149 lines
3.2 KiB
C
149 lines
3.2 KiB
C
#include "generators.h"
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#include "mat.h"
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#define LOOP(i,n) for(int i = 0; i < (n); i++)
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void generators_triangle_reflection_generic(mat *gen, NUMBER sqrho1, NUMBER sqrho2, NUMBER sqrho3, NUMBER t)
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{
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NUMBER tmp;
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NUMBER tinv;
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TYPE type = GETTYPE(sqrho1);
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INIT(tmp, type);
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INIT(tinv, type);
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INV(tinv, t);
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LOOP(i, 3) {
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mat_init(gen[i], 3, type);
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mat_zero(gen[i]);
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LOOP(j, 3) {
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SET_INT(*mat_ref(gen[i], j, j), i == j ? 1 : -1);
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}
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}
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MUL(tmp, t, sqrho1);
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NEG(*mat_ref(gen[2], 1, 2), tmp);
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NEG(*mat_ref(gen[0], 2, 0), sqrho2);
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NEG(*mat_ref(gen[1], 0, 1), sqrho3);
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MUL(tmp, tinv, sqrho1);
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NEG(*mat_ref(gen[1], 2, 1), tmp);
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NEG(*mat_ref(gen[2], 0, 2), sqrho2);
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NEG(*mat_ref(gen[0], 1, 0), sqrho3);
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CLEAR(tmp);
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CLEAR(tinv);
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}
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// warning: this is not compatible anymore!
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int generators_triangle_reflection_group(mat *gen, int p1, int p2, int p3, int q1, int q2, int q3, mpq_t t)
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{
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int p[3] = {p1, p2, p3};
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int q[3] = {q1, q2, q3};
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TYPE type;
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LOOP(i, 3)
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if(p[i] < 2 || p[i] > 6)
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return 0;
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#ifdef QEXT
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type = QT_TRIVIAL;
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LOOP(i, 3)
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if(p[i] == 5)
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type = QT_SQRT5;
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#else
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LOOP(i, 3)
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if(p[i] == 5)
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return 0;
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#endif
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NUMBER rho[3];
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LOOP(i, 3) INIT(rho[i], type);
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// compute rho1, rho2, rho3
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LOOP(i, 3) {
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if(p[i] == 2 && q[i] == 1) {
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SET_INT(rho[i], 0);
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} else if(p[i] == 3 && q[i] == 1) {
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SET_INT(rho[i], 1);
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} else if(p[i] == 4 && q[i] == 1) {
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SET_INT(rho[i], 2);
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} else if(p[i] == 4 && q[i] == 2) {
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SET_INT(rho[i], 0);
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} else if(p[i] == 6 && q[i] == 1) {
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SET_INT(rho[i], 3);
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} else if(p[i] == 6 && q[i] == 2) {
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SET_INT(rho[i], 1);
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} else if(p[i] == 6 && q[i] == 3) {
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SET_INT(rho[i], 0);
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#ifdef QEXT
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} else if(p[i] == 5 && q[i] == 1) {
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mpq_set_si(rho[i]->a[0], 3, 2);
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mpq_set_si(rho[i]->a[1], 1, 2);
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} else if(p[i] == 5 && q[i] == 2) {
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mpq_set_si(rho[i]->a[0], 3, 2);
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mpq_set_si(rho[i]->a[1], -1, 2);
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#endif
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} else {
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return 0;
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}
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}
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NUMBER param;
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INIT(param, type);
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SET_Q(param, t);
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generators_triangle_reflection_generic(gen, rho[0], rho[1], rho[2], param);
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LOOP(i, 3) CLEAR(rho[i]);
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CLEAR(param);
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return 1;
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}
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int generators_triangle_reflection_group_555_complex(mat *gen, int q1, int q2, int q3, mpq_t treal, mpq_t timag)
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{
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int q[3] = {q1, q2, q3};
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NUMBER sqrho[3];
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LOOP(i, 3) INIT(sqrho[i], QT_GAUSS_SQRT5);
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// compute sqrho1, sqrho2, sqrho3
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LOOP(i, 3) {
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if(q[i] == 1) {
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// 2cos(pi/5) = 1/2 + 1/2*sqrt(5) = 1/2 + 7/12 a - 1/24 a^3
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mpq_set_si(sqrho[i]->a[0], 1, 2);
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mpq_set_si(sqrho[i]->a[1], 7, 12);
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mpq_set_si(sqrho[i]->a[2], 0, 1);
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mpq_set_si(sqrho[i]->a[3], -1, 24);
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} else if(q[i] == 2) {
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// 2cos(pi/5) = -1/2 + 1/2*sqrt(5)
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mpq_set_si(sqrho[i]->a[0], -1, 2);
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mpq_set_si(sqrho[i]->a[1], 7, 12);
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mpq_set_si(sqrho[i]->a[2], 0, 1);
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mpq_set_si(sqrho[i]->a[3], -1, 24);
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} else {
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return 0;
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}
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}
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NUMBER param;
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INIT(param, QT_GAUSS_SQRT5);
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mpq_set(param->a[0], treal);
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mpq_set_si(param->a[1], -1, 6);
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mpq_mul(param->a[1], param->a[1], timag);
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mpq_set_si(param->a[2], 0, 1);
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mpq_set_si(param->a[3], 1, 12);
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mpq_mul(param->a[3], param->a[3], timag);
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generators_triangle_reflection_generic(gen, sqrho[0], sqrho[1], sqrho[2], param);
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LOOP(i, 3) CLEAR(sqrho[i]);
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CLEAR(param);
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return 1;
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}
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