triangle_reflection_complex/enumerate_triangle_group.c

266 lines
6.7 KiB
C

#include "enumerate_triangle_group.h"
#include "linalg.h"
int solve_characteristic_polynomial(mps_context *solv, mps_monomial_poly *poly, mpq_t tr, mpq_t trinv, double *eigenvalues)
{
mpq_t coeff1, coeff2, zero;
cplx_t *roots;
double radii[3];
double *radii_p[3];
mps_boolean errors;
int result = 0;
mpq_inits(coeff1, coeff2, zero, NULL);
mpq_set(coeff1, trinv);
mpq_sub(coeff2, zero, tr);
mps_monomial_poly_set_coefficient_int(solv, poly, 0, -1, 0);
mps_monomial_poly_set_coefficient_q(solv, poly, 1, coeff1, zero);
mps_monomial_poly_set_coefficient_q(solv, poly, 2, coeff2, zero);
mps_monomial_poly_set_coefficient_int(solv, poly, 3, 1, 0);
mps_context_set_input_poly(solv, (mps_polynomial*)poly);
mps_mpsolve(solv);
roots = cplx_valloc(3);
for(int i = 0; i < 3; i++)
radii_p[i] = &(radii[i]);
mps_context_get_roots_d(solv, &roots, radii_p);
errors = mps_context_has_errors(solv);
if(errors) {
result = 1;
} else {
for(int i = 0; i < 3; i++) {
eigenvalues[i] = cplx_Re(roots[i]);
if(fabs(cplx_Im(roots[i])) > radii[i]) // non-real root
result = 2;
}
}
cplx_vfree(roots);
mpq_clears(coeff1, coeff2, zero, NULL);
return result;
}
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);
}
// p1,p2,p3 are only allowed to be 2,3,4,6
void initialize_triangle_generators(mat_workspace *ws, mat *gen, int p1, int p2, int p3, mpq_t s, mpq_t q)
{
mat r1,r2,r3;
mpq_t rho1, rho2, rho3;
mpq_t b1,c1,a2,c2,a3,b3;
mpq_t sinv;
mpq_inits(sinv,rho1,rho2,rho3,b1,c1,a2,c2,a3,b3,NULL);
mat_init(r1, 3);
mat_init(r2, 3);
mat_init(r3, 3);
// sinv = s^{-1}
mpq_set_ui(sinv, 1, 1);
mpq_div(sinv, sinv, s);
// rho_i = s^2 + 2s cos(2 pi / p_i) + 1
// coefficient 2 is the value for p=infinity, not sure if that would even work
quartic(rho1, s, 0, 0, 1, p1 == 2 ? -2 : p1 == 3 ? -1 : p1 == 4 ? 0 : p1 == 6 ? 1 : 2, 1);
quartic(rho2, s, 0, 0, 1, p2 == 2 ? -2 : p2 == 3 ? -1 : p2 == 4 ? 0 : p2 == 6 ? 1 : 2, 1);
quartic(rho3, s, 0, 0, 1, p3 == 2 ? -2 : p3 == 3 ? -1 : p3 == 4 ? 0 : p3 == 6 ? 1 : 2, 1);
// c1 = rho2 q, a2 = rho3 q, b3 = rho1 q, b1 = c2 = a3 = 1/q
mpq_mul(c1, rho2, q);
mpq_mul(a2, rho3, q);
mpq_mul(b3, rho1, q);
mpq_set_ui(b1, 1, 1);
mpq_set_ui(c2, 1, 1);
mpq_set_ui(a3, 1, 1);
mpq_div(b1, b1, q);
mpq_div(c2, c2, q);
mpq_div(a3, a3, q);
mat_zero(r1);
mat_zero(r2);
mat_zero(r3);
mpq_set_si(*mat_ref(r1, 0, 0), -1, 1);
mpq_set_si(*mat_ref(r1, 1, 1), 1, 1);
mpq_set_si(*mat_ref(r1, 2, 2), 1, 1);
mpq_set_si(*mat_ref(r2, 0, 0), 1, 1);
mpq_set_si(*mat_ref(r2, 1, 1), -1, 1);
mpq_set_si(*mat_ref(r2, 2, 2), 1, 1);
mpq_set_si(*mat_ref(r3, 0, 0), 1, 1);
