simplify image generation

remove unnecessary function qext_newtype()
add useful help text
2022-06-18 14:54:50 +02:00 · 2022-06-16 15:43:19 +02:00 · 2022-06-15 18:47:55 +02:00 · 2022-06-15 18:04:42 +02:00 · 2022-06-15 15:27:08 +02:00 · 2022-06-15 15:19:38 +02:00
44 changed files with 1032 additions and 52944 deletions
--- a/.gitignore
+++ b/.gitignore
@@ -1,17 +1,7 @@
 *.o
-triangle_group/singular_values
-.#*
-singular_values
-singular_values_mpi
-singular_values_barbot
-output/
-special_element
-max_slope_picture/generate
-convert
-billiard_words
-*.pnm
-*.png
-*.hi
+.\#*
+\#*\#
 gmon.out
-restart
 core
+output/
+complex_anosov
--- a/54
+++ b/54
@@ -1,50 +1,27 @@
-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=-O0 -g -D_DEBUG -DQEXT
 #SPECIAL_OPTIONS=-O3 -pg -g -funroll-loops -fno-inline
-#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -DQEXT
+SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -DQEXT
 #SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -mavx512f -mavx512cd -mavx512er -mavx512pf # KNL
 #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 complex_anosov.o mat.o coxeter.o enumerate.o generators.o qext.o -lgmp -lmps -lm

-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
--- a/complex_anosov.c
+++ b/complex_anosov.c
@@ -0,0 +1,311 @@
+#include "coxeter.h"
+#include "enumerate.h"
+#include "generators.h"
+#include "mat.h"
+#include "qext.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <string.h>
+#include <time.h>
+
+#define LOOP(i,n) for(int i = 0; i < (n); i++)
+#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
+//#define INFO(msg, ...) fprintf(stderr, "[%10.3f] " msg, runtime(), ##__VA_ARGS__)
+#define INFO(msg, ...)
+
+/*
+  Number of elements
+  up to length 0:        1
+  up to length 1:        4
+  up to length 2:       10
+  up to length 3:       22
+  up to length 4:       46
+  up to length 5:       91
+  up to length 6:      175
+  up to length 7:      334
+  up to length 8:      634
+  up to length 9:     1198
+  up to length 10:    2260
+  up to length 11:    4261
+  up to length 12:    8029
+  up to length 13:   15124
+  up to length 14:   28486
+  up to length 15:   53650
+  up to length 16:  101038
+  up to length 17:  190279
+  up to length 18:  358339
+  up to length 19:  674830
+  up to length 20: 1270846
+  up to length 21: 2393266
+  up to length 22: 4507012
+  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;
+}
+
+static int read_idlist(const char *filename, int *list)
+{
+	FILE *f = fopen(filename, "r");
+	if(f == NULL) {
+		fprintf(stderr, "Could not open %s\n", filename);
+		exit(1);
+	}
+
+    char *line = NULL;
+    size_t len = 0;
+    ssize_t read;
+    int n = 0;
+
+    while ((read = getline(&line, &len, f)) != -1)
+	    list[n++] = atoi(line);
+
+    if (line)
+        free(line);
+
+	fclose(f);
+
+	return n;
+}
+
+static int compare_int(const void *a, const void *b)
+{
+    const int *aa = a;
+    const int *bb = b;
+    return (*aa > *bb) - (*aa < *bb);
+}
+
+static double runtime()
+{
+	static struct timespec starttime;
+	static int started = 0;
