174 lines
4.6 KiB
C
174 lines
4.6 KiB
C
#include "triangle.h"
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#include "linalg.h"
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#include "mat.h"
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#include <gsl/gsl_poly.h>
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//#define MAX_ELEMENTS 2800000
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//#define MAX_ELEMENTS 720000
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#define MAX_ELEMENTS 14000
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//#define DRAW_PICTURE 1
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void mpq_quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e)
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{
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mpq_t tmp;
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mpq_init(tmp);
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mpq_set_si(out, a, 1);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, b, 1);
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mpq_add(out, out, tmp);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, c, 1);
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mpq_add(out, out, tmp);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, d, 1);
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mpq_add(out, out, tmp);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, e, 1);
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mpq_add(out, out, tmp);
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mpq_clear(tmp);
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}
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void initialize_triangle_generators(mat_workspace *ws, mat *gen, mpq_t s, mpq_t t)
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{
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mpq_set_ui(*mat_ref(gen[0], 0, 0), 0, 1);
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mpq_set_ui(*mat_ref(gen[0], 0, 1), 0, 1);
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mpq_set_ui(*mat_ref(gen[0], 0, 2), 1, 1);
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mpq_set_ui(*mat_ref(gen[0], 1, 0), 1, 1);
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mpq_set_ui(*mat_ref(gen[0], 1, 1), 0, 1);
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mpq_set_ui(*mat_ref(gen[0], 1, 2), 0, 1);
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mpq_set_ui(*mat_ref(gen[0], 2, 0), 0, 1);
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mpq_set_ui(*mat_ref(gen[0], 2, 1), 1, 1);
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mpq_set_ui(*mat_ref(gen[0], 2, 2), 0, 1);
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mpq_set_ui(*mat_ref(gen[1], 0, 0), 1, 1);
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mpq_set_ui(*mat_ref(gen[1], 1, 0), 0, 1);
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mpq_set_ui(*mat_ref(gen[1], 2, 0), 0, 1);
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mpq_quartic(*mat_ref(gen[1], 0, 1), t, 0, 0, 1, -1, 2);
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mpq_quartic(*mat_ref(gen[1], 1, 1), t, 0, 0, -1, 2, -2);
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mpq_quartic(*mat_ref(gen[1], 2, 1), t, 0, 0, 1, -3, 3);
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mpq_quartic(*mat_ref(gen[1], 0, 2), t, 0, 0, 1, 0, 3);
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mpq_quartic(*mat_ref(gen[1], 1, 2), t, 0, 0, -1, 1, -1);
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mpq_quartic(*mat_ref(gen[1], 2, 2), t, 0, 0, 1, -2, 1);
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mat_pseudoinverse(ws, gen[3], gen[0]); // p^{-1}
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mat_pseudoinverse(ws, gen[4], gen[1]); // q^{-1}
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mat_multiply(ws, gen[2], gen[4], gen[3]); // r = q^{-1}p^{-1}
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mat_pseudoinverse(ws, gen[5], gen[2]);
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// mat_print(gen[0]);
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// mat_print(gen[1]);
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// mat_print(gen[2]);
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// mat_print(gen[3]);
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// mat_print(gen[4]);
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// mat_print(gen[5]);
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}
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char *print_word(groupelement_t *g, char *str)
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{
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int i = g->length - 1;
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str[g->length] = 0;
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while(g->parent) {
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str[i--] = 'a' + g->letter;
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g = g->parent;
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}
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return str;
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}
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int main(int argc, char *argv[])
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{
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groupelement_t *group;
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mat_workspace *ws;
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mat *matrices;
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mat tmp;
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mat gen[6];
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char buf[100], buf2[100], buf3[100];
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mpq_t s,t;
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mpq_t det, tr, trinv;
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// allocate stuff
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group = malloc(MAX_ELEMENTS*sizeof(groupelement_t));
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ws = mat_workspace_init(3);
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matrices = malloc(MAX_ELEMENTS*sizeof(mat));
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for(int i = 0; i < MAX_ELEMENTS; i++)
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mat_init(matrices[i], 3);
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for(int i = 0; i < 6; i++)
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mat_init(gen[i], 3);
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mat_init(tmp, 3);
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mpq_inits(s, t, det, tr, trinv, NULL);
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mpq_set_ui(s,1,1);
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double t_ = atof(argv[1]);
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mpq_set_ui(t,(int)(t_*100),100);
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mpq_canonicalize(s);
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mpq_canonicalize(t);
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// the real action
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generate_triangle_group(group, MAX_ELEMENTS, 3, 3, 4);
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initialize_triangle_generators(ws, gen, s, t);
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mat_identity(matrices[0]);
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for(int i = 1; i < MAX_ELEMENTS; i++) {
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if(group[i].length % 2 != 0)
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continue;
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if(!group[i].inverse)
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continue;
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int parent = group[i].parent->id;
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int grandparent = group[i].parent->parent->id;
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int letter;
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if(group[parent].letter == 1 && group[i].letter == 2)
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letter = 0; // p = bc
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else if(group[parent].letter == 2 && group[i].letter == 0)
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letter = 1; // q = ca
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else if(group[parent].letter == 0 && group[i].letter == 1)
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letter = 2; // r = ab
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if(group[parent].letter == 2 && group[i].letter == 1)
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letter = 3; // p^{-1} = cb
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else if(group[parent].letter == 0 && group[i].letter == 2)
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letter = 4; // q^{-1} = ac
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else if(group[parent].letter == 1 && group[i].letter == 0)
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letter = 5; // r^{-1} = ba
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mat_multiply(ws, matrices[i], matrices[grandparent], gen[letter]);
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}
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for(int i = 0; i < MAX_ELEMENTS; i++) {
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if(group[i].length % 2 != 0)
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continue;
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if(!group[i].inverse)
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continue;
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mat_trace(tr, matrices[i]);
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mat_trace(trinv, matrices[group[i].inverse->id]);
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double lambda1, lambda2, lambda3;
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// int realevs = gsl_poly_solve_cubic(-mpq_get_d(tr), mpq_get_d(trinv), -1, &lambda3, &lambda2, &lambda1);
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// if(realevs != 3)
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// continue;
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// if(lambda1 < 0 || lambda2 < 0 || lambda3 < 0)
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// continue;
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// gmp_printf("%d %d %s %Qd %Qd\n", i, group[i].length, print_word(&group[i], buf), tr, trinv);
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printf("%d %d %s %f %f %f\n", i, group[i].length, print_word(&group[i], buf), log(mpq_get_d(tr)), log(mpq_get_d(trinv)));
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}
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// free stuff
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for(int i = 0; i < MAX_ELEMENTS; i++)
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mat_clear(matrices[i]);
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for(int i = 0; i < 6; i++)
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mat_clear(gen[i]);
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mat_clear(tmp);
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mpq_clears(s, t, det, tr, trinv, NULL);
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mat_workspace_clear(ws);
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return 0;
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}
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