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Mod graph by invariances

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This commit is contained in:
Florian Stecker 2016-11-11 17:07:45 +01:00
parent 03854910b9
commit 993ccfd457
10 changed files with 709 additions and 172 deletions
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1
Makefile
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@ -1,5 +1,6 @@
HEADERS=coxeter.h thickenings.h queue.h
OPTIONS=-O3 -m64 -march=native -flto -funroll-loops -std=gnu99
#OPTIONS=-O0 -g -std=gnu99
all: generate process

31
coxeter.c
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@ -176,6 +176,37 @@ int coxeter_hyperplanes(semisimple_type_t type)
return hyperplanes;
}
unsigned long opposition_involution(semisimple_type_t type, unsigned long theta)
{
int offset = 0;
unsigned long result = 0;
for(int i = 0; i < type.n; i++) {
unsigned long current = (theta >> offset) & ((1 << type.factors[i].rank) - 1);
unsigned long iota_current;
if(type.factors[i].series == 'B' || type.factors[i].series == 'C' || type.factors[i].series == 'F' || type.factors[i].series == 'G') {
iota_current = current;
} else if(type.factors[i].series == 'A') {
iota_current = 0;
for(int j = 0; j < type.factors[i].rank; j++)
iota_current += ((current >> j) & 1) << (type.factors[i].rank - 1 - j);
} else if(type.factors[i].series == 'D') {
if(type.factors[i].rank % 2 == 0) {
iota_current = current;
} else {
ERROR(1, "The opposition involution for type %c%d is not yet implemented!\n", type.factors[i].series, type.factors[i].rank);
}
} else if(type.factors[i].series == 'E') {
ERROR(1, "The opposition involution for En is not yet implemented!\n");
}
result += iota_current << offset;
offset += type.factors[i].rank;
}
return result;
}
static void generate_starting_vector(int rank, gsl_matrix *schlaefli, gsl_vector *result)
{
gsl_matrix *schlaefliLU = gsl_matrix_alloc(rank, rank);

1
coxeter.h
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@ -15,5 +15,6 @@ void generate_coxeter_graph(semisimple_type_t type, int *result);
int coxeter_order(semisimple_type_t type);
int coxeter_hyperplanes(semisimple_type_t type);
int coxeter_rank(semisimple_type_t type);
unsigned long opposition_involution(semisimple_type_t type, unsigned long theta);
#endif

69
generate.c
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@ -8,56 +8,62 @@
int main(int argc, const char *argv[])
{
semisimple_type_t type;
unsigned long right_invariance, left_invariance;
int rank, order, hyperplanes, cosets;
// heap stuff
node_t *graph;
int *left, *right;
edgelist_t *edgelists;
int *words;
int rank, order;
char string_buffer1[1000];
const char *alphabet = "abcdefghijklmnopqrstuvwxyz";
// read arguments
ERROR(argc < 2, "Too few arguments!\n");
type.n = argc - 1;
type.factors = (simple_type_t*)malloc((argc-1)*sizeof(simple_type_t));
type.n = 0;
for(int i = 0; i < argc - 1; i++) {
if(argv[i+1][0] < 'A' || argv[i+1][0] > 'I')
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-I and n out of 0-9\n");
}
rank = coxeter_rank(type);
order = coxeter_order(type);
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'));
}
ERROR(strlen(alphabet) < rank, "The alphabet has too few letters\n");
// initialize
graph = (node_t*)malloc(order*sizeof(node_t));
left = (int*)malloc(order*rank*sizeof(int));
right = (int*)malloc(order*rank*sizeof(int));
for(int i = 0; i < order; i++) {
graph[i].left = &left[rank*i];
graph[i].right = &right[rank*i];
}
// generate graph
prepare_graph(type, graph, &edgelists, &words);
graph = graph_alloc(type);
cosets = prepare_simplified_graph(type, left_invariance, right_invariance, graph);
ERROR(cosets < 0, "The left invariance is not preserved by the opposition involution: %d %d!\n", left_invariance, opposition_involution(type, left_invariance));
// print stuff
int hyperplane_count = coxeter_hyperplanes(type);
rank = coxeter_rank(type); // number of simple roots
order = coxeter_order(type); // number of Weyl group elements
hyperplanes = coxeter_hyperplanes(type); // number of positive roots
fprintf(stderr, "Rank: %d\t\tOrder: %d\t\tHyperplanes: %d\n", rank, order, hyperplane_count);