+
+	if(!started) {
+		clock_gettime(CLOCK_MONOTONIC, &starttime);
+		started = 1;
+	}
+
+	struct timespec curtime;
+	double diff;
+	clock_gettime(CLOCK_MONOTONIC, &curtime);
+	return (curtime.tv_sec - starttime.tv_sec) + (curtime.tv_nsec - starttime.tv_nsec) / 1e9;
+}
+
+enum mode {
+	MODE_HELP,
+	MODE_EIGENVALUES,
+	MODE_SUMMARY,
+	MODE_TRACE_IDS
+};
+
+int main(int argc, char *argv[])
+{
+	char buf[100];
+	int mode;
+
+	runtime(); // start timer
+
+	// parse arguments
+	if(argc < 2 || strcmp(argv[1], "help") == 0)
+		mode = MODE_HELP;
+	else if(strcmp(argv[1], "evs") == 0)
+		mode = MODE_EIGENVALUES;
+	else if(strcmp(argv[1], "summary") == 0)
+		mode = MODE_SUMMARY;
+	else if(strcmp(argv[1], "trace_ids") == 0)
+		mode = MODE_TRACE_IDS;
+	else
+		mode = MODE_HELP;
+
+	if(mode == MODE_HELP) {
+		fprintf(stderr, "Usage: %s <help|evs|summary|trace_ids> [arguments]\n", argv[0]);
+		fprintf(stderr, "%s help                                          display this page\n", argv[0]);
+		fprintf(stderr, "%s evs       <n> <q1> <q2> <q3> <treal> <timag>  enumerate group and output unique (log) eigenvalue triples\n", argv[0]);
+		fprintf(stderr, "%s summary   <n> <q1> <q2> <q3> <treal> <timag>  only output max slope etc.\n", argv[0]);
+		fprintf(stderr, "%s trace_ids <n> <q1> <q2> <q3> <treal> <timag>  list of ids of unique traces\n", argv[0]);
+		fprintf(stderr, "\n");
+		fprintf(stderr, "This program computes the traces and inverse traces of the first n elements of a SL(3,C) representation of the\n");
+		fprintf(stderr, "triangle reflection group with corner orders (5,5,5). The representation is given by the parameters q1,q2,q3,\n");
+		fprintf(stderr, "treal, and timag. q1,q2,q3 can each be 1 or 2 and determine the connected component. (1,1,1) is Hitchin and\n");
+		fprintf(stderr, "(2,2,2) is Barbot. treal and timag are the components of the complex parameter and have to be given as rational\n");
+		fprintf(stderr, "numbers. If the environment variable IDLIST is set to a filename, a list of elements can be read from this file.\n");
+		fprintf(stderr, "Such a list can be precomputed with the \"trace_ids\" subcommand and speeds up the computation considerably.\n");
+		return 0;
+	}
+
+	if(argc < 8) {
+		fprintf(stderr, "Not enough arguments!\n");
+		return 0;
+	}
+
+	int n = atoi(argv[2]);
+	int nlist, nuniq;
+
+	int q[3];
+	mpq_t treal, timag;
+	q[0] = atoi(argv[3]);
+	q[1] = atoi(argv[4]);
+	q[2] = atoi(argv[5]);
+	mpq_inits(treal, timag, NULL);
+	mpq_set_str(treal, argv[6], 10);
+	mpq_set_str(timag, argv[7], 10);
+	mpq_canonicalize(treal);
+	mpq_canonicalize(timag);
+
+	// enumerate group
+	INFO("generate group\n");
+	group_t *group = coxeter_init_triangle(5, 5, 5, n);
+
+	// read list of elements we need to compute, or just fill it with all elements
+	INFO("prepare list\n");
+	int *idlist = malloc(n*sizeof(int));
+	char *id_file = getenv("IDLIST");
+	if(id_file != NULL) {
+		nlist = read_idlist(id_file, idlist);
+		// sort and symmetrize the list
+		qsort(idlist, nlist, sizeof(int), compare_int);
+		int ninverses = 0;
+		LOOP(i, nlist) {
