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enumerate-balanced-ideals
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specialized routine to generate cosets for <bcd..> \ D2n

This commit is contained in:
Florian Stecker 2018-12-01 20:56:23 -08:00
parent 4342a1f3e5
commit d3336bab00
3 changed files with 148 additions and 9 deletions
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133
D2n.c Normal file
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@ -0,0 +1,133 @@
#include "thickenings.h"
#include "weyl.h"
#include "queue.h"
#include <strings.h>
#include <stdio.h>
#include <inttypes.h>
int main(int argc, const char *argv[])
{
if(argc < 2) {
fprintf(stderr, "Rank argument required.\n");
return 1;
}
int rank = atoi(argv[1]);
if(rank <= 0 || rank > 1000) {
fprintf(stderr, "Rank must be a small positive integer.\n");
return 1;
}
if(rank % 2) {
fprintf(stderr, "Rank must be even.\n"); // opposition involution not trivial otherwise
return 1;
}
doublequotient_t *dq = (doublequotient_t*)malloc(sizeof(doublequotient_t));
simple_type_t type;
type.series = 'D';
type.rank = rank;
dq->type.n = 1;
dq->type.factors = &type;
dq->left_invariance = (1<<rank) - 2;
dq->right_invariance = 0;
dq->group = 0;
dq->grouplists = 0;
dq->groupletters = 0;
dq->count = 1 << (rank - 1);
dq->cosets = (doublecoset_t*)malloc(dq->count*sizeof(doublecoset_t));
dq->lists = (doublecoset_list_t*)malloc(2*dq->count*rank*sizeof(doublecoset_list_t)); // conservative estimate
int nlists = 0;
int *bitmask = malloc((1<<(rank-1)) * sizeof(int));
int *bitmask_reverse = malloc((1<<rank) * sizeof(int));
int index = 0;
LOG("Prepare.\n");
for(int i = 0; i < dq->count; i++) {
dq->cosets[i].index = i;
dq->cosets[i].bruhat_lower = (doublecoset_list_t*)0;
dq->cosets[i].bruhat_higher = (doublecoset_list_t*)0;
dq->cosets[i].min = (weylgroup_element_t*)0;
dq->cosets[i].max = (weylgroup_element_t*)0;
}
LOG("Create bitmasks.\n");
for(uint64_t i = 0; i < (1 << rank); i++) {
if(__builtin_popcountll(i) % 2 == 1)
bitmask_reverse[i] = -1;
else {
bitmask[index] = i;
bitmask_reverse[i] = index++;
}
}
LOG("Generate bruhat order.\n");
for(int i = 0; i < dq->count; i++) {
for(int j = 0; j < rank - 1; j++) {
if(!(bitmask[i] & BIT(j)) && (bitmask[i] & BIT(j+1))) {
int lowerind = bitmask_reverse[bitmask[i] ^ (BIT(j) | BIT(j+1))];
dq->lists[nlists].next = dq->cosets[i].bruhat_lower;
dq->cosets[i].bruhat_lower = &dq->lists[nlists];
dq->cosets[i].bruhat_lower->to = &dq->cosets[lowerind];
nlists++;
}
}
if((bitmask[i] & BIT(0)) && (bitmask[i] & BIT(1))) {
int lowerind = bitmask_reverse[bitmask[i] & ~(BIT(0) | BIT(1))];
dq->lists[nlists].next = dq->cosets[i].bruhat_lower;
dq->cosets[i].bruhat_lower = &dq->lists[nlists];
dq->cosets[i].bruhat_lower->to = &dq->cosets[lowerind];
nlists++;
}
}
LOG("Revert bruhat order.\n");
for(int i = 0; i < dq->count; i++) {
for(doublecoset_list_t *cur = dq->cosets[i].bruhat_lower; cur; cur = cur->next) {
dq->lists[nlists].next = cur->to->bruhat_higher;
cur->to->bruhat_higher = &dq->lists[nlists];
cur->to->bruhat_higher->to = &dq->cosets[i];
nlists++;
}
}
LOG("Find opposites.\n");
for(int i = 0; i < dq->count; i++) {
int oppind = bitmask_reverse[~bitmask[i] & ((1<<rank) - 1)];
dq->cosets[i].opposite = &dq->cosets[oppind];
}
/*
printf("\n");
printf("digraph test123 {\n");
for(int i = 0; i < dq->count; i++) {
for(doublecoset_list_t *cur = dq->cosets[i].bruhat_lower; cur; cur = cur->next) {
printf("\"0x%02x\" -> \"0x%02x\";\n", bitmask[i], bitmask[cur->to->index]);
}
}
printf("}\n\n");
printf("Opposites:\n");
for(int i = 0; i < dq->count; i++)
printf("0x%02x <-> %d 0x%02x\n", bitmask[i], dq->cosets[i].opposite->index, bitmask[dq->cosets[i].opposite->index]);
printf("\n");
*/
long count = enumerate_balanced_thickenings(dq, 0, 0);
printf("Found %ld balanced ideals.\n", count);
free(bitmask);
free(bitmask_reverse);
free(dq->lists);
free(dq->cosets);
free(dq);
return 0;
}

