diff --git a/Makefile b/Makefile
index a88cd22..0269d46 100644
--- a/Makefile
+++ b/Makefile
@@ -1,4 +1,4 @@
-HEADERS=linalg.h mat.h coxeter.h
+HEADERS=linalg.h mat.h coxeter.h enumerate_triangle_group.h
 
 #SPECIAL_OPTIONS=-O0 -g -D_DEBUG
 SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
@@ -16,14 +16,14 @@ convert: convert.hs
 billiard_words: billiard_words.hs
 	ghc --make -dynamic billiard_words.hs
 
-singular_values: singular_values.o coxeter.o mat.o
-	gcc $(OPTIONS) -o singular_values coxeter.o singular_values.o mat.o -lm -lgmp -lmps
+singular_values: singular_values.o coxeter.o mat.o enumerate_triangle_group.o
+	gcc $(OPTIONS) -o singular_values coxeter.o singular_values.o mat.o enumerate_triangle_group.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
-	gcc $(OPTIONS) -o special_element coxeter.o linalg.o special_element.o mat.o -lm -lgmp -lmps -lgsl -lcblas
+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
@@ -34,6 +34,9 @@ singular_values_mpi.o: singular_values_mpi.c $(HEADERS)
 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
 
@@ -44,4 +47,4 @@ mat.o: mat.c $(HEADERS)
 	gcc $(OPTIONS) -c mat.c
 
 clean:
-	rm -f singular_values special_element singular_values_mpi coxeter.o linalg.o singular_values.o singular_values_mpi.o mat.o special_element.o convert.hi convert.o convert billiard_words.hi billiard_words.o billiard_words
+	rm -f singular_values special_element singular_values_mpi coxeter.o linalg.o singular_values.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
diff --git a/billiard_words.hs b/billiard_words.hs
index 4d959d3..9e88f51 100644
--- a/billiard_words.hs
+++ b/billiard_words.hs
@@ -1,18 +1,22 @@
 import Data.List
 import Data.Ord
 import Text.Printf
+import System.Environment
 
-main = listWordsUpToLength 200
+main = do
+  argv <- getArgs
+  listWordsUpToLength $ read $ argv !! 0
 
 listWordsUpToLength :: Int -> IO ()
 listWordsUpToLength n = do
-  putStrLn $ unlines [printf "%d/%d\t%d/%d\t%.7f\t%d\t%s" p q (x `div` gcd x y) (y `div` gcd x y) (sqrt 3 / (1 + 2*fromIntegral q / fromIntegral p) :: Double) (length w) w | ((p,q),w) <- wordlist (n`div`2) (n`div`2), length w <= n, let x = 2*q + p, let y = 2*p + q]
+  putStrLn $ unlines [printf "%s %d/%d %f" w (x `div` gcd x y) (y `div` gcd x y) (fromIntegral x / fromIntegral y :: Double) | ((p,q),w) <- wordlist (n`div`2) (n`div`2), length w <= n, let x = 2*q + p, let y = 2*p + q]
+--  putStrLn $ unlines [printf "%d/%d\t%d/%d\t%.7f\t%d\t%s" p q (x `div` gcd x y) (y `div` gcd x y) (sqrt 3 / (1 + 2*fromIntegral q / fromIntegral p) :: Double) (length w) w | ((p,q),w) <- wordlist (n`div`2) (n`div`2), length w <= n, let x = 2*q + p, let y = 2*p + q]
 
 
   --  putStrLn $ unlines [printf "%d/%d\t%.5f\t%.5f\t%d\t%s" p q (fromIntegral p / fromIntegral q :: Double) (sqrt 3 / (1 + 2*fromIntegral q / fromIntegral p) :: Double) (length w) w | ((p,q),w) <- wordlist (n`div`2) (n`div`2), length w <= n]
 
 wordlist :: Int -> Int -> [((Int,Int),String)]
-wordlist pmax qmax = nub $ sortBy (comparing sl) [((p `div` gcd p q, q `div` gcd p q), slopeWord "bca" p q) | p <- [0..200], q <- [0..200], p /= 0 || q /= 0]
+wordlist pmax qmax = nub $ sortBy (comparing sl) [((p `div` gcd p q, q `div` gcd p q), slopeWord "bca" p q) | p <- [0..pmax], q <- [0..qmax], p /= 0 || q /= 0]
     where
       sl ((p,q),_) = fromIntegral p / fromIntegral q
 