+			int id = idlist[i];
+			int invid = group->elements[id].inverse->id;
+			if(!bsearch(&invid, idlist, nlist, sizeof(int), compare_int)) {
+				idlist[nlist+ninverses] = invid;
+				ninverses++;
+			}
+		}
+		nlist += ninverses;
+		qsort(idlist, nlist, sizeof(int), compare_int);
+	} else {
+		// just list all elements which have inverses
+		nlist = 0;
+		LOOP(i, n) {
+			if(group->elements[i].inverse)
+				idlist[nlist++] = i;
+		}
+	}
+
+	// get generator matrices
+	INFO("make generators\n");
+	mat gen[3];
+	LOOP(i, 3) mat_init(gen[i], 3, QT_GAUSS_SQRT5);
+	generators_triangle_reflection_group_555_complex(gen, q[0], q[1], q[2], treal, timag);
+
+	// compute the traces of all elements in idlist
+	INFO("enumerate traces\n");
+	struct tracedata *traces;
+	nuniq = enumerate_coxeter_group_traces(group, gen, &traces, idlist, nlist, 1);
+
+	// compute eigenvalues out of traces
+	INFO("compute eigenvalues\n");
+	mps_context *solver = mps_context_new();
+	mps_monomial_poly *poly = mps_monomial_poly_new(solver, 3);
+	mps_context_set_output_prec(solver, 20); // relative precision
+	mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
+
+	double ev_real[3], ev_imag[3], ev_abs2[3];
+	double max_slope = 0;
+	int max_slope_id = 0;
+
+	LOOP(i, nuniq) {
+		solve_characteristic_polynomial_d(solver, poly,
+		                                  gaussian_sqrt5_real(traces[i].tr),
+		                                  gaussian_sqrt5_imag(traces[i].tr),
+		                                  gaussian_sqrt5_real(traces[i].trinv),
+		                                  gaussian_sqrt5_imag(traces[i].trinv),
+		                                  ev_real, ev_imag);
+
+		LOOP(j, 3) ev_abs2[j] = ev_real[j]*ev_real[j] + ev_imag[j]*ev_imag[j];
+
+		if(fabs(ev_abs2[0]) < fabs(ev_abs2[1]))
+			SWAP(double, ev_abs2[0], ev_abs2[1]);
+		if(fabs(ev_abs2[1]) < fabs(ev_abs2[2]))
+			SWAP(double, ev_abs2[1], ev_abs2[2]);
+		if(fabs(ev_abs2[0]) < fabs(ev_abs2[1]))
+			SWAP(double, ev_abs2[0], ev_abs2[1]);
+
+		if(mode == MODE_TRACE_IDS) {
+			// we only want to record unordered pairs here
+			if(CMP(traces[i].tr, traces[i].trinv) >= 0)
+				printf("%d\n", traces[i].id);
+			continue;
+		}
+
+		if(log(ev_abs2[0]) < 1e-6) // we regard this as a finite order element
+			continue;
+
+		double slope = - log(ev_abs2[0]) / log(ev_abs2[2]);
+		if(slope > max_slope) {
+			max_slope = slope;
+			max_slope_id = traces[i].id;
+		}
+
+		if(mode == MODE_EIGENVALUES) {
+			printf("%d %f %f %f\n",
+			       traces[i].id, log(ev_abs2[0])/2, log(ev_abs2[1])/2, log(ev_abs2[2])/2);
+		}
+	}
+
+	// output summary
+	coxeter_snprint(buf, sizeof(buf), &group->elements[max_slope_id]);
+	if(mode == MODE_SUMMARY) {
+		gmp_fprintf(stdout, "%f %f %d %d %d %f %s\n", mpq_get_d(treal), mpq_get_d(timag), n, nlist, nuniq, max_slope, buf);
+	} else if(mode == MODE_EIGENVALUES) {
+		gmp_fprintf(stderr, "q = %.2f + i*%.2f\tn = %d\tnlist = %d\tnuniq = %d\tMaximal slope: %f at %s\n", mpq_get_d(treal), mpq_get_d(timag), n, nlist, nuniq, max_slope, buf);
+	} else if(mode == MODE_TRACE_IDS) {