10
Makefile
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@ -7,7 +7,7 @@ SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
OPTIONS=-m64 -march=native -mtune=native -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS)
NAME=enumerate-balanced-ideals
all: enumerate graph
all: enumerate graph D2n
$(NAME).tar.bz2: $(NAME) $(HEADERS) enumerate.c weyl.c thickenings.c
tar cjhf $(NAME).tar.bz2 $(NAME)/enumerate.c $(NAME)/weyl.c $(NAME)/thickenings.c $(NAME)/weyl.h $(NAME)/thickenings.h $(NAME)/queue.h $(NAME)/bitvec.h $(NAME)/Makefile $(NAME)/graph.c
@ -21,12 +21,18 @@ enumerate: enumerate.o weyl.o thickenings.o
graph: graph.o weyl.o
gcc $(OPTIONS) -o graph graph.o weyl.o
D2n: D2n.o weyl.o thickenings.o
gcc $(OPTIONS) -o D2n D2n.o weyl.o thickenings.o
enumerate.o: enumerate.c $(HEADERS)
gcc $(OPTIONS) -c enumerate.c
thickenings.o: thickenings.c $(HEADERS)
gcc $(OPTIONS) -c thickenings.c
D2n.o: D2n.c $(HEADERS)
gcc $(OPTIONS) -c D2n.c
weyl.o: weyl.c $(HEADERS)
gcc $(OPTIONS) -c weyl.c
@ -34,4 +40,4 @@ graph.o: graph.c $(HEADERS)
gcc $(OPTIONS) -c graph.c
clean:
rm -f enumerate graph thickenings.o weyl.o enumerate.o graph.o $(NAME) $(NAME).tar.bz2
rm -f enumerate graph D2n thickenings.o weyl.o enumerate.o graph.o D2n.o $(NAME) $(NAME).tar.bz2

14
thickenings.c
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@ -110,12 +110,12 @@ static void generate_principal_ideals(doublequotient_t *dq, bitvec_t *pos, bitve
}
#ifdef _DEBUG
if(is_slim[i]) {
fprintf(stderr, " ids: [0");
for(int j = 1; j < size; j++)
if(principal[j])
fprintf(stderr, ", %d", dq->cosets[j].min->id);
fprintf(stderr, "]\n");
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++)
if(principal[j])
fprintf(stderr, ", %d", dq->cosets[j].min->id);
fprintf(stderr, "]\n");
}
#endif
@ -160,7 +160,7 @@ long enumerate_balanced_thickenings(doublequotient_t *dq, enumeration_callback c
// 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->min->id == dq->cosets[i].min->id)
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