diff --git a/coxeter.c b/coxeter.c
index b8ca58f..128d9cd 100644
--- a/coxeter.c
+++ b/coxeter.c
@@ -9,9 +9,9 @@
 group_t *coxeter_init_triangle(int p, int q, int r, int nmax)
 {
 	int coxeter_matrix[9] = {
-		1, p, r,
-		p, 1, q,
-		r, q, 1};
+		1, r, q,
+		r, 1, p,
+		q, p, 1};
 
 	return coxeter_init(3, coxeter_matrix, nmax);
 }
diff --git a/singular_values.c b/singular_values.c
index fe0cff0..e613e69 100644
--- a/singular_values.c
+++ b/singular_values.c
@@ -1,17 +1,12 @@
 #include "coxeter.h"
 #include "linalg.h"
 #include "mat.h"
-
-#include <gsl/gsl_poly.h>
-#include <mps/mps.h>
+#include "enumerate_triangle_group.h"
 
 #define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
 //#define DEBUG(msg, ...) fprintf(stderr, msg, ##__VA_ARGS__)
 #define DEBUG(msg, ...)
 
-#define OUTPUT_POINTS
-//#define OUTPUT_POINTS
-
 struct result {
 	int id;
 	int count;
@@ -67,326 +62,6 @@ static int compare_result_by_slope(const void *a_, const void *b_)
 	return slopea > slopeb ? -1 : slopea < slopeb ? 1 : 0;
 }
 
-
-int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues)
-{
-	mpq_t coeff1, coeff2, zero;
-	cplx_t *roots;
-	double radii[3];
-	double *radii_p[3];
-	mps_monomial_poly *poly;
-	mps_boolean errors;
-	int result = 0;
-
-	mpq_inits(coeff1, coeff2, zero, NULL);
-	mpq_set(coeff1, trinv);
-	mpq_sub(coeff2, zero, tr);
-
-	poly = mps_monomial_poly_new(solv, 3);
-	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);
-}
-
-void initialize_triangle_generators(mat_workspace *ws, mat *gen, 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);
-
-	mpq_set_ui(sinv, 1, 1);
-	mpq_div(sinv, sinv, s);
-
-	quartic(rho1, s, 0, 0, 1, -1, 1);
-	quartic(rho2, s, 0, 0, 1, -1, 1);
-	quartic(rho3, s, 0, 0, 1,  0, 1);
-
-	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);
-
-	// actually, we want minus everything
-	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]);
-
-	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);
-
-	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);
-
-	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);
-
-	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);
-
-	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, mpq_t s, mpq_t t)
-{
-	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, s, t);
-
-	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;
-
-		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);
-}
-
-void output_invariants(group_t *group, mat *matrices, mpq_t s, mpq_t q, mps_context *solver)
-{
-	mpq_t tr, trinv;
-	char buf[100];
-	double evs[3];
-	int retval;
-
-	mpq_inits(tr, trinv, NULL);
-
-	for(int i = 0; i < group->size; i++) {
-		if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
-			continue;
-
-		mat_trace(tr, matrices[i]);
-		mat_trace(trinv, matrices[group->elements[i].inverse->id]);
-
-		retval = solve_characteristic_polynomial(solver, tr, trinv, evs);
-		if(retval == 1) {
-			fprintf(stderr, "Error! Could not solve polynomial.\n");
-			continue;
-		} else if(retval == 2) {
-			continue;
-		}
-
-		if(fabs(evs[0]) < fabs(evs[1]))
-			SWAP(double, evs[0], evs[1]);
-		if(fabs(evs[1]) < fabs(evs[2]))
-			SWAP(double, evs[1], evs[2]);
-		if(fabs(evs[0]) < fabs(evs[1]))
-			SWAP(double, evs[0], evs[1]);
-
-		gmp_printf("%d %d %s %Qd %Qd %f %f\n", i, group->elements[i].length, print_word(&group->elements[i], buf), tr, trinv, log(evs[0]), -log(evs[2]));
-	}
-
-	mpq_clears(tr, trinv, NULL);
-}
-
-/*
-double max_slope(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t, int *index)
-{
-	double max = 0;
-	double slope;
-
-	mpq_t tr, trinv;
-	char buf[100];
-
-	mpq_inits(tr, trinv, NULL);
-
-	for(int i = 0; i < MAX_ELEMENTS; i++) {
-		if(group[i].length % 2 != 0 || !group[i].inverse)
-			continue;
-
-		mat_trace(tr, matrices[i]);
-		mat_trace(trinv, matrices[group[i].inverse->id]);
-
-		slope = log(mpq_get_d(trinv))/log(mpq_get_d(tr));
-		if(slope > max)
-		{
-			*index = i;
-			max = slope;
-		}
-	}
-
-	mpq_clears(tr, trinv, NULL);
-
-	return max;
-}
-*/
-
 int main(int argc, char *argv[])
 {
 	mpq_t s, q, t, tmp;
@@ -407,7 +82,7 @@ int main(int argc, char *argv[])
 	struct result **distinct_invariants;
 
 	if(argc < 4) {
-		fprintf(stderr, "Usage: %s <N> <s> <t>\n", argv[0]);
+		fprintf(stderr, "Usage: %s <N> <s> <q>\n", argv[0]);
 		exit(1);
 	}
 