+		gmp_fprintf(stderr, "q = %.2f + i*%.2f\tElements: %d\tTraces: %d\n", mpq_get_d(treal), mpq_get_d(timag), n, nuniq);
+	}
+
+	// clean up
+	INFO("clean up\n");
+//	mps_monomial_poly_free(solver, MPS_POLYNOMIAL(poly));
+	mps_context_free(solver);
+	enumerate_tracedata_clear(traces, nuniq);
+	free(idlist);
+	LOOP(i, 3) mat_clear(gen[i]);
+	coxeter_clear(group);
+	mpq_clears(treal, timag, NULL);
+
+	return 0;
+}
--- a/compute_picture.sh
+++ b/compute_picture.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+
+for i in $(seq -50 50); do
+	for j in $(seq 0 50); do
+		if [ $i -ne 0 ] || [ $j -ne 0 ]; then
+			IDLIST=output/idlist_13 ./complex_anosov summary 15124 1 1 1 $i/50 $j/50
+		fi
+	done
+done
--- a/coxeter.c
+++ b/coxeter.c
@@ -5,6 +5,8 @@
 #include "coxeter.h"

 #define LOOP(i,n) for(int i = 0; i < (n); i++)
+#define MIN(x,y) ((x) > (y) ? (y) : (x))
+#define MAX(x,y) ((x) > (y) ? (x) : (y))

 group_t *coxeter_init_triangle(int p, int q, int r, int nmax)
 {
@@ -185,3 +187,17 @@ void coxeter_clear(group_t *g)
 	free(g->lists);
 	free(g);
 }
+
+int coxeter_snprint(char *str, int buflen, groupelement_t *g)
+{
+	int n = MIN(g->length, buflen-1); // number of characters without null byte
+
+	str[n] = 0;
+	int i = n-1;
+	while(g->parent) {
+		str[i--] = 'a' + g->letter;
+		g = g->parent;
+	}
+
+	return n;
+}
--- a/coxeter.h
+++ b/coxeter.h
@@ -13,6 +13,7 @@ typedef struct _groupelement {
 	struct _groupelement *inverse;
 	struct _groupelement **left;
 	struct _groupelement **right;
+	struct _groupelement *conjugacy_class;
 } groupelement_t;

 typedef struct _group {
@@ -26,5 +27,6 @@ typedef struct _group {
 group_t *coxeter_init(int rank, int *coxeter_matrix, int nmax);
 group_t *coxeter_init_triangle(int p, int q, int r, int nmax);
 void coxeter_clear(group_t *g);
+int coxeter_snprint(char *str, int buflen, groupelement_t *g);

 #endif
--- a/enumerate.c
+++ b/enumerate.c
@@ -0,0 +1,231 @@
+#include "enumerate.h"
+
+#include <stdlib.h>
+
+#define LOOP(i,n) for(int i = 0; i < (n); i++)
+// #define INFO(msg, ...) fprintf(stderr, "[%10.3f] " msg, runtime(), ##__VA_ARGS__)
+#define INFO(msg, ...)
+
+static int compare_int(const void *a, const void *b)
+{
+    const int *aa = a;
+    const int *bb = b;
+    return (*aa > *bb) - (*aa < *bb);
+}
+
+static int index_in_list(const int *list, int n, int key)
+{
+	int *ptr = bsearch(&key, list, n, sizeof(int), compare_int);
+	if(ptr)
+		return ptr - list;
+	else
+		return -1;
+}
+
+// idlist is assumed to be sorted and symmetric
+void enumerate_coxeter_group(group_t *group, mat *gen, mat *matrices, const int *idlist, int nlist)
+{
+	TYPE type = GETTYPE(gen[0]->x[0]);
+	mat_workspace *ws;
+
+	// mark elements which we need to compute
+	int ncompute = 0;
+	LOOP(i, group->size) group->elements[i].need_to_compute = 0;
+	LOOP(i, nlist) {
+		groupelement_t *cur = &group->elements[idlist[i]];
+		while(cur && cur->need_to_compute == 0) {
+			cur->need_to_compute = 1;
+			ncompute++;
+			cur = cur->parent;
+		}
+	}
+	INFO("need to compute %d elements for %d elements in list\n", ncompute, nlist);
+
+	// compute them depth first