fprintf(stderr, "Rank: %d\tOrder: %d\tPositive Roots: %d\tCosets: %d\n", rank, order, hyperplanes, cosets);
fprintf(stderr, "\n");
fprintf(stderr, "Group elements: \n");
for(int i = 0, wl = 0; i < order; i++) {
fprintf(stderr, "Shortest coset representatives: \n");
for(int i = 0, wl = 0; i < cosets; i++) {
if(i == 0) {
fprintf(stderr, "1");
} else if(graph[i].wordlength > wl) {
@ -72,16 +78,15 @@ int main(int argc, const char *argv[])
fwrite(&type.n, sizeof(int), 1, stdout);
fwrite(type.factors, sizeof(simple_type_t), type.n, stdout);
long count = enumerate_balanced_thickenings(type, graph, order, alphabet, stdout);
fwrite(&left_invariance, sizeof(unsigned long), type.n, stdout);
fwrite(&right_invariance, sizeof(unsigned long), type.n, stdout);
long count = enumerate_balanced_thickenings(type, graph, cosets, alphabet, stdout);
fprintf(stderr, "\n");
fprintf(stderr, "Found %ld balanced thickenings\n\n", count);
free(graph);
free(left);
free(right);
free(edgelists);
free(words);
graph_free(type, graph);
free(type.factors);
return 0;

193
process-old.c Normal file
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@ -0,0 +1,193 @@
#include <stdio.h>
#include <string.h>
#include <sys/stat.h>
#include "thickenings.h"
#include "coxeter.h"
#include "queue.h"
#define SWAP(t, a, b) do {t tmp = a; a = b; b = tmp;} while(0)
char *stringify_SLn1_permutation(int *word, int wordlength, int rank, char *str)
{
for(int i = 0; i <= rank; i++)
str[i] = '1' + i;
str[rank+1] = 0;
for(int i = 0; i < wordlength; i++) {
char tmp = str[word[i]];
str[word[i]] = str[word[i]+1];
str[word[i]+1] = tmp;
}
return str;
}
char *stringify_Onn1_permutation(int *word, int wordlength, int rank, char *str)
{
for(int i = 0; i <= rank*2; i++)
str[i] = '1' + i;
str[2*rank+1] = 0;
for(int i = 0; i < wordlength; i++) {
if(word[i] == 0)
SWAP(char, str[rank-1], str[rank+1]);
else {
SWAP(char, str[rank-word[i]], str[rank-word[i]-1]);
SWAP(char, str[rank+word[i]], str[rank+word[i]+1]);
}
}
return str;
}
int main(int argc, const char *argv[])
{
FILE *infile;
struct stat st;
int rank, order, hyperplanes;
semisimple_type_t type;
int n;
signed char *level;
node_t *graph;
int *left, *right;
int left_invariant, right_invariant;
int left_invariant_wanted = 0, right_invariant_wanted = 0;
unsigned long left_invariance, right_invariance;
edgelist_t *edgelists;
int *words;
queue_t queue;
int current;
int *seen;
int *generators;
int ngens;
char string_buffer1[1000];
const char *alphabet = "abcdefghijklmnopqrstuvwxyz";
// parse arguments
if(argc < 2)
infile = stdin;
else {
if(strcmp(argv[1], "-") == 0)
infile = stdin;
else
infile = fopen(argv[1], "rb");
if(argc >= 4) {
if(strcmp(argv[2], "-") != 0)
for(int i = 0; i < strlen(argv[2]); i++)
left_invariant_wanted |= (1 << (argv[2][i] - 'a'));
if(strcmp(argv[3], "-") != 0)
for(int i = 0; i < strlen(argv[3]); i++)
right_invariant_wanted |= (1 << (argv[3][i] - 'a'));
}
}
fread(&type.n, sizeof(int), 1, infile); // we completely trust the input data
type.factors = malloc(type.n * sizeof(simple_type_t));
fread(type.factors, sizeof(simple_type_t), type.n, infile);
fread(&left_invariance, sizeof(simple_type_t), type.n, infile);
fread(&right_invariance, sizeof(simple_type_t), type.n, infile);
// get graph
rank = coxeter_rank(type);
order = coxeter_order(type);
hyperplanes = coxeter_hyperplanes(type);
ERROR(strlen(alphabet) < rank, "The alphabet has too few letters\n");
seen = (int*)malloc(order*sizeof(int));
generators = (int*)malloc(order*sizeof(int));
level = (signed char*)malloc(order*sizeof(int));
graph = graph_alloc(type);
prepare_graph(type, graph);
// finally do stuff
int counter = 0;
while(fread(level, sizeof(signed char), order, infile) == order) {
/*
if((counter++) % 100000 == 0)
print_thickening(rank, order, level, 0, 0, 0, alphabet, stdout);
continue;
*/
left_invariant = right_invariant = -1; // all 1s
for(int j = 0; j < order; j++) {
for(int k = 0; k < rank; k++) {
if(level[j] > 0 && level[graph[j].left[k]] < 0 || level[j] < 0 && level[graph[j].left[k]] > 0) {
left_invariant &= ~(1 << k);
}