mpq_set_si(*mat_ref(r3, 1, 1), 1, 1);
mpq_set_si(*mat_ref(r3, 2, 2), -1, 1);
mpq_set(*mat_ref(r1, 1, 0), b1);
mpq_set(*mat_ref(r1, 2, 0), c1);
mpq_set(*mat_ref(r2, 0, 1), a2);
mpq_set(*mat_ref(r2, 2, 1), c2);
mpq_set(*mat_ref(r3, 0, 2), a3);
mpq_set(*mat_ref(r3, 1, 2), b3);
mat_zero(gen[0]);
mat_zero(gen[1]);
mat_zero(gen[2]);
// gen[0] = diag(1,s^{-1},s)
mpq_set_ui(*mat_ref(gen[0], 0, 0), 1, 1);
mat_set(gen[0], 1, 1, sinv);
mat_set(gen[0], 2, 2, s);
// gen[1] = diag(s,1,s^{-1})
mat_set(gen[1], 0, 0, s);
mpq_set_ui(*mat_ref(gen[1], 1, 1), 1, 1);
mat_set(gen[1], 2, 2, sinv);
// gen[3] = diag(s^{-1},s,1)
mat_set(gen[2], 0, 0, sinv);
mat_set(gen[2], 1, 1, s);
mpq_set_ui(*mat_ref(gen[2], 2, 2), 1, 1);
// gen[0] = r2 * gen[0] * r3
// gen[1] = r3 * gen[1] * r1
// gen[2] = r1 * gen[2] * r2
mat_multiply(ws, gen[0], r2, gen[0]);
mat_multiply(ws, gen[0], gen[0], r3);
mat_multiply(ws, gen[1], r3, gen[1]);
mat_multiply(ws, gen[1], gen[1], r1);
mat_multiply(ws, gen[2], r1, gen[2]);
mat_multiply(ws, gen[2], gen[2], r2);
// gen[3] = gen[0]^{-1}
// gen[4] = gen[1]^{-1}
// gen[5] = gen[2]^{-1}
mat_pseudoinverse(ws, gen[3], gen[0]);
mat_pseudoinverse(ws, gen[4], gen[1]);
mat_pseudoinverse(ws, gen[5], gen[2]);
/*
mat_print(r1);
mat_print(r2);
mat_print(r3);
mat_print(gen[0]);
mat_print(gen[1]);
mat_print(gen[2]);
mat_print(gen[3]);
mat_print(gen[4]);
mat_print(gen[5]);
*/
mpq_clears(sinv,rho1,rho2,rho3,b1,c1,a2,c2,a3,b3,NULL);
mat_clear(r1);
mat_clear(r2);
mat_clear(r3);
}
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(group_t *group, mat *matrices, int p1, int p2, int p3, mpq_t s, mpq_t q)
{
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, p1, p2, p3, s, q);
mat_identity(matrices[0]);
for(int i = 1; i < group->size; i++) {
if(group->elements[i].length % 2 != 0)
continue;
if(!group->elements[i].inverse)
continue;
if(!group->elements[i].need_to_compute)
continue;
int parent = group->elements[i].parent->id;
int grandparent = group->elements[i].parent->parent->id;
int letter;
if(group->elements[parent].letter == 1 && group->elements[i].letter == 2)
letter = 0; // p = bc
else if(group->elements[parent].letter == 2 && group->elements[i].letter == 0)
letter = 1; // q = ca
else if(group->elements[parent].letter == 0 && group->elements[i].letter == 1)
letter = 2; // r = ab
if(group->elements[parent].letter == 2 && group->elements[i].letter == 1)
letter = 3; // p^{-1} = cb
else if(group->elements[parent].letter == 0 && group->elements[i].letter == 2)
letter = 4; // q^{-1} = ac
else if(group->elements[parent].letter == 1 && group->elements[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);
}