diff --git a/Makefile b/Makefile
index 5766967..daf8750 100644
--- a/Makefile
+++ b/Makefile
@@ -1,4 +1,4 @@
-HEADERS=linalg.h mat.h coxeter.h enumerate_triangle_group.h parallel.h qext.h
+HEADERS=mat.h coxeter.h enumerate.h generators.h qext.h
 
 SPECIAL_OPTIONS=-O0 -g -D_DEBUG -DQEXT
 #SPECIAL_OPTIONS=-O3 -pg -g -funroll-loops -fno-inline
@@ -7,44 +7,21 @@ SPECIAL_OPTIONS=-O0 -g -D_DEBUG -DQEXT
 #SPECIAL_OPTIONS=
 
 OPTIONS=-I../mps/include -L../mps/lib -pthread -m64 -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS)
+CC=gcc
 
-all: singular_values special_element convert billiard_words
+all: complex_anosov
 
-convert: convert.hs
-	ghc --make -dynamic convert.hs
+complex_anosov: complex_anosov.o mat.o coxeter.o enumerate.o generators.o qext.o
+	$(CC) $(OPTIONS) -o complex_anosov -lm complex_anosov.o mat.o coxeter.o enumerate.o generators.o qext.o -lgmp -lmps
 
-billiard_words: billiard_words.hs
-	ghc --make -dynamic billiard_words.hs
+complex_anosov.o: complex_anosov.c $(HEADERS)
+	gcc $(OPTIONS) -c complex_anosov.c
 
-singular_values: singular_values.o coxeter.o mat.o enumerate_triangle_group.o parallel.o
-	mpicc $(OPTIONS) -o singular_values coxeter.o singular_values.o mat.o enumerate_triangle_group.o parallel.o -lm -lgmp -lmps
+enumerate.o: enumerate.c $(HEADERS)
+	gcc $(OPTIONS) -c enumerate.c
 
-singular_values_barbot: singular_values_barbot.o coxeter.o mat.o enumerate_triangle_group.o parallel.o qext.o
-	mpicc $(OPTIONS) -o singular_values_barbot coxeter.o singular_values_barbot.o mat.o enumerate_triangle_group.o parallel.o qext.o -lm -lgmp -lmps
-
-#singular_values_mpi: singular_values_mpi.o coxeter.o mat.o
-#	mpicc $(OPTIONS) -o singular_values_mpi coxeter.o singular_values_mpi.o mat.o -lm -lgmp -lmps
-
-special_element: special_element.o coxeter.o linalg.o mat.o enumerate_triangle_group.o
-	gcc $(OPTIONS) -o special_element coxeter.o linalg.o special_element.o mat.o enumerate_triangle_group.o -lm -lgmp -lmps -lgsl -lcblas
-
-singular_values.o: singular_values.c $(HEADERS)
-	gcc $(OPTIONS) -c singular_values.c
-
-singular_values_barbot.o: singular_values_barbot.c $(HEADERS)
-	gcc $(OPTIONS) -c singular_values_barbot.c
-
-#singular_values_mpi.o: singular_values_mpi.c $(HEADERS)
-#	mpicc $(OPTIONS) -c singular_values_mpi.c
-
-special_element.o: special_element.c $(HEADERS)
-	gcc $(OPTIONS) -c special_element.c
-
-enumerate_triangle_group.o: enumerate_triangle_group.c $(HEADERS)
-	gcc $(OPTIONS) -c enumerate_triangle_group.c
-
-linalg.o: linalg.c $(HEADERS)
-	gcc $(OPTIONS) -c linalg.c
+generators.o: generators.c $(HEADERS)
+	gcc $(OPTIONS) -c generators.c
 
 coxeter.o: coxeter.c $(HEADERS)
 	gcc $(OPTIONS) -c coxeter.c
@@ -52,11 +29,8 @@ coxeter.o: coxeter.c $(HEADERS)
 mat.o: mat.c $(HEADERS)
 	gcc $(OPTIONS) -c mat.c
 
