compute complex traces

complex_anosov.c

@@ -5,9 +5,148 @@
 #include "qext.h"
 
 #include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+#define LOOP(i,n) for(int i = 0; i < (n); i++)
+
+/*
+  Elements up to length 0: 1
+  Elements up to length 1: 4
+  Elements up to length 2: 10
+  Elements up to length 3: 22
+  Elements up to length 4: 46
+  Elements up to length 5: 91
+  Elements up to length 6: 175
+  Elements up to length 7: 334
+  Elements up to length 8: 634
+  Elements up to length 9: 1198
+  Elements up to length 10: 2260
+  Elements up to length 11: 4261
+  Elements up to length 12: 8029
+  Elements up to length 13: 15124
+  Elements up to length 14: 28486
+  Elements up to length 15: 53650
+  Elements up to length 16: 101038
+  Elements up to length 17: 190279
+  Elements up to length 18: 358339
+  Elements up to length 19: 674830
+  Elements up to length 20: 1270846
+  Elements up to length 21: 2393266
+  Elements up to length 22: 4507012
+  Elements up to length 23: 8487625
+*/
+
+static double gaussian_sqrt5_real(NUMBER x)
+{
+	double result = 0.0;
+
+	mpq_t tmp;
+	mpq_init(tmp);
+
+	// a_0 + sqrt(5)a_1 + 4a_2 + 2sqrt(5)a_3
+	mpq_set_si(tmp, 4, 1);
+	mpq_mul(tmp, tmp, x->a[2]);
+	mpq_add(tmp, tmp, x->a[0]);
+	result = mpq_get_d(tmp);
+	mpq_set_si(tmp, 2, 1);
+	mpq_mul(tmp, tmp, x->a[3]);
+	mpq_add(tmp, tmp, x->a[1]);
+	result += mpq_get_d(tmp)*sqrt(5);
+
+	mpq_clear(tmp);
+
+	return result;
+}
+
+static double gaussian_sqrt5_imag(NUMBER x)
+{
+	double result = 0.0;
+
+	mpq_t tmp;
+	mpq_init(tmp);
+
+	// a_1 + 2sqrt(5)a_2 + 14a_3
+	mpq_set_si(tmp, 14, 1);
+	mpq_mul(tmp, tmp, x->a[3]);
+	mpq_add(tmp, tmp, x->a[1]);
+	result = mpq_get_d(tmp);
+	mpq_set_si(tmp, 2, 1);
+	mpq_mul(tmp, tmp, x->a[2]);
+	result += mpq_get_d(tmp)*sqrt(5);
+
+	mpq_clear(tmp);
+
+	return result;
+}
 
 int main(int argc, char *argv[])
 {
-	printf("initial main function.\n");
+	char buf[100];
+	int n = atoi(argv[1]);
+
+	mpq_t qreal, qimag;
+	mpq_inits(qreal, qimag, NULL);
+	mpq_set_si(qreal, 50, 10);
+	mpq_set_si(qimag, 1, 10);
+	mpq_canonicalize(qreal);
+	mpq_canonicalize(qimag);
+
+	/*
+	int length = 0;
+	LOOP(i, n) {
+		if(group->elements[i].length > length) {
+			printf("Elements up to length %d: %d\n", length, i);
+			length = group->elements[i].length;
+		}
+	}
+	return 0;
+	*/
+
+	/*
+	LOOP(i, n) {
+		groupelement_t *cur = &group->elements[i];
+		groupelement_t *other;
+
+		cur->conjugacy_class = cur; // start with itself and reduce if possible
+
+		LOOP(j, 3) {
+			if(cur->left[j] && cur->left[j]->right[j]) {
+				other = cur->left[j]->right[j];
+				if(other->id < cur->id)
+					cur->conjugacy_class = other->conjugacy_class;
+			}
+			if(cur->right[j] && cur->right[j]->left[j]) {
+				other = cur->right[j]->left[j];
+				if(other->id < cur->id)
+					cur->conjugacy_class = other->conjugacy_class;
+			}
+		}
+	}
+	*/
+
+	group_t *group = coxeter_init_triangle(5, 5, 5, n);
+
+	mat gen[3];
+	LOOP(i, 3) mat_init(gen[i], 3, QT_GAUSS_SQRT5);
+	generators_triangle_reflection_group_555_complex(gen, 2, 2, 2, qreal, qimag);
+
+	struct tracedata *traces;
+	int nuniq = enumerate_coxeter_group_traces(group, gen, &traces);
+
+	LOOP(i, nuniq) {
+		printf("%d %f %f %f %f\n",
+		       traces[i].id,
+		       gaussian_sqrt5_real(traces[i].tr),
+		       gaussian_sqrt5_imag(traces[i].tr),
+		       gaussian_sqrt5_real(traces[i].trinv),
+		       gaussian_sqrt5_imag(traces[i].trinv));
+	}
+
+	enumerate_tracedata_clear(traces, nuniq);
+	LOOP(i, 3) mat_clear(gen[i]);
+	coxeter_clear(group);
+	mpq_clears(qreal, qimag, NULL);
+
 	return 0;
 }