if(level[j] > 0 && level[graph[j].right[k]] < 0 || level[j] < 0 && level[graph[j].right[k]] > 0) {
right_invariant &= ~(1 << k);
}
}
}
if((~left_invariant & left_invariant_wanted) == 0 && (~right_invariant & right_invariant_wanted) == 0) {
ngens = 0;
memset(generators, 0, order*sizeof(int));
for(int j = 0; j < order; j++) {
if(level[j] == HEAD_MARKER && generators[j] == 0) { // ignore the generator, if it is equivalent to one already seen
ngens++;
queue_init(&queue);
queue_put(&queue, j);
while((current = queue_get(&queue)) != -1) {
if(generators[current] == 0) { // visit everyone only once
generators[current] = ngens;
for(int k = 0; k < rank; k++) {
if(left_invariant & (1 << k))
queue_put(&queue, graph[current].left[k]);
if(right_invariant & (1 << k))
queue_put(&queue, graph[current].right[k]);
}
}
}
}
}
printf("left: ");
for(int j = 0; j < rank; j++)
printf("%c", left_invariant & (1 << j) ? alphabet[j] : ' ');
printf(" right: ");
for(int j = 0; j < rank; j++)
printf("%c", right_invariant & (1 << j) ? alphabet[j] : ' ');
printf(" generators: ");
memset(seen, 0, order*sizeof(int));
for(int i = 0; i < order; i++) {
if(generators[i] != 0 && seen[generators[i]-1] == 0) {
seen[generators[i]-1] = 1;
// if(type.n == 1 && type.factors[0].series == 'A')
// printf("%s ", stringify_SLn1_permutation(graph[i].word, graph[i].wordlength, rank, string_buffer1));
// else if(type.n == 1 && (type.factors[0].series == 'B' || type.factors[0].series == 'C'))
// printf("%s ", stringify_Onn1_permutation(graph[i].word, graph[i].wordlength, rank, string_buffer1));
// else
if(i == 0)
printf("1 ");
else
printf("%s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
}
}
printf("\n");
}
}
if(infile != stdin)
fclose(infile);
// cleanup
graph_free(type, graph);
free(seen);
free(generators);
free(type.factors);
return 0;
}

190
process.c
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@ -6,105 +6,117 @@
#include "coxeter.h"
#include "queue.h"
#define SWAP(t, a, b) do {t tmp = a; a = b; b = tmp;} while(0)
char *stringify_SLn1_permutation(int *word, int wordlength, int rank, char *str)
{
for(int i = 0; i <= rank; i++)
str[i] = '1' + i;
str[rank+1] = 0;
for(int i = 0; i < wordlength; i++) {
char tmp = str[word[i]];
str[word[i]] = str[word[i]+1];
str[word[i]+1] = tmp;
}
return str;
}
char *stringify_Onn1_permutation(int *word, int wordlength, int rank, char *str)
{
for(int i = 0; i <= rank*2; i++)
str[i] = '1' + i;
str[2*rank+1] = 0;
for(int i = 0; i < wordlength; i++) {
if(word[i] == 0)
SWAP(char, str[rank-1], str[rank+1]);
else {
SWAP(char, str[rank-word[i]], str[rank-word[i]-1]);
SWAP(char, str[rank+word[i]], str[rank+word[i]+1]);
}
}
return str;
}
int main(int argc, const char *argv[])
{
FILE *infile;
struct stat st;
int rank, order;
semisimple_type_t type;
int n;
int *thickenings;
signed char *level;
unsigned long left_invariance, right_invariance; // these are the invariances we have already modded out
unsigned long left_invariant, right_invariant; // these are the invariances of the thickening under consideration
int rank, cosets;
node_t *graph;
int *left, *right;
int left_invariant, right_invariant;
int left_invariant_wanted = 0, right_invariant_wanted = 0;
edgelist_t *edgelists;
int *words;
signed char *thickening;
int *seen, *generators;
queue_t queue;
int ngenerators;
int current;
int *seen;
int *generators;
int ngens;
char string_buffer1[1000];
const char *alphabet = "abcdefghijklmnopqrstuvwxyz";
// parse arguments
if(argc < 2)
infile = stdin;
else {
if(strcmp(argv[1], "-") == 0)
infile = stdin;
else
infile = fopen(argv[1], "rb");
if(argc >= 4) {
if(strcmp(argv[2], "-") != 0)
for(int i = 0; i < strlen(argv[2]); i++)
left_invariant_wanted |= (1 << (argv[2][i] - 'a'));
if(strcmp(argv[3], "-") != 0)
for(int i = 0; i < strlen(argv[3]); i++)
right_invariant_wanted |= (1 << (argv[3][i] - 'a'));
}
}
fread(&type.n, sizeof(int), 1, infile); // we completely trust the input data
// we completely trust the input data
ERROR(fread(&type.n, sizeof(int), 1, infile) == 0, "The input file seems to be empty!\n");
type.factors = malloc(type.n * sizeof(simple_type_t));
fread(type.factors, sizeof(simple_type_t), type.n, infile);