-parallel.o: parallel.c $(HEADERS)
-	gcc $(OPTIONS) -c parallel.c
-
 qext.o: qext.c $(HEADERS)
 	gcc $(OPTIONS) -c qext.c
 
 clean:
-	rm -f singular_values singular_values_barbot special_element singular_values_mpi coxeter.o linalg.o singular_values.o singular_values_barbot.o singular_values_mpi.o mat.o special_element.o convert.hi convert.o convert billiard_words.hi billiard_words.o billiard_words enumerate_triangle_group.o parallel.o qext.o
+	rm -f complex_anosov complex_anosov.o mat.o coxeter.o enumerate.o generators.o qext.o
diff --git a/complex_anosov.c b/complex_anosov.c
new file mode 100644
index 0000000..62c2301
--- /dev/null
+++ b/complex_anosov.c
@@ -0,0 +1,13 @@
+#include "coxeter.h"
+#include "enumerate.h"
+#include "generators.h"
+#include "mat.h"
+#include "qext.h"
+
+#include <stdio.h>
+
+int main(int argc, char *argv[])
+{
+	printf("initial main function.\n");
+	return 0;
+}
diff --git a/enumerate.c b/enumerate.c
new file mode 100644
index 0000000..90ea826
--- /dev/null
+++ b/enumerate.c
@@ -0,0 +1,24 @@
+#include "enumerate.h"
+
+#define LOOP(i,n) for(int i = 0; i < (n); i++)
+
+void enumerate_coxeter_group(group_t *group, mat *gen, mat *matrices)
+{
+	TYPE t = GETTYPE(gen[0]->x[0]);
+	mat_workspace *ws;
+
+	ws = mat_workspace_init(3, t);
+
+	mat_identity(matrices[0]);
+	for(int i = 1; i < group->size; i++) {
+		if(!group->elements[i].inverse)
+			continue;
+
+		int parent = group->elements[i].parent->id;
+		int letter = group->elements[i].letter;
+
+		mat_multiply(ws, matrices[i], matrices[parent], gen[letter]);
+	}
+
+	mat_workspace_clear(ws);
+}
diff --git a/enumerate.h b/enumerate.h
new file mode 100644
index 0000000..6e1a83c
--- /dev/null
+++ b/enumerate.h
@@ -0,0 +1,9 @@
+#ifndef ENUMERATE_H
+#define ENUMERATE_H
+
+#include "mat.h"
+#include "coxeter.h"
+
+void enumerate_coxeter_group(group_t *group, mat *gen, mat *matrices);
+
+#endif
diff --git a/generators.c b/generators.c
new file mode 100644
index 0000000..5639e2d
--- /dev/null
+++ b/generators.c
@@ -0,0 +1,111 @@
+#include "generators.h"
+
+#define LOOP(i,n) for(int i = 0; i < (n); i++)
+
+void generators_triangle_reflection_generic(mat *gen, NUMBER rho1, NUMBER rho2, NUMBER rho3, mpq_t q)
+{
+	NUMBER b1,c1,a2,c2,a3,b3;
+	mpq_t qinv;
+	TYPE t = GETTYPE(rho1);
+
+	INIT(b1,t);INIT(c1,t);INIT(a2,t);INIT(c2,t);INIT(a3,t);INIT(b3,t);
+
+	// qinv = q^{-1}
+	mpq_init(qinv);
+	mpq_inv(qinv, q);
+
+	// c1 = rho2 q, a2 = rho3 q, b3 = rho1 q, b1 = c2 = a3 = 1/q
+	SET_ZERO(c1);
+	SET_Q(c1, q);
+	SET_Q(a2, q);
+	SET_Q(b3, q);
+	MUL(c1, c1, rho2);
+	MUL(a2, a2, rho3);
+	MUL(b3, b3, rho1);
+	SET_INT(b1, 1);
+	SET_INT(c2, 1);
+	SET_INT(a3, 1);
+	SET_Q(b1, qinv);
+	SET_Q(c2, qinv);
+	SET_Q(a3, qinv);
+
+	LOOP(i, 3) {
+		mat_init(gen[i], 3, t);
+		mat_zero(gen[i]);
+		LOOP(j, 3) {
+			SET_INT(*mat_ref(gen[i], j, j), i == j ? 1 : -1);
+		}
+	}
+
+	NEG(*mat_ref(gen[0], 1, 0), b1);
+	NEG(*mat_ref(gen[0], 2, 0), c1);
