triangle_reflection_complex/special_element.c

170 lines
4.5 KiB
C

#include "coxeter.h"
#include "linalg.h"
#include "mat.h"
#include "enumerate_triangle_group.h"
#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
#define DEBUG(msg, ...)
double mpq_log(mpq_t m_op)
{
static double logB = log(ULONG_MAX);
// Undefined logs (should probably return NAN in second case?)
if (mpz_get_ui(mpq_numref(m_op)) == 0 || mpz_sgn(mpq_numref(m_op)) < 0)
return -INFINITY;
// Log of numerator
double lognum = log(mpq_numref(m_op)->_mp_d[abs(mpq_numref(m_op)->_mp_size) - 1]);
lognum += (abs(mpq_numref(m_op)->_mp_size)-1) * logB;
// Subtract log of denominator, if it exists
if (abs(mpq_denref(m_op)->_mp_size) > 0)
{
lognum -= log(mpq_denref(m_op)->_mp_d[abs(mpq_denref(m_op)->_mp_size)-1]);
lognum -= (abs(mpq_denref(m_op)->_mp_size)-1) * logB;
}
return lognum;
}
int main(int argc, char *argv[])
{
mpq_t m, t, s, q, tmp, tmp2;
mat_workspace *ws;
mat gen[6];
mps_context *solver;
mat element, inverse;
int letter1, letter2, letter;
mpq_t tr, trinv;
double x, y, slope;
int retval;
double evs[3];
char buf[100];
double max_slope = 0;
int max_slope_index = 0;
double min_slope = INFINITY;
int min_slope_index = 0;
char *env;
int mode;
if(argc < 2) {
fprintf(stderr,
"Usage: %s <s> <q> <word1> <word2> ...\n"
"Computes jordan slopes of a list of group elements for a fixed representation.\n"
"s,q: representation in the Hitchin component, given as rational numbers, e.g. 2/7\n"
"word1, word2, ...: elements in the triangle rotation group, given as reflection group words\n"
"output: word - jordan slope pairs\n"
"+max slope index, max slope value, max slope word, min slope index, min slope value, min slope word\n"
"controlled by environment variable MAXIMUM=no/yes/only, default yes\n",
argv[0]);
exit(0);
}
mpq_inits(m, t, s, q, tmp, tmp2, tr, trinv, NULL);
ws = mat_workspace_init(3);
for(int i = 0; i < 6; i++)
mat_init(gen[i], 3);
mat_init(element, 3);
mat_init(inverse, 3);
solver = mps_context_new();
mps_context_set_output_prec(solver, 20); // relative precision
mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
mpq_set_str(s, argv[1], 10);
mpq_set_str(q, argv[2], 10);
env = getenv("MAXIMUM");
if(!env || strcmp(env, "yes") == 0) {
mode = 1; // yes
} else if(strcmp(env, "no") == 0) {
mode = 0; // no
} else if(strcmp(env, "only") == 0) {
mode = 2; // only
}
for(int w = 0; w < argc - 3; w++) {
initialize_triangle_generators(ws, gen, 4, 4, 4, s, q);
mat_identity(element);
mat_identity(inverse);
for(int k = 0; k < strlen(argv[w+3]); k+=2) {
letter1 = argv[w+3][k] - 'a';
letter2 = argv[w+3][k+1] - 'a';
if(letter1 == 1 && letter2 == 2)
letter = 0; // p = bc
else if(letter1 == 2 && letter2 == 0)
letter = 1; // q = ca
else if(letter1 == 0 && letter2 == 1)
letter = 2; // r = ab
else if(letter1 == 2 && letter2 == 1)
letter = 3; // p^{-1} = cb
else if(letter1 == 0 && letter2 == 2)
letter = 4; // q^{-1} = ac
else if(letter1 == 1 && letter2 == 0)
letter = 5; // r^{-1} = ba
mat_multiply(ws, element, element, gen[letter]);
mat_multiply(ws, inverse, gen[(letter+3)%6], inverse);
}
mat_trace(tr, element);
mat_trace(trinv, inverse);
retval = solve_characteristic_polynomial(solver, tr, trinv, evs);
if(retval == 1) {
fprintf(stderr, "Error! Could not solve polynomial.\n");
return 1;
}
if(fabs(evs[0]) < fabs(evs[1]))
SWAP(double, evs[0], evs[1]);
if(fabs(evs[1]) < fabs(evs[2]))
SWAP(double, evs[1], evs[2]);
if(fabs(evs[0]) < fabs(evs[1]))
SWAP(double, evs[0], evs[1]);
x = log(fabs(evs[0]));
y = -log(fabs(evs[2]));
if(x > DBL_MAX || y > DBL_MAX) {
mpq_abs(tmp, tr);
mpq_abs(tmp2, trinv);
slope = mpq_log(tmp)/mpq_log(tmp2);
} else {
slope = y/x;
}
if(slope < 1)
slope = 1/slope;
if(slope > max_slope) {
max_slope = slope;
max_slope_index = w;
}
if(slope < min_slope) {
min_slope = slope;
min_slope_index = w;
}
if(mode != 2)
gmp_printf("%s %.9f\n", argv[w+3], slope);
}
if(mode != 0)
printf("%d %.9f %s %d %.9f %s\n",
max_slope_index, max_slope, argv[max_slope_index+3],
min_slope_index, min_slope, argv[min_slope_index+3]);
fflush(stdout);
mpq_clears(m, t, s, q, tmp, tmp2, tr, trinv, NULL);
mat_workspace_clear(ws);
for(int i = 0; i < 6; i++)
mat_clear(gen[i]);
mat_clear(element);
mat_clear(inverse);
mps_context_free(solver);
}