310 lines
8.7 KiB
C
310 lines
8.7 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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node_t *graph;
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int cosets;
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int rank;
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int order;
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int hyperplanes;
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semisimple_type_t type;
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unsigned long left_invariance;
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unsigned long right_invariance;
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const char *alphabet;
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int *buffer;
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} info_t;
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int shorten(int i, unsigned long left, unsigned long right, node_t *graph, 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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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->graph[i].left[j];
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right = info->graph[i].right[j];
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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("left: ");
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for(int j = 0; j < info->rank; j++)
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printf("%c", left_invariance & (1 << j) ? info->alphabet[j] : ' ');
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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) ? info->alphabet[j] : ' ');
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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 current, left, right, shortest;
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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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int shortest = shorten(i, left_invariance, right_invariance, info->graph, info-> rank);
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printf(" %s", alphabetize(info->graph[shortest].word,
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info->graph[shortest].wordlength,
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info->alphabet,
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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((current = queue_get(&queue)) != -1) {
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for(edgelist_t *edge = info->graph[current].bruhat_lower; edge != (edgelist_t*)0; edge = edge->next) {
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if(buffer[edge->to]) {
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buffer[edge->to] = 0;
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queue_put(&queue, edge->to);
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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->graph[current].left[j];
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if(left_invariance & (1 << j) &&
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info->graph[left].wordlength < info->graph[current].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[current].left[j];
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if(right_invariance & (1 << j) &&
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info->graph[right].wordlength < info->graph[current].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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}
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printf("\n");
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}
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/*
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if((++totcount) % 100000000 == 0) {
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fprintf(stderr, "Found balanced ideal: ");
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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, hyperplanes, cosets;
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int fixpoints;
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node_t *graph;
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char string_buffer1[1000];
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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] > 'I')
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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-I and n out of 0-9\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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graph = graph_alloc(type);
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cosets = prepare_simplified_graph(type, left_invariance, right_invariance, graph);
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ERROR(cosets < 0, "The left invariance is not preserved by the opposition involution!\n");
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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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hyperplanes = weyl_hyperplanes(type); // number of positive roots
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if(output_level >= 1) {
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printf("Poset: ");
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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, hyperplanes, cosets);
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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 < cosets; i++) {
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if(i == 0) {
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fprintf(stdout, "1");
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} else if(graph[i].wordlength > wl) {
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fprintf(stdout, "\n%s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
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wl = graph[i].wordlength;
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} else
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fprintf(stdout, "%s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
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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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edgelist_t *edge;
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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 < cosets; i++) {
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edge = graph[i].bruhat_lower;
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while(edge) {
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fprintf(stdout, "%s -> %s;\n",
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alphabetize(graph[i].word, graph[i].wordlength, alphabet, stringbuffer),
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alphabetize(graph[edge->to].word, graph[edge->to].wordlength, alphabet, stringbuffer2));
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edge = edge->next;
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}
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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, "Opposites:\n");
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for(int i = 0; i < cosets; i++) {
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fprintf(stdout, "%s <-> %s\n",
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alphabetize(graph[i].word, graph[i].wordlength, alphabet, stringbuffer),
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alphabetize(graph[graph[i].opposite].word, graph[graph[i].opposite].wordlength, alphabet, stringbuffer2));
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}
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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 < cosets; i++)
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if(graph[i].opposite == 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: %s", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
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else
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fprintf(stdout, " %s", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
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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(cosets*sizeof(int));
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info_t info;
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info.graph = graph;
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info.cosets = cosets;
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info.rank = rank;
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info.order = order;
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info.hyperplanes = hyperplanes;
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info.type = type;
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info.left_invariance = left_invariance;
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info.right_invariance = right_invariance;
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info.alphabet = alphabet;
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info.buffer = buffer;
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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(graph, cosets, balanced_thickening_callback, &info);
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fprintf(stdout, "\n", count);
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}
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else
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count = enumerate_balanced_thickenings(graph, cosets, 0, 0);
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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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graph_free(type, graph);
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free(type.factors);
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return 0;
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}
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