// get graph
fread(&left_invariance, sizeof(simple_type_t), type.n, infile);
fread(&right_invariance, sizeof(simple_type_t), type.n, infile);
rank = coxeter_rank(type);
order = coxeter_order(type);
ERROR(strlen(alphabet) < rank, "The alphabet has too few letters\n");
graph = (node_t*)malloc(order*sizeof(node_t));
left = (int*)malloc(order*rank*sizeof(int));
right = (int*)malloc(order*rank*sizeof(int));
graph = graph_alloc(type);
cosets = prepare_simplified_graph(type, left_invariance, right_invariance, graph);
thickening = (signed char*)malloc(cosets*sizeof(signed char));
generators = (int*)malloc(cosets*sizeof(int));
seen = (int*)malloc(cosets*sizeof(int));
while(fread(thickening, sizeof(signed char), cosets, infile) == cosets) {
// determine invariances of this thickening
left_invariant = right_invariant = -1; // set all bits to 1
for(int j = 0; j < cosets; j++) {
for(int k = 0; k < rank; k++) {
if(thickening[j] > 0 && thickening[graph[j].left[k]] < 0 ||
thickening[j] < 0 && thickening[graph[j].left[k]] > 0)
left_invariant &= ~(1 << k);
if(thickening[j] > 0 && thickening[graph[j].right[k]] < 0 ||
thickening[j] < 0 && thickening[graph[j].right[k]] > 0)
right_invariant &= ~(1 << k);
}
}
// print this stuff
printf("left: ");
for(int j = 0; j < rank; j++)
printf("%c", left_invariant & (1 << j) ? alphabet[j] : ' ');
printf(" right: ");
for(int j = 0; j < rank; j++)
printf("%c", right_invariant & (1 << j) ? alphabet[j] : ' ');
printf(" generators: ");
// find a minimal set of weyl group elements such that the union of the ideals generated by their cosets wrt the invariances determined above gives the thickening
// in the first step, mark everything which is equivalent to a "head" by a generator id
ngenerators = 0;
memset(generators, 0, cosets*sizeof(int));
for(int j = 0; j < cosets; j++) {
if(thickening[j] == HEAD_MARKER && generators[j] == 0) { // ignore the generator, if it is equivalent to one already seen
ngenerators++;
queue_init(&queue);
queue_put(&queue, j);
while((current = queue_get(&queue)) != -1) {
if(generators[current] == 0) { // visit everyone only once
generators[current] = ngenerators;
for(int k = 0; k < rank; k++) {
if(left_invariant & (1 << k))
queue_put(&queue, graph[current].left[k]);
if(right_invariant & (1 << k))
queue_put(&queue, graph[current].right[k]);
}
}
}
}
}
// in the second step, go through the list in ascending word length order and print the first appearance of each generator id
memset(seen, 0, cosets*sizeof(int));
for(int i = 0; i < cosets; i++) {
if(generators[i] != 0 && seen[generators[i]-1] == 0) {
seen[generators[i]-1] = 1;
printf("%s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
}
}
printf("\n");
}
if(infile != stdin)
fclose(infile);
graph_free(type, graph);
free(type.factors);
free(thickening);
}
/*******************************************************************************************
seen = (int*)malloc(order*sizeof(int));
generators = (int*)malloc(order*sizeof(int));
level = (signed char*)malloc(order*sizeof(int));
for(int i = 0; i < order; i++) {
graph[i].left = &left[i*rank];
graph[i].right = &right[i*rank];
}
prepare_graph(type, graph, &edgelists, &words);
graph = graph_alloc(type);
prepare_graph(type, graph);
// finally do stuff
@ -112,24 +124,6 @@ int main(int argc, const char *argv[])
while(fread(level, sizeof(signed char), order, infile) == order) {
/*
if((counter++) % 100000 == 0)
print_thickening(rank, order, level, 0, 0, 0, alphabet, stdout);
continue;
*/
left_invariant = right_invariant = -1; // all 1s
for(int j = 0; j < order; j++) {
for(int k = 0; k < rank; k++) {
if(level[j] > 0 && level[graph[j].left[k]] < 0 || level[j] < 0 && level[graph[j].left[k]] > 0) {
left_invariant &= ~(1 << k);
}
if(level[j] > 0 && level[graph[j].right[k]] < 0 || level[j] < 0 && level[graph[j].right[k]] > 0) {
right_invariant &= ~(1 << k);
}
}
}
if((~left_invariant & left_invariant_wanted) == 0 && (~right_invariant & right_invariant_wanted) == 0) {
ngens = 0;
memset(generators, 0, order*sizeof(int));
@ -185,15 +179,11 @@ int main(int argc, const char *argv[])
// cleanup
free(thickenings);
