153 lines
3.3 KiB
C
153 lines
3.3 KiB
C
#include "coxeter.h"
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#include "enumerate.h"
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#include "generators.h"
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#include "mat.h"
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#include "qext.h"
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#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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#define LOOP(i,n) for(int i = 0; i < (n); i++)
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/*
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Elements up to length 0: 1
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Elements up to length 1: 4
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Elements up to length 2: 10
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Elements up to length 3: 22
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Elements up to length 4: 46
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Elements up to length 5: 91
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Elements up to length 6: 175
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Elements up to length 7: 334
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Elements up to length 8: 634
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Elements up to length 9: 1198
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Elements up to length 10: 2260
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Elements up to length 11: 4261
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Elements up to length 12: 8029
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Elements up to length 13: 15124
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Elements up to length 14: 28486
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Elements up to length 15: 53650
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Elements up to length 16: 101038
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Elements up to length 17: 190279
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Elements up to length 18: 358339
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Elements up to length 19: 674830
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Elements up to length 20: 1270846
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Elements up to length 21: 2393266
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Elements up to length 22: 4507012
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Elements up to length 23: 8487625
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*/
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static double gaussian_sqrt5_real(NUMBER x)
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{
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double result = 0.0;
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mpq_t tmp;
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mpq_init(tmp);
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// a_0 + sqrt(5)a_1 + 4a_2 + 2sqrt(5)a_3
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mpq_set_si(tmp, 4, 1);
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mpq_mul(tmp, tmp, x->a[2]);
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mpq_add(tmp, tmp, x->a[0]);
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result = mpq_get_d(tmp);
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mpq_set_si(tmp, 2, 1);
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mpq_mul(tmp, tmp, x->a[3]);
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mpq_add(tmp, tmp, x->a[1]);
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result += mpq_get_d(tmp)*sqrt(5);
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mpq_clear(tmp);
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return result;
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}
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static double gaussian_sqrt5_imag(NUMBER x)
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{
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double result = 0.0;
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mpq_t tmp;
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mpq_init(tmp);
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// a_1 + 2sqrt(5)a_2 + 14a_3
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mpq_set_si(tmp, 14, 1);
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mpq_mul(tmp, tmp, x->a[3]);
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mpq_add(tmp, tmp, x->a[1]);
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result = mpq_get_d(tmp);
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mpq_set_si(tmp, 2, 1);
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mpq_mul(tmp, tmp, x->a[2]);
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result += mpq_get_d(tmp)*sqrt(5);
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mpq_clear(tmp);
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return result;
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}
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int main(int argc, char *argv[])
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{
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char buf[100];
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int n = atoi(argv[1]);
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mpq_t qreal, qimag;
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mpq_inits(qreal, qimag, NULL);
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mpq_set_si(qreal, 50, 10);
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mpq_set_si(qimag, 1, 10);
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mpq_canonicalize(qreal);
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mpq_canonicalize(qimag);
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/*
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int length = 0;
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LOOP(i, n) {
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if(group->elements[i].length > length) {
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printf("Elements up to length %d: %d\n", length, i);
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length = group->elements[i].length;
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}
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}
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return 0;
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*/
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/*
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LOOP(i, n) {
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groupelement_t *cur = &group->elements[i];
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groupelement_t *other;
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cur->conjugacy_class = cur; // start with itself and reduce if possible
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LOOP(j, 3) {
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if(cur->left[j] && cur->left[j]->right[j]) {
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other = cur->left[j]->right[j];
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if(other->id < cur->id)
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cur->conjugacy_class = other->conjugacy_class;
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}
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if(cur->right[j] && cur->right[j]->left[j]) {
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other = cur->right[j]->left[j];
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if(other->id < cur->id)
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cur->conjugacy_class = other->conjugacy_class;
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}
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}
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}
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*/
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group_t *group = coxeter_init_triangle(5, 5, 5, n);
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mat gen[3];
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LOOP(i, 3) mat_init(gen[i], 3, QT_GAUSS_SQRT5);
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generators_triangle_reflection_group_555_complex(gen, 2, 2, 2, qreal, qimag);
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struct tracedata *traces;
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int nuniq = enumerate_coxeter_group_traces(group, gen, &traces);
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LOOP(i, nuniq) {
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printf("%d %f %f %f %f\n",
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traces[i].id,
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gaussian_sqrt5_real(traces[i].tr),
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gaussian_sqrt5_imag(traces[i].tr),
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gaussian_sqrt5_real(traces[i].trinv),
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gaussian_sqrt5_imag(traces[i].trinv));
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}
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enumerate_tracedata_clear(traces, nuniq);
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LOOP(i, 3) mat_clear(gen[i]);
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coxeter_clear(group);
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mpq_clears(qreal, qimag, NULL);
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return 0;
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}
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