108 lines
3.5 KiB
C
108 lines
3.5 KiB
C
#include <string.h>
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#include <stdio.h>
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#include "coxeter.h"
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#include "queue.h"
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#include "thickenings.h"
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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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ERROR(strlen(alphabet) < rank, "The alphabet has too few letters\n");
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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: %d %d!\n", left_invariance, opposition_involution(type, left_invariance));
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// print stuff
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rank = coxeter_rank(type); // number of simple roots
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order = coxeter_order(type); // number of Weyl group elements
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hyperplanes = coxeter_hyperplanes(type); // number of positive roots
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fprintf(stderr, "Rank: %d\tOrder: %d\tPositive Roots: %d\tCosets: %d\n", rank, order, hyperplanes, cosets);
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fprintf(stderr, "\n");
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fprintf(stderr, "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(stderr, "1");
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} else if(graph[i].wordlength > wl) {
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fprintf(stderr, "\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(stderr, "%s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
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}
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fprintf(stderr, "\n\n");
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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(fixpoints == 0)
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fprintf(stderr, "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(stderr, " %s", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
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fixpoints++;
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}
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if(fixpoints > 0) {
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fprintf(stderr, "\n\n");
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} else {
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// enumerate balanced thickenings
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fwrite(&type.n, sizeof(int), 1, stdout);
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fwrite(type.factors, sizeof(simple_type_t), type.n, stdout);
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fwrite(&left_invariance, sizeof(unsigned long), type.n, stdout);
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fwrite(&right_invariance, sizeof(unsigned long), type.n, stdout);
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long count = enumerate_balanced_thickenings(type, graph, cosets, alphabet, stdout);
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fprintf(stderr, "Found %ld balanced thickenings\n\n", count);
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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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