@@ -435,9 +110,10 @@ int main(int argc, char *argv[])
 
 	// get approximate s and q values
 	sapprox = atof(argv[2]);
-	tapprox = atof(argv[3]);
-	tqfactor = pow((sapprox*sapprox-sapprox+1)*(sapprox*sapprox-sapprox+1)*(sapprox*sapprox+1), 1/6.0);
-	qapprox = tapprox/tqfactor;
+	qapprox = atof(argv[3]);
+//	tapprox = atof(argv[3]);
+//	tqfactor = pow((sapprox*sapprox-sapprox+1)*(sapprox*sapprox-sapprox+1)*(sapprox*sapprox+1), 1/6.0);
+//	qapprox = tapprox/tqfactor;
 
 	for(int i = 0; ; i++) {
 		continued_fraction_approximation(tmp, sapprox, i);
@@ -459,16 +135,14 @@ int main(int argc, char *argv[])
 
 	tqfactor = pow((mpq_get_d(s)*mpq_get_d(s)-mpq_get_d(s)+1)*(mpq_get_d(s)*mpq_get_d(s)-mpq_get_d(s)+1)*(mpq_get_d(s)*mpq_get_d(s)+1), 1/6.0);
 
-#ifdef OUTPUT_POINTS
-//	gmp_fprintf(stdout, "\"s = %Qd = %.3f, q = %Qd, t = %.3f\"\n", s, mpq_get_d(s), q, mpq_get_d(q)*tqfactor);
-#endif
-
 	// group
+	// order of the triangle reflection generators: a, b, c
+	// order of the rotation orders: bc, ac, ab
 	DEBUG("Generate group\n");
 	group = coxeter_init_triangle(4, 3, 3, nmax);
 
 	DEBUG("Compute matrices\n");
-	enumerate(group, matrices, s, q);
+	enumerate(group, matrices, 4, 3, 3, s, q);
 
 	n = 0;
 	DEBUG("Compute traces\n");
@@ -538,6 +212,8 @@ int main(int argc, char *argv[])
 
 	qsort(distinct_invariants, nuniq, sizeof(struct result*), compare_result_by_slope);
 
+	gmp_fprintf(stdout, "\"s = %Qd = %.3f, q = %Qd, t = %.3f\"\n", s, mpq_get_d(s), q, mpq_get_d(q)*tqfactor);
+
 //	printf("- 0 0 - - - - 0.5\n");
 	int cumulative = 0;
 	double slope;
@@ -572,19 +248,6 @@ int main(int argc, char *argv[])
 	}
 //	printf("- 0 %d - - - - 2.0\n", cumulative);
 
-#ifdef OUTPUT_SUMMARY
-	fprintf(stdout, "%.3f %.3f %f %s\n", mpq_get_d(s), mpq_get_d(q)*tqfactor, max_slope, print_word(&group->elements[max_slope_index], buf));
-#endif
-
-//	output_invariants(group, matrices, s, q, solver);
-
-//	for(int i = 0; i < 10; i++) {
-//		mpq_set_ui(t,100+i,100);
-//		mpq_canonicalize(t);
-
-		//printf("%f %f\n", mpq_get_d(t), max_slope(group, matrices, s, t, &index));
-//	}
-
 	DEBUG("Clean up\n");
 	for(int i = 0; i < nmax; i++) {
 		mpq_clear(invariants[i].tr);
diff --git a/special_element.c b/special_element.c
index 84c382c..98c60b0 100644
--- a/special_element.c
+++ b/special_element.c
@@ -1,10 +1,7 @@
-
 #include "coxeter.h"
 #include "linalg.h"
 #include "mat.h"
-
-#include <gsl/gsl_poly.h>
-#include <mps/mps.h>
+#include "enumerate_triangle_group.h"
 
 #define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
 #define DEBUG(msg, ...)
@@ -14,180 +11,30 @@
 #define HEIGHT 300
 #define IDX(i,j) (((i)-1)*HEIGHT + ((j)-1))
 