free(edgelists);
free(words);
free(graph);
free(left);
free(right);
graph_free(type, graph);
free(seen);
free(generators);
free(type.factors);
return 0;
}
*/

2
queue.h
View File

@ -4,7 +4,7 @@
#include <stdio.h>
#include <stdlib.h>
#define QUEUE_SIZE 2000
#define QUEUE_SIZE 5000
#define ERROR(condition, msg, ...) if(condition){fprintf(stderr, msg, ##__VA_ARGS__); exit(1);}

55
test.c
View File

@ -24,6 +24,60 @@ edgelist_t *edgelist_add(edgelist_t *list, int new, edgelist_t *storage, int *st
return new_link;
}
int main(int argc, const char *argv[])
{
unsigned long left_invariance = atoi(argv[2]);
unsigned long right_invariance = atoi(argv[3]);
semisimple_type_t type;
type.n = 1;
type.factors = (simple_type_t*)malloc(type.n*sizeof(simple_type_t));
type.factors[0].series = 'B';
type.factors[0].rank = atoi(argv[1]);
char alphabet[] = "abcdefghijklmnopqrstuvwxyz";
char buffer[1024], buffer2[1024];
node_t *graph;
int *leftbuf, *rightbuf;
edgelist_t *edgelists;
int *words;
int rank, order, hyperplanes, cosets;
// initialize
rank = coxeter_rank(type);
order = coxeter_order(type);
hyperplanes = coxeter_hyperplanes(type);
graph = (node_t*)malloc(order*sizeof(node_t));
leftbuf = (int*)malloc(order*rank*sizeof(int));
rightbuf = (int*)malloc(order*rank*sizeof(int));
edgelists = (edgelist_t*)malloc(4*order*hyperplanes*sizeof(edgelist_t));
words = (int*)malloc(order*hyperplanes*sizeof(int));
for(int i = 0; i < order; i++) {
graph[i].left = &leftbuf[rank*i];
graph[i].right = &rightbuf[rank*i];
}
// generate graph
cosets = prepare_simplified_graph(type, left_invariance, right_invariance, graph, edgelists, words);
// do something
fprintf(stderr, "There are %d double cosets.\n", cosets);
// cleanup
free(leftbuf);
free(rightbuf);
free(graph);
free(edgelists);
free(words);
}
/*
int main(int argc, const char *argv[])
{
semisimple_type_t type;
@ -245,3 +299,4 @@ int main(int argc, const char *argv[])
return 0;
}
*/

319
thickenings.c
View File

@ -57,24 +57,28 @@ static int compare_wordlength(const void *a, const void *b, void *gr)
return graph[i].wordlength - graph[j].wordlength;
}
void prepare_graph(semisimple_type_t type, node_t *graph, edgelist_t **edgelists_pointer, int **words_pointer) // the edgelists_pointer and words_pointer arguments are just for freeing afterwards
void prepare_graph(semisimple_type_t type, node_t *graph)
{
queue_t queue;
int rank, order;
edgelist_t *edgelists_lower, *edgelists_higher;
int rank, order, hyperplanes;
edgelist_t *edge, *previous;
int edgelist_count, max_wordlength, hyperplane_count;
int edgelist_count, hyperplane_count;
int current;
int *graph_data;
node_t *graph_unsorted;
int *wordlength_order, *reverse_wordlength_order, *seen, *words;
edgelist_t *edgelists;
int *wordlength_order, *reverse_wordlength_order, *seen;
// initialize
rank = coxeter_rank(type);
order = coxeter_order(type);
hyperplanes = coxeter_hyperplanes(type);
edgelists_higher = graph[0].bruhat_higher;
edgelists_lower = &graph[0].bruhat_higher[order*hyperplanes/2];
graph_data = (int*)malloc(order*rank*sizeof(int));
graph_unsorted = (node_t*)malloc(order*sizeof(node_t));
@ -83,13 +87,10 @@ void prepare_graph(semisimple_type_t type, node_t *graph, edgelist_t **edgelists
seen = (int*)malloc(order*sizeof(int));
for(int i = 0; i < order; i++) {
graph_unsorted[i].left = graph[i].left;
graph_unsorted[i].right = graph[i].right;
graph_unsorted[i].word = 0;
graph_unsorted[i].wordlength = INT_MAX;
graph_unsorted[i].bruhat_lower = 0;
graph_unsorted[i].bruhat_higher = 0;
graph_unsorted[i].is_hyperplane_reflection = 0;
graph[i].bruhat_lower = 0;
graph[i].bruhat_higher = 0;
graph[i].is_hyperplane_reflection = 0;
}
// get coxeter graph
@ -98,7 +99,7 @@ void prepare_graph(semisimple_type_t type, node_t *graph, edgelist_t **edgelists
for(int i = 0; i < order; i++)
for(int j = 0; j < rank; j++)
graph_unsorted[i].left[j] = graph_data[i*rank + j];
graph_unsorted[i].left = &graph_data[i*rank];
// find wordlengths
@ -115,11 +116,6 @@ void prepare_graph(semisimple_type_t type, node_t *graph, edgelist_t **edgelists
}
}
max_wordlength = 0;
for(int i = 0; i < order; i++)
