257 lines
6.1 KiB
C
257 lines
6.1 KiB
C
#include "triangle.h"
|
|
#include "linalg.h"
|
|
#include "mat.h"
|
|
|
|
#include <gsl/gsl_poly.h>
|
|
|
|
//#define MAX_ELEMENTS 2800000
|
|
//#define MAX_ELEMENTS 720000
|
|
#define MAX_ELEMENTS 14000
|
|
//#define DRAW_PICTURE 1
|
|
|
|
void continued_fraction_approximation(mpq_t out, double in, int level)
|
|
{
|
|
mpq_t tmp;
|
|
|
|
if(in < 0) {
|
|
mpq_init(tmp);
|
|
mpq_set_ui(tmp, 0, 1);
|
|
continued_fraction_approximation(out, -in, level);
|
|
mpq_sub(out, tmp, out);
|
|
mpq_clear(tmp);
|
|
return;
|
|
}
|
|
|
|
if(level == 0) {
|
|
mpq_set_si(out, (signed long int)round(in), 1); // floor(in)
|
|
} else {
|
|
continued_fraction_approximation(out, 1/(in - floor(in)), level - 1);
|
|
mpq_init(tmp);
|
|
mpq_set_ui(tmp, 1, 1);
|
|
mpq_div(out, tmp, out); // out -> 1/out
|
|
mpq_set_si(tmp, (signed long int)in, 1); // floor(in)
|
|
mpq_add(out, out, tmp);
|
|
mpq_clear(tmp);
|
|
}
|
|
}
|
|
|
|
void quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e)
|
|
{
|
|
mpq_t tmp;
|
|
mpq_init(tmp);
|
|
|
|
mpq_set_si(out, a, 1);
|
|
mpq_mul(out, out, in);
|
|
mpq_set_si(tmp, b, 1);
|
|
mpq_add(out, out, tmp);
|
|
mpq_mul(out, out, in);
|
|
mpq_set_si(tmp, c, 1);
|
|
mpq_add(out, out, tmp);
|
|
mpq_mul(out, out, in);
|
|
mpq_set_si(tmp, d, 1);
|
|
mpq_add(out, out, tmp);
|
|
mpq_mul(out, out, in);
|
|
mpq_set_si(tmp, e, 1);
|
|
mpq_add(out, out, tmp);
|
|
|
|
mpq_clear(tmp);
|
|
}
|
|
|
|
void initialize_triangle_generators(mat_workspace *ws, mat *gen, mpq_t s, mpq_t t)
|
|
{
|
|
mpq_set_ui(*mat_ref(gen[0], 0, 0), 0, 1);
|
|
mpq_set_ui(*mat_ref(gen[0], 0, 1), 0, 1);
|
|
mpq_set_ui(*mat_ref(gen[0], 0, 2), 1, 1);
|
|
mpq_set_ui(*mat_ref(gen[0], 1, 0), 1, 1);
|
|
mpq_set_ui(*mat_ref(gen[0], 1, 1), 0, 1);
|
|
mpq_set_ui(*mat_ref(gen[0], 1, 2), 0, 1);
|
|
mpq_set_ui(*mat_ref(gen[0], 2, 0), 0, 1);
|
|
mpq_set_ui(*mat_ref(gen[0], 2, 1), 1, 1);
|
|
mpq_set_ui(*mat_ref(gen[0], 2, 2), 0, 1);
|
|
|
|
mpq_set_ui(*mat_ref(gen[1], 0, 0), 1, 1);
|
|
mpq_set_ui(*mat_ref(gen[1], 1, 0), 0, 1);
|
|
mpq_set_ui(*mat_ref(gen[1], 2, 0), 0, 1);
|
|
quartic(*mat_ref(gen[1], 0, 1), t, 0, 0, 1, -1, 2);
|
|
quartic(*mat_ref(gen[1], 1, 1), t, 0, 0, -1, 2, -2);
|
|
quartic(*mat_ref(gen[1], 2, 1), t, 0, 0, 1, -3, 3);
|
|
quartic(*mat_ref(gen[1], 0, 2), t, 0, 0, 1, 0, 3);
|
|
quartic(*mat_ref(gen[1], 1, 2), t, 0, 0, -1, 1, -1);
|
|
quartic(*mat_ref(gen[1], 2, 2), t, 0, 0, 1, -2, 1);
|
|
|
|
mat_pseudoinverse(ws, gen[3], gen[0]); // p^{-1}
|
|
mat_pseudoinverse(ws, gen[4], gen[1]); // q^{-1}
|
|
mat_multiply(ws, gen[2], gen[4], gen[3]); // r = q^{-1}p^{-1}
|
|
mat_pseudoinverse(ws, gen[5], gen[2]);
|
|
|
|
// mat_print(gen[0]);
|
|
// mat_print(gen[1]);
|
|
// mat_print(gen[2]);
|
|
// mat_print(gen[3]);
|
|
// mat_print(gen[4]);
|
|
// mat_print(gen[5]);
|
|
}
|
|
|
|
char *print_word(groupelement_t *g, char *str)
|
|
{
|
|
int i = g->length - 1;
|
|
|
|
str[g->length] = 0;
|
|
while(g->parent) {
|
|
str[i--] = 'a' + g->letter;
|
|
g = g->parent;
|
|
}
|
|
|
|
return str;
|
|
}
|
|
|
|
void enumerate(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t)
|
|
{
|
|
mat_workspace *ws;
|
|
mat tmp;
|
|
mat gen[6];
|
|
char buf[100], buf2[100], buf3[100];
|
|
|
|
// allocate stuff
|
|
ws = mat_workspace_init(3);
|
|
for(int i = 0; i < 6; i++)
|
|
mat_init(gen[i], 3);
|
|
mat_init(tmp, 3);
|
|
|
|
initialize_triangle_generators(ws, gen, s, t);
|
|
|
|
mat_identity(matrices[0]);
|
|
for(int i = 1; i < MAX_ELEMENTS; i++) {
|
|
if(group[i].length % 2 != 0)