-int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues)
+double mpq_log(mpq_t m_op)
 {
-	mpq_t coeff1, coeff2, zero;
-	cplx_t *roots;
-	double radii[3];
-	double *radii_p[3];
-	mps_monomial_poly *poly;
-	mps_boolean errors;
-	int result = 0;
+	static double logB = log(ULONG_MAX);
 
-	mpq_inits(coeff1, coeff2, zero, NULL);
-	mpq_set(coeff1, trinv);
-	mpq_sub(coeff2, zero, tr);
+        // Undefined logs (should probably return NAN in second case?)
+	if (mpz_get_ui(mpq_numref(m_op)) == 0 || mpz_sgn(mpq_numref(m_op)) < 0)
+		return -INFINITY;
 
-	poly = mps_monomial_poly_new(solv, 3);
-	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);
+	// Log of numerator
+	double lognum = log(mpq_numref(m_op)->_mp_d[abs(mpq_numref(m_op)->_mp_size) - 1]);
+	lognum += (abs(mpq_numref(m_op)->_mp_size)-1) * logB;
 
-	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;
-		}
+	// Subtract log of denominator, if it exists
+	if (abs(mpq_denref(m_op)->_mp_size) > 0)
+	{
+		lognum -= log(mpq_denref(m_op)->_mp_d[abs(mpq_denref(m_op)->_mp_size)-1]);
+		lognum -= (abs(mpq_denref(m_op)->_mp_size)-1) * logB;
 	}
-
-	cplx_vfree(roots);
-	mpq_clears(coeff1, coeff2, zero, NULL);
-
-	return result;
-}
-
-// this version is only for the (4,4,4) group
-void initialize_triangle_generators(mat_workspace *ws, mat *gen, mpq_t m, mpq_t t)
-{
-	mpq_t s,sinv,q,x,y;
-	mpq_t zero, one, two;
-	mpq_t tmp;
-
-	mpq_inits(s,sinv,q,x,y,zero,one,two,tmp,NULL);
-	mpq_set_ui(zero, 0, 1);
-	mpq_set_ui(one, 1, 1);
-	mpq_set_ui(two, 2, 1);
-
-	// s = (1-m^2)/2m
-	mpq_mul(s, m, m);
-	mpq_sub(s, one, s);
-	mpq_div(s, s, m);
-	mpq_div(s, s, two);
-	mpq_div(sinv, one, s);
-
-	// q = (1+m^2)/(1-m^2) = 2/(1-m^2) - 1
-	mpq_mul(q, m, m);
-	mpq_sub(q, one, q);
-	mpq_div(q, two, q);
-	mpq_sub(q, q, one);
-
-	// x = -tq, y = -q/t
-	mpq_mul(x, q, t);
-	mpq_sub(x, zero, x);
-	mpq_div(y, q, t);
-	mpq_sub(y, zero, y);
-
-	// q^2 = xy = 1 + 1/s^2
-	// [         -s         s*y           0]
-	// [       -s*x s*x*y - 1/s           0]
-	// [       -s*y   s*y^2 - x           1]
-	LOOP(i,3) {
-		mat_zero(gen[i]);
-		mpq_sub(tmp, zero, s);
-		mat_set(gen[i%3], i%3, i%3, tmp);
-		mpq_mul(tmp, s, y);
-		mat_set(gen[i%3], i%3, (i+1)%3, tmp);
-		mpq_mul(tmp, s, x);
-		mpq_sub(tmp, zero, tmp);
-		mat_set(gen[i%3], (i+1)%3, i%3, tmp);
-		mpq_mul(tmp, s, x);
-		mpq_mul(tmp, tmp, y);
-		mpq_sub(tmp, tmp, sinv);
-		mat_set(gen[i%3], (i+1)%3, (i+1)%3, tmp);
-		mpq_mul(tmp, s, y);
-		mpq_sub(tmp, zero, tmp);
-		mat_set(gen[i%3], (i+2)%3, i%3, tmp);
-		mpq_mul(tmp, s, y);
-		mpq_mul(tmp, tmp, y);
-		mpq_sub(tmp, tmp, x);
-		mat_set(gen[i%3], (i+2)%3, (i+1)%3, tmp);
-		mat_set(gen[i%3], (i+2)%3, (i+2)%3, one);
-	}
-
-	LOOP(i,3) mat_pseudoinverse(ws, gen[i+3], gen[i]);
-
-	mpq_inits(s,sinv,q,x,y,zero,one,two,tmp,NULL);
-}
-
-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, mpq_t m, mpq_t t)
-{
-	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, m, t);
-
-	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;
-
-		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);
+	return lognum;
 }
 
 int main(int argc, char *argv[])
 {
-	mpq_t m, t, tmp;
-	double s;
+	mpq_t m, t, s, q, tmp, tmp2;
 	mat_workspace *ws;
 	mat gen[6];
 	mps_context *solver;
@@ -203,7 +50,7 @@ int main(int argc, char *argv[])
 