if(graph_unsorted[i].wordlength > max_wordlength)
max_wordlength = graph_unsorted[i].wordlength;
// sort by wordlength
for(int i = 0; i < order; i++)
@ -128,23 +124,22 @@ void prepare_graph(semisimple_type_t type, node_t *graph, edgelist_t **edgelists
for(int i = 0; i < order; i++)
reverse_wordlength_order[wordlength_order[i]] = i; // reverse_wordlength_order is a map old index -> new index
for(int i = 0; i < order; i++) {
graph[i] = graph_unsorted[wordlength_order[i]]; // copy the whole thing
// we have only set left and wordlength so far, so just copy these
graph[i].wordlength = graph_unsorted[wordlength_order[i]].wordlength;
for(int j = 0; j < rank; j++)
graph[i].left[j] = reverse_wordlength_order[graph[i].left[j]]; // rewrite references
graph[i].left[j] = reverse_wordlength_order[graph_unsorted[wordlength_order[i]].left[j]]; // rewrite references
}
// find words
words = (int*)malloc(order*max_wordlength*sizeof(int));
memset(words, 0, order*max_wordlength*sizeof(int));
graph[0].word = &words[0];
for(int i = 0; i < order; i++)
memset(graph[i].word, 0, hyperplanes*sizeof(int));
queue_init(&queue);
queue_put(&queue, 0);
while((current = queue_get(&queue)) != -1) {
for(int i = 0; i < rank; i++) {
int neighbor = graph[current].left[i];
if(graph[neighbor].wordlength == graph[current].wordlength + 1 && graph[neighbor].word == 0) {
graph[neighbor].word = &words[neighbor*max_wordlength];
if(graph[neighbor].wordlength == graph[current].wordlength + 1 && graph[neighbor].word[0] == 0) {
memcpy(&graph[neighbor].word[1], &graph[current].word[0], graph[current].wordlength*sizeof(int));
graph[neighbor].word[0] = i;
queue_put(&queue, neighbor);
@ -197,7 +192,6 @@ void prepare_graph(semisimple_type_t type, node_t *graph, edgelist_t **edgelists
// generate folding order
edgelists = (edgelist_t*)malloc(order*hyperplane_count*sizeof(edgelist_t));
edgelist_count = 0;
for(int i = 0; i < order; i++) {
if(graph[i].is_hyperplane_reflection) {
@ -208,9 +202,9 @@ void prepare_graph(semisimple_type_t type, node_t *graph, edgelist_t **edgelists
current = graph[current].left[graph[i].word[k]];
if(graph[j].wordlength < graph[current].wordlength) { // current has higher bruhat order than j
edgelists[edgelist_count].to = j;
edgelists[edgelist_count].next = graph[current].bruhat_lower;
graph[current].bruhat_lower = &edgelists[edgelist_count];
edgelists_lower[edgelist_count].to = j;
edgelists_lower[edgelist_count].next = graph[current].bruhat_lower;
graph[current].bruhat_lower = &edgelists_lower[edgelist_count];
edgelist_count++;
} else if(graph[j].wordlength > graph[current].wordlength) { // j has higher bruhat order than current; these are already included from the other side
} else {
@ -263,20 +257,18 @@ void prepare_graph(semisimple_type_t type, node_t *graph, edgelist_t **edgelists
// reverse folding order
edgelist_count = 0;
for(int i = 0; i < order; i++) {
edge = graph[i].bruhat_lower;
while(edge) {
edgelists[edgelist_count].to = i;
edgelists[edgelist_count].next = graph[edge->to].bruhat_higher;
graph[edge->to].bruhat_higher = &edgelists[edgelist_count];
edgelists_higher[edgelist_count].to = i;
edgelists_higher[edgelist_count].next = graph[edge->to].bruhat_higher;
graph[edge->to].bruhat_higher = &edgelists_higher[edgelist_count];
edgelist_count++;
edge = edge->next;
}
}
*edgelists_pointer = edgelists;
*words_pointer = words;
free(graph_data);
free(graph_unsorted);
free(wordlength_order);
@ -284,6 +276,264 @@ void prepare_graph(semisimple_type_t type, node_t *graph, edgelist_t **edgelists
free(seen);
}
static int edgelist_contains(edgelist_t *list, int x) {
while(list) {
if(list->to == x)
return 1;
list = list->next;
}
return 0;
}
static edgelist_t *edgelist_add(edgelist_t *list, int new, edgelist_t *storage, int *storage_index)
{
edgelist_t *new_link = &storage[*storage_index];
new_link->next = list;
new_link->to = new;
(*storage_index)++;
return new_link;
}
int prepare_simplified_graph(semisimple_type_t type, unsigned long left, unsigned long right, node_t *simplified_graph)
{
node_t *full_graph;
int edgelists_used;
int rank, order, hyperplanes;
int *reduced, *group, *simplified;
int *seen;
