triangle_reflection_complex/generators.c

#include "generators.h"
#include "mat.h"

#define LOOP(i,n) for(int i = 0; i < (n); i++)

void generators_triangle_reflection_generic(mat *gen, NUMBER rho1, NUMBER rho2, NUMBER rho3, NUMBER q)
{
	NUMBER tmp;
	NUMBER qinv;
	TYPE t = GETTYPE(rho1);

	INIT(tmp, t);
	INIT(qinv, t);
	INV(qinv, q);

	LOOP(i, 3) {
		mat_init(gen[i], 3, t);
		mat_zero(gen[i]);
		LOOP(j, 3) {
			SET_INT(*mat_ref(gen[i], j, j), i == j ? 1 : -1);
		}
	}

	MUL(tmp, q, rho1);
	NEG(*mat_ref(gen[2], 1, 2), tmp);
	MUL(tmp, q, rho2);
	NEG(*mat_ref(gen[0], 2, 0), tmp);
	MUL(tmp, q, rho3);
	NEG(*mat_ref(gen[1], 0, 1), tmp);

	NEG(*mat_ref(gen[1], 2, 1), qinv);
	NEG(*mat_ref(gen[2], 0, 2), qinv);
	NEG(*mat_ref(gen[0], 1, 0), qinv);

	CLEAR(tmp);
	CLEAR(qinv);
}

int generators_triangle_reflection_group(mat *gen, int p1, int p2, int p3, int q1, int q2, int q3, mpq_t t)
{
	int p[3] = {p1, p2, p3};
	int q[3] = {q1, q2, q3};
	TYPE type;

	LOOP(i, 3)
		if(p[i] < 2 || p[i] > 6)
			return 0;

#ifdef QEXT
	type = QT_TRIVIAL;
	LOOP(i, 3)
		if(p[i] == 5)
			type = QT_SQRT5;
#else
	LOOP(i, 3)
		if(p[i] == 5)
			return 0;
#endif


	NUMBER rho[3];
	LOOP(i, 3) INIT(rho[i], type);

	// compute rho1, rho2, rho3
	LOOP(i, 3) {
		if(p[i] == 2 && q[i] == 1) {
			SET_INT(rho[i], 0);
		} else if(p[i] == 3 && q[i] == 1) {
			SET_INT(rho[i], 1);
		} else if(p[i] == 4 && q[i] == 1) {
			SET_INT(rho[i], 2);
		} else if(p[i] == 4 && q[i] == 2) {
			SET_INT(rho[i], 0);
		} else if(p[i] == 6 && q[i] == 1) {
			SET_INT(rho[i], 3);
		} else if(p[i] == 6 && q[i] == 2) {
			SET_INT(rho[i], 1);
		} else if(p[i] == 6 && q[i] == 3) {
			SET_INT(rho[i], 0);
#ifdef QEXT
		} else if(p[i] == 5 && q[i] == 1) {
			mpq_set_si(rho[i]->a[0], 3, 2);
			mpq_set_si(rho[i]->a[1], 1, 2);
		} else if(p[i] == 5 && q[i] == 2) {
			mpq_set_si(rho[i]->a[0], 3, 2);
			mpq_set_si(rho[i]->a[1], -1, 2);
#endif
		} else {
			return 0;
		}
	}

	NUMBER param;
	INIT(param, type);
	SET_Q(param, t);

	generators_triangle_reflection_generic(gen, rho[0], rho[1], rho[2], param);

	LOOP(i, 3) CLEAR(rho[i]);
	CLEAR(param);

	return 1;
}

int generators_triangle_reflection_group_555_complex(mat *gen, int q1, int q2, int q3, mpq_t treal, mpq_t timag)
{

	int q[3] = {q1, q2, q3};

	NUMBER rho[3];
	LOOP(i, 3) INIT(rho[i], QT_GAUSS_SQRT5);

	// compute rho1, rho2, rho3
	LOOP(i, 3) {
		if(q[i] == 1) {
			// 4cos(pi/5)^2 = 3/2 + 1/2*sqrt(5)
			mpq_set_si(rho[i]->a[0], 3, 2);
			mpq_set_si(rho[i]->a[1], 7, 12);
			mpq_set_si(rho[i]->a[2], 0, 1);
			mpq_set_si(rho[i]->a[3], -1, 24);
		} else if(q[i] == 2) {
			// 4cos(pi/5)^2 = 3/2 - 1/2*sqrt(5)
			mpq_set_si(rho[i]->a[0], 3, 2);
			mpq_set_si(rho[i]->a[1], -7, 12);
			mpq_set_si(rho[i]->a[2], 0, 1);
			mpq_set_si(rho[i]->a[3], 1, 24);
		} else {
			return 0;
		}
	}

	NUMBER param;
	INIT(param, QT_GAUSS_SQRT5);
	mpq_set(param->a[0], treal);
	mpq_set_si(param->a[1], -1, 6);
	mpq_mul(param->a[1], param->a[1], timag);
	mpq_set_si(param->a[2], 0, 1);
	mpq_set_si(param->a[3], 1, 12);
	mpq_mul(param->a[3], param->a[3], timag);

	generators_triangle_reflection_generic(gen, rho[0], rho[1], rho[2], param);

	LOOP(i, 3) CLEAR(rho[i]);
	CLEAR(param);

	return 1;

}