 	DEBUG("Allocate\n");
 
-	mpq_inits(m, t, tmp, tr, trinv, NULL);
+	mpq_inits(m, t, s, q, tmp, tmp2, tr, trinv, NULL);
 	ws = mat_workspace_init(3);
 	for(int i = 0; i < 6; i++)
 		mat_init(gen[i], 3);
@@ -218,15 +65,18 @@ int main(int argc, char *argv[])
 	mps_context_set_output_prec(solver, 20); // relative precision
 	mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
 
-	for(int i = STARTX; i <= WIDTH; i++) {
-		for(int j = 1; j <= HEIGHT; j++) {
-			for(int w = 1; w < argc; w++) {
-				mpq_set_ui(t, j, DENOMINATOR);
-				mpq_set_ui(m, i, DENOMINATOR); // 414/1000 ~ sqrt(2)-1 <-> s=1
-				s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m));
+	mpq_set_str(s, argv[1], 10);
+	mpq_set_str(q, argv[2], 10);
+
+//	for(int i = STARTX; i <= WIDTH; i++) {
+//		for(int j = 1; j <= HEIGHT; j++) {
+			for(int w = 3; w < argc; w++) {
+//				mpq_set_ui(t, j, DENOMINATOR);
+//				mpq_set_ui(m, i, DENOMINATOR); // 414/1000 ~ sqrt(2)-1 <-> s=1
+//				s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m));
 
 				DEBUG("Compute matrix\n");
-				initialize_triangle_generators(ws, gen, m, t);
+				initialize_triangle_generators(ws, gen, 6, 4, 3, s, q);
 
 				mat_identity(element);
 				mat_identity(inverse);
@@ -272,25 +122,39 @@ int main(int argc, char *argv[])
 
 				x = log(fabs(evs[0]));
 				y = -log(fabs(evs[2]));
-				slope = y/x > 1 ? y/x : x/y;
 
-				if(slope > max_slope[IDX(i,j)]) {
-					max_slope[IDX(i,j)] = slope;
-					max_slope_index[IDX(i,j)] = w;
+				if(x > DBL_MAX || y > DBL_MAX) {
+					mpq_abs(tmp, tr);
+					mpq_abs(tmp2, trinv);
+					slope = mpq_log(tmp)/mpq_log(tmp2);
+				} else {
+					slope = y/x;
 				}
 
+				if(slope < 1)
+					slope = 1/slope;
+
+
+//				if(slope > max_slope[IDX(i,j)]) {
+//					max_slope[IDX(i,j)] = slope;
+//					max_slope_index[IDX(i,j)] = w;
+//				}
+
 //	gmp_printf("%Qd %Qd %f %f %f\n", tr, trinv, x, y, y/x);
-//				gmp_printf("%.5f %.5f %.7f %.9f\n", mpq_get_d(t), mpq_get_d(m), s, slope);
+//				gmp_printf("%s %.5f %.5f %Qd %Qd %.9f %.9f %.9f\n", argv[w], mpq_get_d(s), mpq_get_d(q),
+//				           tr, trinv,
+//				           x, y, slope);
+				gmp_printf("%s %.9f\n", argv[w], slope);
 
 			}
 
-			printf("%.5f %.5f %d %.9f\n", (double)i/DENOMINATOR, (double)j/DENOMINATOR, max_slope_index[IDX(i,j)], max_slope[IDX(i,j)]);
+//			printf("%.5f %.5f %d %.9f\n", (double)i/DENOMINATOR, (double)j/DENOMINATOR, max_slope_index[IDX(i,j)], max_slope[IDX(i,j)]);
 			fflush(stdout);
-		}
-	}
+//		}
+//	}
 
 	DEBUG("Clean up\n");
-	mpq_clears(m, t, tmp, tr, trinv, NULL);
+	mpq_clears(m, t, s, q, tmp, tmp2, tr, trinv, NULL);
 	mat_workspace_clear(ws);
 	for(int i = 0; i < 6; i++)
 		mat_clear(gen[i]);