int current;
edgelist_t *edge, *previous;
queue_t queue;
int ncosets;
if(opposition_involution(type, left) != left)
return -1;
edgelist_t *edgelists_higher = &simplified_graph[0].bruhat_higher[0];
edgelist_t *edgelists_lower = &simplified_graph[0].bruhat_higher[order*hyperplanes/2];
// get full graph
full_graph = graph_alloc(type);
prepare_graph(type, full_graph);
// initialize stuff
rank = coxeter_rank(type);
order = coxeter_order(type);
hyperplanes = coxeter_hyperplanes(type);
reduced = (int*)malloc(order*sizeof(int));
group = (int*)malloc(order*sizeof(int));
simplified = (int*)malloc(order*sizeof(int));
for(int i = 0; i < order; i++) {
group[i] = -1;
reduced[i] = i;
}
// step 1: group
for(int i = 0; i < order; i++) {
if(group[i] != -1)
continue;
queue_init(&queue);
queue_put(&queue, i);
while((current = queue_get(&queue)) != -1) {
if(group[current] != -1)
continue;
group[current] = i;
for(int j = 0; j < rank; j++) {
if(left & (1 << j))
queue_put(&queue, full_graph[current].left[j]);
if(right & (1 << j))
queue_put(&queue, full_graph[current].right[j]);
}
}
}
// step 2: find minimum
for(int i = 0; i < order; i++)
if(full_graph[i].wordlength < full_graph[reduced[group[i]]].wordlength)
reduced[group[i]] = i;
// step 3: assign minimum to all
for(int i = 0; i < order; i++)
reduced[i] = reduced[group[i]];
// step 4: assign indices to cosets
ncosets = 0;
for(int i = 0; i < order; i++)
if(reduced[i] == i)
simplified[i] = ncosets++;
for(int i = 0; i < order; i++)
simplified[i] = simplified[reduced[i]];
// fprintf(stderr, "Number of double cosets: %d\n\n", ncosets);
// simplified_graph = (node_t*) malloc(ncosets*sizeof(node_t));
seen = (int*) malloc(ncosets*sizeof(int));
edgelists_used = 0;
// step 5: set up nodes from minima
current = 0;
for(int i = 0; i < order; i++)
if(reduced[i] == i) { // is minimum
memcpy(simplified_graph[simplified[i]].word, full_graph[i].word, full_graph[i].wordlength*sizeof(int));
simplified_graph[simplified[i]].wordlength = full_graph[i].wordlength;
simplified_graph[simplified[i]].opposite = simplified[full_graph[i].opposite];
simplified_graph[simplified[i]].bruhat_lower = (edgelist_t*)0;
simplified_graph[simplified[i]].bruhat_higher = (edgelist_t*)0;
for(int j = 0; j < rank; j++) {
simplified_graph[simplified[i]].left[j] = simplified[full_graph[i].left[j]];
simplified_graph[simplified[i]].right[j] = simplified[full_graph[i].right[j]];
}
}
// step 6: find order relations
for(int i = 0; i < order; i++) {
edge = full_graph[i].bruhat_lower;
while(edge) {
int this = simplified[i];
int that = simplified[edge->to];
if(this != that) {
// found something
if(!edgelist_contains(simplified_graph[this].bruhat_lower, that))
simplified_graph[this].bruhat_lower = edgelist_add(simplified_graph[this].bruhat_lower, that, edgelists_lower, &edgelists_used);
ERROR(simplified_graph[this].wordlength <= simplified_graph[that].wordlength, "The order assumption is being violated!\n");
}
edge = edge->next;
}
}
// step 7: remove redundant edges
for(int i = 0; i < ncosets; i++) {
memset(seen, 0, ncosets*sizeof(int));
queue_init(&queue);
for(int len = 1; len <= simplified_graph[i].wordlength; len++) {
edge = simplified_graph[i].bruhat_lower;
previous = (edgelist_t*)0;
while(edge) {
// only look at edges of this length now
if(simplified_graph[i].wordlength - simplified_graph[edge->to].wordlength != len) {
// we only consider edges of length len in this pass
previous = edge;
} else if(seen[edge->to]) {
// this edge is redundant, remove it
// fprintf(stderr, "removing edge from %d to %d\n", i, edge->to);
if(previous)
previous->next = edge->next;
else
simplified_graph[i].bruhat_lower = edge->next;
} else {
// this edge was not redundant, add to seen
previous = edge;
seen[edge->to] = 1;
queue_put(&queue, edge->to);
}
edge = edge->next;
}
// calculate transitive closure of seen nodes
while((current = queue_get(&queue)) != -1) {
edge = simplified_graph[current].bruhat_lower;
while(edge) {
if(!seen[edge->to]) {
seen[edge->to] = 1;
queue_put(&queue, edge->to);
}
edge = edge->next;
}
}
}
}
// step 8: revert order
for(int i = 0; i < ncosets; i++) {