+	int maxlen = group->elements[group->size-1].length;
+
+	groupelement_t **stack = malloc((maxlen+1)*sizeof(groupelement_t));
+	int *letter_stack = malloc((maxlen+1)*sizeof(int));
+	mat *matrix_stack = malloc((maxlen+1)*sizeof(mat));
+	int level = 0;
+
+	LOOP(i, maxlen+1) mat_init(matrix_stack[i], 3, type);
+	ws = mat_workspace_init(3, type);
+
+	stack[0] = &group->elements[0];
+	mat_identity(matrix_stack[0]);
+	letter_stack[0] = 0;
+
+	while(level >= 0) {
+		int letter = letter_stack[level];
+		groupelement_t *next = stack[level]->left[letter];
+		if(next && next->length > level && next->need_to_compute) {
+			mat_multiply(ws, matrix_stack[level+1], gen[letter], matrix_stack[level]);
+			int id = next->id;
+			int listid = index_in_list(idlist, nlist, id);
+			if(listid != -1)
+				mat_copy(matrices[listid], matrix_stack[level+1]);
+			next->need_to_compute = 0;
+			stack[level+1] = next;
+			letter_stack[level+1] = 0;
+			level++;
+		} else {
+			letter = ++letter_stack[level];
+			while(letter >= group->rank) { // done with this level, go back down
+				level--;
+				if(level < 0)
+					break;
+				letter = ++letter_stack[level];
+			}
+		}
+	}
+
+	LOOP(i, maxlen+1) mat_clear(matrix_stack[i]);
+	mat_workspace_clear(ws);
+}
+
+static int compare_tracedata(const void *a_, const void *b_)
+{
+        int d = 0;
+
+        struct tracedata **a = (struct tracedata **)a_;
+        struct tracedata **b = (struct tracedata **)b_;
+
+        d = CMP((*a)->tr,(*b)->tr);
+        if(d == 0) {
+                d = CMP((*a)->trinv, (*b)->trinv);
+        }
+
+        return d;
+}
+
+static int compare_tracedata_id(const void *a, const void *b)
+{
+        int ida = (*(struct tracedata **)a)->id;
+        int idb = (*(struct tracedata **)b)->id;
+
+        return ida > idb ? 1 : ida < idb ? -1 : 0;
+}
+
+int enumerate_coxeter_group_traces(group_t *group, mat *gen, struct tracedata **traces_out, const int *idlist, int nlist, int unique)
+{
+	TYPE t = GETTYPE(gen[0]->x[0]);
+	int nuniq;
+
+	mat *matrices = malloc(nlist*sizeof(mat));
+	struct tracedata *traces = malloc(nlist*sizeof(struct tracedata));
+	struct tracedata **distinct_traces = malloc(nlist*sizeof(struct tracedata*));
+
+	LOOP(i, nlist) mat_init(matrices[i], 3, t);
+	enumerate_coxeter_group(group, gen, matrices, idlist, nlist);
+
+	LOOP(i, nlist) {
+		INIT(traces[i].tr, t);
+		INIT(traces[i].trinv, t);
+		int inv_id_in_list = index_in_list(idlist, nlist, group->elements[idlist[i]].inverse->id);
+		mat_trace(traces[i].tr, matrices[i]);
+		mat_trace(traces[i].trinv, matrices[inv_id_in_list]);
+		traces[i].id = idlist[i];
+		distinct_traces[i] = &traces[i];
+	}
+
+	if(unique) {
+		qsort(distinct_traces, nlist, sizeof(struct tracedata*), compare_tracedata);
+
+		nuniq = 0;
+		LOOP(i, nlist) {
+			if(i == 0 || compare_tracedata(&distinct_traces[i], &distinct_traces[nuniq-1]) != 0) {
+				distinct_traces[nuniq] = distinct_traces[i];
+				nuniq++;
+			} else {
+				int oldlength = group->elements[distinct_traces[nuniq-1]->id].length;
+				int newlength = group->elements[distinct_traces[i]->id].length;