+	NEG(*mat_ref(gen[1], 0, 1), a2);
+	NEG(*mat_ref(gen[1], 2, 1), c2);
+	NEG(*mat_ref(gen[2], 0, 2), a3);
+	NEG(*mat_ref(gen[2], 1, 2), b3);
+
+	CLEAR(b1);CLEAR(c1);CLEAR(a2);CLEAR(c2);CLEAR(a3);CLEAR(b3);
+	mpq_clear(qinv);
+}
+
+
+int generators_triangle_reflection_group(mat *gen, int p1, int p2, int p3, int q1, int q2, int q3, mpq_t t)
+{
+	int p[3] = {p1, p2, p3};
+	int q[3] = {q1, q2, q3};
+	TYPE type;
+
+	LOOP(i, 3)
+		if(p[i] < 2 || p[i] > 6)
+			return 0;
+
+#ifdef QEXT
+	type = QT_TRIVIAL;
+	LOOP(i, 3)
+		if(p[i] == 5)
+			type = QT_SQRT5;
+#else
+	LOOP(i, 3)
+		if(p[i] == 5)
+			return 0;
+#endif
+
+
+	NUMBER rho[3];
+	LOOP(i, 3) INIT(rho[i], type);
+
+	// compute rho1, rho2, rho3
+	LOOP(i, 3) {
+		if(p[i] == 2 && q[i] == 1) {
+			SET_INT(rho[i], 0);
+		} else if(p[i] == 3 && q[i] == 1) {
+			SET_INT(rho[i], 1);
+		} else if(p[i] == 4 && q[i] == 1) {
+			SET_INT(rho[i], 2);
+		} else if(p[i] == 4 && q[i] == 2) {
+			SET_INT(rho[i], 0);
+		} else if(p[i] == 6 && q[i] == 1) {
+			SET_INT(rho[i], 3);
+		} else if(p[i] == 6 && q[i] == 2) {
+			SET_INT(rho[i], 1);
+		} else if(p[i] == 6 && q[i] == 3) {
+			SET_INT(rho[i], 0);
+#ifdef QEXT
+		} else if(p[i] == 5 && q[i] == 1) {
+			mpq_set_si(rho[i]->a[0], 3, 2);
+			mpq_set_si(rho[i]->a[1], 1, 2);
+		} else if(p[i] == 5 && q[i] == 2) {
+			mpq_set_si(rho[i]->a[0], 3, 2);
+			mpq_set_si(rho[i]->a[1], -1, 2);
+#endif
+		} else {
+			return 0;
+		}
+	}
+
+	generators_triangle_reflection_generic(gen, rho[0], rho[1], rho[2], t);
+
+	LOOP(i, 3) CLEAR(rho[i]);
+
+	return 1;
+}
diff --git a/generators.h b/generators.h
new file mode 100644
index 0000000..ca97d52
--- /dev/null
+++ b/generators.h
@@ -0,0 +1,9 @@
+#ifndef GENERATORS_H
+#define GENERATORS_H
+
+#include "mat.h"
+
+void generators_triangle_reflection_generic(mat *gen, NUMBER rho1, NUMBER rho2, NUMBER rho3, mpq_t q);
+int generators_triangle_reflection_group(mat *gen, int p1, int p2, int p3, int q1, int q2, int q3, mpq_t q);
+
+#endif
diff --git a/enumerate_triangle_group.c b/old/enumerate_triangle_group.c
similarity index 100%
rename from enumerate_triangle_group.c
rename to old/enumerate_triangle_group.c
diff --git a/enumerate_triangle_group.h b/old/enumerate_triangle_group.h
similarity index 100%
rename from enumerate_triangle_group.h
rename to old/enumerate_triangle_group.h
diff --git a/singular_values.c b/old/singular_values.c
similarity index 100%
rename from singular_values.c
rename to old/singular_values.c
diff --git a/singular_values_barbot.c b/old/singular_values_barbot.c
similarity index 100%
rename from singular_values_barbot.c
rename to old/singular_values_barbot.c
diff --git a/parallel.c b/parallelization/parallel.c
similarity index 100%
rename from parallel.c
rename to parallelization/parallel.c
diff --git a/parallel.h b/parallelization/parallel.h
similarity index 100%
rename from parallel.h
rename to parallelization/parallel.h