edge = simplified_graph[i].bruhat_lower;
while(edge) {
simplified_graph[edge->to].bruhat_higher =
edgelist_add(simplified_graph[edge->to].bruhat_higher,
i, edgelists_higher, &edgelists_used);
edge = edge->next;
}
}
// output as graphviz dot file
/*
fprintf(stdout, "difull_graph test123 {\n");
for(int i = 0; i < ncosets; i++) {
edge = simplified_graph[i].bruhat_lower;
while(edge) {
fprintf(stdout, "%s -> %s;\n",
alphabetize(simplified_graph[i].word, simplified_graph[i].wordlength, alphabet, buffer),
alphabetize(simplified_graph[edge->to].word, simplified_graph[edge->to].wordlength, alphabet, buffer2));
edge = edge->next;
}
}
fprintf(stdout, "}\n"); */
// some output
/* for(int i = 0; i < ncosets; i++)
fprintf(stderr, "%s <=> %s\n", simplified_graph[i].wordlength == 0 ? "1" : alphabetize(simplified_graph[i].word, simplified_graph[i].wordlength, alphabet, buffer), simplified_graph[simplified_graph[i].opposite].wordlength == 0 ? "1" : alphabetize(simplified_graph[simplified_graph[i].opposite].word, simplified_graph[simplified_graph[i].opposite].wordlength, alphabet, buffer2)); */
// fprintf(stderr, "\nAdded %d edges.\n\n", edgelists_used);
free(seen);
free(reduced);
free(group);
free(simplified);
graph_free(type, full_graph);
return ncosets;
}
node_t *graph_alloc(semisimple_type_t type)
{
int rank = coxeter_rank(type);
int order = coxeter_order(type);
int hyperplanes = coxeter_hyperplanes(type);
node_t *graph = (node_t*)malloc(order*sizeof(node_t));
int *left = (int*)malloc(order*rank*sizeof(int));
int *right = (int*)malloc(order*rank*sizeof(int));
edgelist_t *edgelists = (edgelist_t*)malloc(order*hyperplanes*sizeof(edgelist_t));
int *words = (int*)malloc(order*hyperplanes*sizeof(int));
for(int i = 0; i < order; i++) {
graph[i].left = &left[rank*i];
graph[i].right = &right[rank*i];
graph[i].word = &words[hyperplanes*i];
}
graph[0].bruhat_higher = edgelists;
return graph;
}
void graph_free(semisimple_type_t type, node_t *graph)
{
free(graph[0].left);
free(graph[0].right);
free(graph[0].word);
int order = coxeter_order(type);
// find the head of all edgelists by just taking the one having the lowest address
edgelist_t *edgelists = graph[0].bruhat_lower;
for(int i = 0; i < order; i++) {
if(graph[i].bruhat_lower < edgelists && graph[i].bruhat_lower != 0)
edgelists = graph[i].bruhat_lower;
if(graph[i].bruhat_higher < edgelists && graph[i].bruhat_higher != 0)
edgelists = graph[i].bruhat_higher;
}
free(edgelists);
}
/*********************************** THE ACTUAL ENUMERATION ****************************************/
typedef struct {
@ -401,7 +651,6 @@ static long enumerate_tree(const enumeration_info_t *info, signed char *level, i
long enumerate_balanced_thickenings(semisimple_type_t type, node_t *graph, int size, const char *alphabet, FILE *outfile)
{
// int rank, order;
signed char *level;
long count = 0;
enumeration_info_t info;

16
thickenings.h
View File

@ -25,10 +25,22 @@ typedef struct {
int is_hyperplane_reflection; // boolean value
} node_t;
// printing functions
char *alphabetize(int *word, int len, const char *alphabet, char *buffer);
void print_thickening(int rank, int order, const signed char *thickening, int level, const char *alphabet, FILE *f);
static int compare_wordlength(const void *a, const void *b, void *gr);
void prepare_graph(semisimple_type_t type, node_t *graph, edgelist_t **edgelists_pointer, int **words_pointer);
// generating the graph of the bruhat order
void prepare_graph(semisimple_type_t type, node_t *graph);
int prepare_simplified_graph(semisimple_type_t type, unsigned long left, unsigned long right, node_t *simplified_graph);
// enumerate balanced thickenings
long enumerate_balanced_thickenings(semisimple_type_t type, node_t *graph, int size, const char *alphabet, FILE *outfile);
node_t *graph_alloc(semisimple_type_t type);
void graph_free(semisimple_type_t type, node_t *graph);
// various helper functions
static int compare_wordlength(const void *a, const void *b, void *gr);
static int edgelist_contains(edgelist_t *list, int x);
static edgelist_t *edgelist_add(edgelist_t *list, int new, edgelist_t *storage, int *storage_index);
#endif