+				if(newlength < oldlength)
+					distinct_traces[nuniq-1]->id = distinct_traces[i]->id;
+			}
+		}
+	} else {
+		nuniq = nlist;
+	}
+
+	qsort(distinct_traces, nuniq, sizeof(struct tracedata*), compare_tracedata_id);
+
+	struct tracedata *unique_traces = malloc(nuniq*sizeof(struct tracedata));
+	LOOP(i, nuniq) {
+		INIT(unique_traces[i].tr, t);
+		INIT(unique_traces[i].trinv, t);
+		SET(unique_traces[i].tr, distinct_traces[i]->tr);
+		SET(unique_traces[i].trinv, distinct_traces[i]->trinv);
+		unique_traces[i].id = distinct_traces[i]->id;
+	}
+
+	LOOP(i, nlist) mat_clear(matrices[i]);
+	LOOP(i, nlist) {
+		CLEAR(traces[i].tr);
+		CLEAR(traces[i].trinv);
+	}
+	free(matrices);
+	free(traces);
+	free(distinct_traces);
+
+	*traces_out = unique_traces;
+	return nuniq;
+}
+
+void enumerate_tracedata_clear(struct tracedata *traces, int n)
+{
+	LOOP(i, n) {
+		CLEAR(traces[i].tr);
+		CLEAR(traces[i].trinv);
+	}
+	free(traces);
+}
+
+// returns squares of absolute values
+int solve_characteristic_polynomial_d(mps_context *solv, mps_monomial_poly *poly, double tr_real, double tr_imag, double trinv_real, double trinv_imag, double *eigenvalues_real, double *eigenvalues_imag)
+{
+//        mpq_t coeff1, coeff2, zero;
+        cplx_t *roots;
+        double radii[3];
+        double *radii_p[3];
+        mps_boolean errors;
+        int result = 0;
+
+        /*
+        mpq_inits(coeff1, coeff2, zero, NULL);
+        mpq_set(coeff1, trinv);
+        mpq_sub(coeff2, zero, tr);
+        */
+
+        mps_monomial_poly_set_coefficient_d(solv, poly, 0, -1, 0);
+        mps_monomial_poly_set_coefficient_d(solv, poly, 1, trinv_real, trinv_imag);
+        mps_monomial_poly_set_coefficient_d(solv, poly, 2, -tr_real, -tr_imag);
+//        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_d(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_real[i] = cplx_Re(roots[i]);
+                        eigenvalues_imag[i] = cplx_Im(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;
+}
--- a/enumerate.h
+++ b/enumerate.h
@@ -0,0 +1,22 @@
+#ifndef ENUMERATE_H
+#define ENUMERATE_H
+
+#include "mat.h"
+#include "coxeter.h"
+
+#include <mps/mps.h>
+
+struct tracedata {
+	int id;
+	NUMBER tr;
+	NUMBER trinv;
+};
+
+void enumerate_coxeter_group(group_t *group, mat *gen, mat *matrices, const int *idlist, int nlist);
+int enumerate_coxeter_group_traces(group_t *group, mat *gen, struct tracedata **traces_out, const int *idlist, int nlist, int unique);
+
+void enumerate_tracedata_clear(struct tracedata *traces, int n);
+
+int solve_characteristic_polynomial_d(mps_context *solv, mps_monomial_poly *poly, double tr_real, double tr_imag, double trinv_real, double trinv_imag, double *eigenvalues_real, double *eigenvalues_imag);
+
+#endif
--- a/enumerate_triangle_group.c
+++ b/enumerate_triangle_group.c
@@ -1,335 +0,0 @@
-#include "enumerate_triangle_group.h"
-#include "linalg.h"
-
-int solve_characteristic_polynomial(mps_context *solv, mps_monomial_poly *poly, mpq_t tr, mpq_t trinv, double *eigenvalues)
-{
-	mpq_t coeff1, coeff2, zero;
-	cplx_t *roots;
-	double radii[3];
