int positive;
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int *buffer;
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int level;
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} info_t;
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static char* alphabetize(weylgroup_element_t *e, char *str)
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{
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if(e->wordlength == 0)
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sprintf(str, "1");
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else {
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for(int j = 0; j < e->wordlength; j++)
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str[j] = e->word[j] + 'a';
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str[e->wordlength] = 0;
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}
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return str;
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}
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/*
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int shorten(int i, unsigned long left, unsigned long right, doublequotient_t *dq, int rank)
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{
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int other, shorter = i;
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do {
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i = shorter;
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for(int j = 0; j < rank; j++) {
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other = graph[shorter].left[j];
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if(left & (1 << j) &&
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graph[other].wordlength < graph[shorter].wordlength)
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shorter = other;
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other = graph[shorter].right[j];
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if(right & (1 << j) &&
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graph[other].wordlength < graph[shorter].wordlength)
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shorter = other;
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}
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} while(shorter != i);
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return shorter;
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}
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*/
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void balanced_thickening_callback(const bitvec_t *pos, int size, void *data)
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{
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static long totcount = 0;
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if(data) {
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info_t *info = (info_t*)data;
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unsigned long right_invariance = FIRSTBITS(info->rank);
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unsigned long left_invariance = FIRSTBITS(info->rank);
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int bit1, bit2left, bit2right, left, right;
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for(int i = 0; i < size; i++) {
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bit1 = i < size/2 ? bv_get_bit(pos, i) : !bv_get_bit(pos, size - 1 - i);
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for(int j = 0; j < info->rank; j++) {
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left = info->dq->cosets[i].min->left[j]->coset - info->dq->cosets;
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right = info->dq->cosets[i].min->right[j]->coset - info->dq->cosets;
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bit2left = left < size/2 ? bv_get_bit(pos, left) : !bv_get_bit(pos, size - 1 - left);
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bit2right = right < size/2 ? bv_get_bit(pos, right) : !bv_get_bit(pos, size - 1 - right);
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if(bit1 != bit2left)
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left_invariance &= ~BIT(j);
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if(bit1 != bit2right)
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right_invariance &= ~BIT(j);
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}
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}
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printf("%4d left: ", totcount++);
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for(int j = 0; j < info->rank; j++)
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printf("%c", left_invariance & (1 << j) ? j + 'a' : ' ');
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printf(" right: ");
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for(int j = 0; j < info->rank; j++)
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printf("%c", right_invariance & (1 << j) ? j + 'a' : ' ');
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/*
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if(info->buffer) {
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printf(" generators:");
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queue_t queue;
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int cur, left, right;
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int *buffer = info->buffer;
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for(int i = 0; i < size/2; i++) {
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buffer[i] = bv_get_bit(pos, i);
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buffer[size-1-i] = !buffer[i];
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}
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for(int i = size-1; i >= 0; i--) {
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if(buffer[i]) {
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weylgroup_element_t *shortest = shorten(i, left_invariance, right_invariance, info->dq);
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printf(" %s", alphabetize(shortest, stringbuffer));
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buffer[i] = 0;
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queue_init(&queue);
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queue_put(&queue, i);
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while((cur = queue_get(&queue)) != -1) {
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for(doublecoset_list_t *current = info->dq->coset[cur].bruhat_lower; current; current = current->next) {
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int idx = current->to - info->dq->cosets;
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if(buffer[idx]) {
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buffer[idx] = 0;
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queue_put(&queue, idx);
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}
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}
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for(int j = 0; j < info->rank; j++) {
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left = info->dq->coset[cur].min.left[j] - info->dq->cosets;
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if(left_invariance & (1 << j) &&
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info->graph[left].wordlength < info->graph[cur].wordlength &&
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buffer[left]) {
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buffer[left] = 0;
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queue_put(&queue, left);
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}
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right = info->graph[cur].left[j];
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if(right_invariance & (1 << j) &&
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info->graph[right].wordlength < info->graph[cur].wordlength &&
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buffer[right]) {
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buffer[right] = 0;
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queue_put(&queue, right);
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}
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}
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}
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}
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}
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if(info->level >= 5) {
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printf(" ids: [0");
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for(int i = 1; i < size/2; i++)
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if(bv_get_bit(pos, i))
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printf(", %d", info->graph[i].id);
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for(int i = 0; i < size/2; i++)
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if(!bv_get_bit(pos, i))
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printf(", %d", info->graph[size-1-i].id);
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printf("]");
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}
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}
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*/
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printf("\n");
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}
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}
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void balanced_thickening_simple_callback(const bitvec_t *pos, int size, void *data)
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{
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long *count = (long*)data;
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if((++(*count)) % 100000000 == 0) {
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bv_print(stderr, pos, size/2);
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fprintf(stderr, "\n");
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}
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}
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int main(int argc, const char *argv[])
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{
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semisimple_type_t type;
