triangle_reflection_complex/complex_anosov.c

#include "coxeter.h"
#include "enumerate.h"
#include "generators.h"
#include "mat.h"
#include "qext.h"

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>

#define LOOP(i,n) for(int i = 0; i < (n); i++)
#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);

/*
  Elements up to length 0: 1
  Elements up to length 1: 4
  Elements up to length 2: 10
  Elements up to length 3: 22
  Elements up to length 4: 46
  Elements up to length 5: 91
  Elements up to length 6: 175
  Elements up to length 7: 334
  Elements up to length 8: 634
  Elements up to length 9: 1198
  Elements up to length 10: 2260
  Elements up to length 11: 4261
  Elements up to length 12: 8029
  Elements up to length 13: 15124
  Elements up to length 14: 28486
  Elements up to length 15: 53650
  Elements up to length 16: 101038
  Elements up to length 17: 190279
  Elements up to length 18: 358339
  Elements up to length 19: 674830
  Elements up to length 20: 1270846
  Elements up to length 21: 2393266
  Elements up to length 22: 4507012
  Elements up to length 23: 8487625
*/

static double gaussian_sqrt5_real(NUMBER x)
{
	double result = 0.0;

	mpq_t tmp;
	mpq_init(tmp);

	// a_0 + sqrt(5)a_1 + 4a_2 + 2sqrt(5)a_3
	mpq_set_si(tmp, 4, 1);
	mpq_mul(tmp, tmp, x->a[2]);
	mpq_add(tmp, tmp, x->a[0]);
	result = mpq_get_d(tmp);
	mpq_set_si(tmp, 2, 1);
	mpq_mul(tmp, tmp, x->a[3]);
	mpq_add(tmp, tmp, x->a[1]);
	result += mpq_get_d(tmp)*sqrt(5);

	mpq_clear(tmp);

	return result;
}

static double gaussian_sqrt5_imag(NUMBER x)
{
	double result = 0.0;

	mpq_t tmp;
	mpq_init(tmp);

	// a_1 + 2sqrt(5)a_2 + 14a_3
	mpq_set_si(tmp, 14, 1);
	mpq_mul(tmp, tmp, x->a[3]);
	mpq_add(tmp, tmp, x->a[1]);
	result = mpq_get_d(tmp);
	mpq_set_si(tmp, 2, 1);
	mpq_mul(tmp, tmp, x->a[2]);
	result += mpq_get_d(tmp)*sqrt(5);

	mpq_clear(tmp);

	return result;
}

enum mode {
	MODE_HELP,
	MODE_TRACES,
	MODE_SUMMARY,
	MODE_TRACE_IDS
};

int main(int argc, char *argv[])
{
	char buf[100];
	int mode;

	if(argc < 2 || strcmp(argv[1], "help") == 0)
		mode = MODE_HELP;
	else if(strcmp(argv[1], "traces") == 0)
		mode = MODE_TRACES;
	else if(strcmp(argv[1], "summary") == 0)
		mode = MODE_SUMMARY;
	else if(strcmp(argv[1], "trace_ids") == 0)
		mode = MODE_TRACE_IDS;
	else
		mode = MODE_HELP;

	if(mode == MODE_HELP) {
		fprintf(stderr, "Usage: %s <help|traces|summary|trace_ids> [arguments]\n", argv[0]);
		fprintf(stderr, "%s help                           display this page\n", argv[0]);
		fprintf(stderr, "%s traces <n> <qreal> <qimag>     enumerate group and output unique trace/trace inverse pairs\n", argv[0]);
		fprintf(stderr, "%s summary <n> <qreal> <qimag>    only output max slope etc.\n", argv[0]);
		fprintf(stderr, "%s trace_ids <n> <qreal> <qimag>  list of ids of unique traces\n", argv[0]);
		return 0;
	}

	if(argc < 5) {
		fprintf(stderr, "Not enough arguments!\n");
		return 0;
	}

	int n = atoi(argv[2]);

	mpq_t qreal, qimag;
	mpq_inits(qreal, qimag, NULL);
	mpq_set_str(qreal, argv[3], 10);
	mpq_set_str(qimag, argv[4], 10);
//	mpq_set_si(qreal, 50, 10);
//	mpq_set_si(qimag, 1, 10);
	mpq_canonicalize(qreal);
	mpq_canonicalize(qimag);