|
|
continue;
|
|
if(!group[i].inverse)
|
|
continue;
|
|
|
|
int parent = group[i].parent->id;
|
|
int grandparent = group[i].parent->parent->id;
|
|
int letter;
|
|
|
|
if(group[parent].letter == 1 && group[i].letter == 2)
|
|
letter = 0; // p = bc
|
|
else if(group[parent].letter == 2 && group[i].letter == 0)
|
|
letter = 1; // q = ca
|
|
else if(group[parent].letter == 0 && group[i].letter == 1)
|
|
letter = 2; // r = ab
|
|
if(group[parent].letter == 2 && group[i].letter == 1)
|
|
letter = 3; // p^{-1} = cb
|
|
else if(group[parent].letter == 0 && group[i].letter == 2)
|
|
letter = 4; // q^{-1} = ac
|
|
else if(group[parent].letter == 1 && group[i].letter == 0)
|
|
letter = 5; // r^{-1} = ba
|
|
|
|
mat_multiply(ws, matrices[i], matrices[grandparent], gen[letter]);
|
|
}
|
|
|
|
// free stuff
|
|
for(int i = 0; i < 6; i++)
|
|
mat_clear(gen[i]);
|
|
mat_clear(tmp);
|
|
mat_workspace_clear(ws);
|
|
}
|
|
|
|
void output_invariants(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t)
|
|
{
|
|
mpq_t tr, trinv;
|
|
char buf[100];
|
|
|
|
mpq_inits(tr, trinv, NULL);
|
|
|
|
for(int i = 0; i < MAX_ELEMENTS; i++) {
|
|
if(group[i].length % 2 != 0 || !group[i].inverse)
|
|
continue;
|
|
|
|
mat_trace(tr, matrices[i]);
|
|
mat_trace(trinv, matrices[group[i].inverse->id]);
|
|
|
|
gmp_printf("%d %d %s %Qd %Qd %f %f\n", i, group[i].length, print_word(&group[i], buf), tr, trinv, log(mpq_get_d(tr)), log(mpq_get_d(trinv)));
|
|
}
|
|
|
|
mpq_clears(tr, trinv, NULL);
|
|
}
|
|
|
|
double max_slope(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t, int *index)
|
|
{
|
|
double max = 0;
|
|
double slope;
|
|
|
|
mpq_t tr, trinv;
|
|
char buf[100];
|
|
|
|
mpq_inits(tr, trinv, NULL);
|
|
|
|
for(int i = 0; i < MAX_ELEMENTS; i++) {
|
|
if(group[i].length % 2 != 0 || !group[i].inverse)
|
|
continue;
|
|
|
|
mat_trace(tr, matrices[i]);
|
|
mat_trace(trinv, matrices[group[i].inverse->id]);
|
|
|
|
slope = log(mpq_get_d(trinv))/log(mpq_get_d(tr));
|
|
if(slope > max)
|
|
{
|
|
*index = i;
|
|
max = slope;
|
|
}
|
|
}
|
|
|
|
mpq_clears(tr, trinv, NULL);
|
|
|
|
return max;
|
|
}
|
|
|
|
int main(int argc, char *argv[])
|
|
{
|
|
mpq_t s, t, tmp;
|
|
mpz_t accuracy;
|
|
double t_;
|
|
mat *matrices;
|
|
groupelement_t *group;
|
|
int index;
|
|
|
|
mpq_inits(s, t, tmp, NULL);
|
|
mpz_init(accuracy);
|
|
group = malloc(MAX_ELEMENTS*sizeof(groupelement_t));
|
|
matrices = malloc(MAX_ELEMENTS*sizeof(mat));
|
|
for(int i = 0; i < MAX_ELEMENTS; i++)
|
|
mat_init(matrices[i], 3);
|
|
|
|
// mpq_set_str(t, argv[1], 10);
|
|
mpz_set_ui(accuracy, 100);
|
|
for(int i = 0; ; i++) {
|
|
mpq_set(t, tmp);
|
|
continued_fraction_approximation(tmp, atof(argv[1]), i);
|
|
if(mpz_cmp(mpq_numref(tmp),accuracy) > 0 && mpz_cmp(mpq_denref(tmp),accuracy) > 0)
|
|
break;
|
|
}
|
|
mpq_canonicalize(t);
|
|
gmp_fprintf(stdout, "\"t = %Qd = %.3f\"\n", mpq_get_d(t), t);
|
|
|
|
if(argc > 2 && strcmp(argv[2],"p") == 0) {
|
|
gmp_fprintf(stdout, "%Qd\n", t);
|
|
return 0;
|
|
}
|
|
|
|
generate_triangle_group(group, MAX_ELEMENTS, 3, 3, 4);
|
|
|
|
// for(int i = 0; i < 10; i++) {
|
|
// mpq_set_ui(t,100+i,100);
|
|
// mpq_canonicalize(t);
|
|
|
|
enumerate(group, matrices, s, t);
|
|
//printf("%f %f\n", mpq_get_d(t), max_slope(group, matrices, s, t, &index));
|
|
output_invariants(group, matrices, s, t);
|
|
// }
|
|
|
|
for(int i = 0; i < MAX_ELEMENTS; i++)
|
|
mat_clear(matrices[i]);
|
|
free(matrices);
|
|
free(group);
|
|
mpq_clears(s, t, tmp, NULL);
|
|
mpz_clear(accuracy);
|
|
}
|