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unsigned long right_invariance, left_invariance;
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int rank, order, positive;
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int fixpoints;
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doublequotient_t *dq;
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const char *alphabet = "abcdefghijklmnopqrstuvwxyz";
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// read arguments
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ERROR(argc < 2, "Too few arguments!\n");
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type.n = 0;
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for(int i = 0; i < argc - 1; i++) {
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if(argv[i+1][0] < 'A' || argv[i+1][0] > 'G')
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break;
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type.n++;
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}
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type.factors = (simple_type_t*)malloc(type.n*sizeof(simple_type_t));
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for(int i = 0; i < type.n; i++) {
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type.factors[i].series = argv[i+1][0];
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type.factors[i].rank = argv[i+1][1] - '0';
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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");
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}
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left_invariance = right_invariance = 0;
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if(argc - type.n >= 3) {
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if(strcmp(argv[type.n + 1], "-") != 0)
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for(int i = 0; i < strlen(argv[type.n + 1]); i++)
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left_invariance |= (1 << (argv[type.n + 1][i] - 'a'));
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if(strcmp(argv[type.n + 2], "-") != 0)
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for(int i = 0; i < strlen(argv[type.n + 2]); i++)
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right_invariance |= (1 << (argv[type.n + 2][i] - 'a'));
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}
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// generate graph
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dq = weyl_generate_bruhat(type, left_invariance, right_invariance);
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// print stuff
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int output_level = 2;
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if(getenv("OUTPUT_LEVEL"))
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output_level = atoi(getenv("OUTPUT_LEVEL"));
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rank = weyl_rank(type); // number of simple roots
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order = weyl_order(type); // number of Weyl group elements
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positive = weyl_positive(type); // number of positive roots
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if(output_level >= 1) {
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if(left_invariance) {
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printf("<");
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for(int j = 0; j < rank; j++)
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if(left_invariance & BIT(j))
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fputc(alphabet[j], stdout);
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printf("> \\ ");
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}
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for(int i = 0; i < type.n; i++)
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printf("%s%c%d", i == 0 ? "" : " x ", type.factors[i].series, type.factors[i].rank);
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if(right_invariance) {
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printf(" / <");
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for(int j = 0; j < rank; j++)
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if(right_invariance & BIT(j))
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fputc(alphabet[j], stdout);
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printf(">");
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}
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fprintf(stdout, "\n");
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fprintf(stdout, "Rank: %d\tOrder: %d\tPositive Roots: %d\tCosets: %d\n\n", rank, order, positive, dq->count);
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}
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if(output_level >= 3) {
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fprintf(stdout, "Shortest coset representatives: \n");
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for(int i = 0, wl = 0; i < dq->count; i++) {
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if(dq->cosets[i].min->wordlength > wl) {
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printf("\n");
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wl = dq->cosets[i].min->wordlength;
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}
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fprintf(stdout, "%s ", alphabetize(dq->cosets[i].min, stringbuffer));
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}
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fprintf(stdout, "\n\n");
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}
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if(output_level >= 4) {
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fprintf(stdout, "Bruhat order in graphviz format:\n");
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fprintf(stdout, "digraph test123 {\n");
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for(int i = 0; i < dq->count; i++)
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for(doublecoset_list_t *current = dq->cosets[i].bruhat_lower; current; current = current->next)
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fprintf(stdout, "%s -> %s;\n",
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alphabetize(dq->cosets[i].min, stringbuffer),
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alphabetize(current->to->min, stringbuffer2));
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fprintf(stdout, "}\n\n");
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}
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if(output_level >= 4) {
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fprintf(stdout, "Opposites:\n");
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for(int i = 0; i < dq->count; i++)
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fprintf(stdout, "%s <-> %s\n",
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alphabetize(dq->cosets[i].min, stringbuffer),
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alphabetize(dq->cosets[i].opposite->min, stringbuffer2));
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fprintf(stdout, "\n");
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}
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fixpoints = 0;
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for(int i = 0; i < dq->count; i++)
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if(dq->cosets[i].opposite == &dq->cosets[i]) {
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if(output_level >= 1) {
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if(fixpoints == 0)
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fprintf(stdout, "No thickenings since the longest element fixes the following cosets:");
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fprintf(stdout, " %s", alphabetize(dq->cosets[i].min, stringbuffer));
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}
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fixpoints++;
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}
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if(output_level >= 1 && fixpoints)
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fprintf(stdout, "\n\n");
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if(!fixpoints) {
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int *buffer = (int*)malloc(dq->count*sizeof(int));
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info_t info;
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info.dq = dq;
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info.rank = weyl_rank(type);
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info.order = weyl_order(type);
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info.positive = weyl_positive(type);
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info.buffer = buffer;
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info.level = output_level;
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long count;
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if(output_level >= 2) {
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fprintf(stdout, "Balanced ideals:\n", count);
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count = enumerate_balanced_thickenings(dq, balanced_thickening_callback, &info);
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fprintf(stdout, "\n", count);
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} else {
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long outputcount = 0;
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count = enumerate_balanced_thickenings(dq, balanced_thickening_simple_callback, &outputcount);
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}
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if(output_level >= 1)
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fprintf(stdout, "Found %ld balanced ideal%s\n", count, count == 1 ? "" : "s");
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}
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weyl_destroy_bruhat(dq);
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free(type.factors);
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return 0;
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}
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