	/*
	int length = 0;
	LOOP(i, n) {
		if(group->elements[i].length > length) {
			printf("Elements up to length %d: %d\n", length, i);
			length = group->elements[i].length;
		}
	}
	return 0;
	*/

	/*
	LOOP(i, n) {
		groupelement_t *cur = &group->elements[i];
		groupelement_t *other;

		cur->conjugacy_class = cur; // start with itself and reduce if possible

		LOOP(j, 3) {
			if(cur->left[j] && cur->left[j]->right[j]) {
				other = cur->left[j]->right[j];
				if(other->id < cur->id)
					cur->conjugacy_class = other->conjugacy_class;
			}
			if(cur->right[j] && cur->right[j]->left[j]) {
				other = cur->right[j]->left[j];
				if(other->id < cur->id)
					cur->conjugacy_class = other->conjugacy_class;
			}
		}
	}
	*/

	group_t *group = coxeter_init_triangle(5, 5, 5, n);

	mat gen[3];
	LOOP(i, 3) mat_init(gen[i], 3, QT_GAUSS_SQRT5);
	generators_triangle_reflection_group_555_complex(gen, 2, 2, 2, qreal, qimag);

	struct tracedata *traces;
	int nuniq = enumerate_coxeter_group_traces(group, gen, &traces);

	mps_context *solver = mps_context_new();
	mps_monomial_poly *poly = mps_monomial_poly_new(solver, 3);
	mps_context_set_output_prec(solver, 20); // relative precision
	mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);

	double ev_real[3], ev_imag[3], ev_abs2[3];
	double max_slope = 0;
	int max_slope_id = 0;

	LOOP(i, nuniq) {
		solve_characteristic_polynomial_d(solver, poly,
		                                  gaussian_sqrt5_real(traces[i].tr),
		                                  gaussian_sqrt5_imag(traces[i].tr),
		                                  gaussian_sqrt5_real(traces[i].trinv),
		                                  gaussian_sqrt5_imag(traces[i].trinv),
		                                  ev_real, ev_imag);

		LOOP(j, 3) ev_abs2[j] = ev_real[j]*ev_real[j] + ev_imag[j]*ev_imag[j];

		if(fabs(ev_abs2[0]) < fabs(ev_abs2[1]))
			SWAP(double, ev_abs2[0], ev_abs2[1]);
		if(fabs(ev_abs2[1]) < fabs(ev_abs2[2]))
			SWAP(double, ev_abs2[1], ev_abs2[2]);
		if(fabs(ev_abs2[0]) < fabs(ev_abs2[1]))
			SWAP(double, ev_abs2[0], ev_abs2[1]);

		if(log(ev_abs2[0]) < 1e-3) // we regard this as a finite order element
			continue;

		double slope = - log(ev_abs2[0]) / log(ev_abs2[2]);
		if(slope > max_slope) {
			max_slope = slope;
			max_slope_id = traces[i].id;
		}

		if(mode == MODE_TRACES) {
			printf("%d %f %f %f\n",
			       traces[i].id, log(ev_abs2[0]), log(ev_abs2[1]), log(ev_abs2[2]));
		} else if(mode == MODE_TRACE_IDS) {
			printf("%d\n", traces[i].id);
		}
	}

	coxeter_snprint(buf, sizeof(buf), &group->elements[max_slope_id]);

	if(mode == MODE_SUMMARY) {
		gmp_fprintf(stdout, "%f %f %d %d %f %s\n", mpq_get_d(qreal), mpq_get_d(qimag), n, nuniq, max_slope, buf);
	} else {
		gmp_fprintf(stderr, "q = %Qd + i*%Qd\tElements: %d\tTraces: %d\tMaximal slope: %f at %s\n", qreal, qimag, n, nuniq, max_slope, buf);
	}

	mps_monomial_poly_free(solver, MPS_POLYNOMIAL(poly));
	mps_context_free(solver);
	enumerate_tracedata_clear(traces, nuniq);
	LOOP(i, 3) mat_clear(gen[i]);
	coxeter_clear(group);
	mpq_clears(qreal, qimag, NULL);

	return 0;
}