-	double *radii_p[3];
-	mps_boolean errors;
-	int result = 0;
-
-	mpq_inits(coeff1, coeff2, zero, NULL);
-	mpq_set(coeff1, trinv);
-	mpq_sub(coeff2, zero, tr);
-
-	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(NUMBER out, NUMBER in, int a, int b, int c, int d, int e)
-{
-	NUMBER tmp;
-	INIT(tmp, GETTYPE(in));
-
-	SET_INT(out, a);
-
-	MUL(out, out, in);
-	SET_INT(tmp, b);
-	ADD(out, out, tmp);
-
-	MUL(out, out, in);
-	SET_INT(tmp, c);
-	ADD(out, out, tmp);
-
-	MUL(out, out, in);
-	SET_INT(tmp, d);
-	ADD(out, out, tmp);
-
-	MUL(out, out, in);
-	SET_INT(tmp, e);
-	ADD(out, out, tmp);
-
-	CLEAR(tmp);
-}
-
-// discriminant of the polynomial z^3 - x z^2 + y z - 1
-// that is the function x^2 y^2 - 4 x^3 - 4 y^3 - 27 + 18 xy
-void discriminant(NUMBER out, NUMBER x, NUMBER y)
-{
-	TYPE type = GETTYPE(out);
-	NUMBER x2, x3, y2, y3, tmp;
-	INIT(x2, type);INIT(x3, type);INIT(y2, type);INIT(y3, type);INIT(tmp, type);
-
-	MUL(x2, x, x);
-	MUL(x3, x2, x);
-	MUL(y2, y, y);
-	MUL(y3, y2, y);
-
-	MUL(out, x2, y2);
-
-	SET_INT(tmp, -4);
-	MUL(tmp, tmp, x3);
-	ADD(out, out, tmp);
-
-	SET_INT(tmp, -4);
-	MUL(tmp, tmp, y3);
-	ADD(out, out, tmp);
-
-	SET_INT(tmp, -27);
-	ADD(out, out, tmp);
-
-	SET_INT(tmp, 18);
-	MUL(tmp, tmp, x);
-	MUL(tmp, tmp, y);
-	ADD(out, out, tmp);
-
-	CLEAR(x2);CLEAR(x3);CLEAR(y2);CLEAR(y3);CLEAR(tmp);
-}
-
-void generators_triangle_rotation_generic(mat *gen, NUMBER rho1, NUMBER rho2, NUMBER rho3, mpq_t s, mpq_t q)
-{
-	mat_workspace *ws;
-	mat r1,r2,r3;
-	NUMBER b1,c1,a2,c2,a3,b3;
-	TYPE type = GETTYPE(rho1);
-	mpq_t sinv, qinv;
-
-	ws = mat_workspace_init(3, type);
-	INIT(b1, type);INIT(c1, type);INIT(a2, type);INIT(c2, type);INIT(a3, type);INIT(b3, type);
-	mpq_init(sinv);
-	mpq_init(qinv);
-	mat_init(r1, 3, type);
-	mat_init(r2, 3, type);
-	mat_init(r3, 3, type);
-
-	// sinv = s^{-1}
-	mpq_inv(sinv, s);
-	mpq_inv(qinv, q);
-
-	// c1 = rho2 q, a2 = rho3 q, b3 = rho1 q, b1 = c2 = a3 = 1/q
-	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);
-
-	mat_zero(r1);
-	mat_zero(r2);
-	mat_zero(r3);
-	SET_INT(*mat_ref(r1, 0, 0), -1);
-	SET_INT(*mat_ref(r1, 1, 1), 1);
-	SET_INT(*mat_ref(r1, 2, 2), 1);
-	SET_INT(*mat_ref(r2, 0, 0), 1);
-	SET_INT(*mat_ref(r2, 1, 1), -1);
-	SET_INT(*mat_ref(r2, 2, 2), 1);
-	SET_INT(*mat_ref(r3, 0, 0), 1);
-	SET_INT(*mat_ref(r3, 1, 1), 1);
-	SET_INT(*mat_ref(r3, 2, 2), -1);
-
-	SET(*mat_ref(r1, 1, 0), b1);
-	SET(*mat_ref(r1, 2, 0), c1);
-	SET(*mat_ref(r2, 0, 1), a2);
-	SET(*mat_ref(r2, 2, 1), c2);
-	SET(*mat_ref(r3, 0, 2), a3);
-	SET(*mat_ref(r3, 1, 2), b3);
-
-	mat_zero(gen[0]);
-	mat_zero(gen[1]);
-	mat_zero(gen[2]);
-
-	// gen[0] = diag(1,s^{-1},s)
-	SET_INT(*mat_ref(gen[0], 0, 0), 1);
-	SET_Q  (*mat_ref(gen[0], 1, 1), sinv);
-	SET_Q  (*mat_ref(gen[0], 2, 2), s);
-
-	// gen[1] = diag(s,1,s^{-1})
-	SET_Q  (*mat_ref(gen[1], 0, 0), s);
-	SET_INT(*mat_ref(gen[1], 1, 1), 1);
-	SET_Q  (*mat_ref(gen[1], 2, 2), sinv);
-
-	// gen[2] = diag(s^{-1},s,1)
-	SET_Q  (*mat_ref(gen[2], 0, 0), sinv);
-	SET_Q  (*mat_ref(gen[2], 1, 1), s);
-	SET_INT(*mat_ref(gen[2], 2, 2), 1);
-
-	// gen[0] = r2 * gen[0] * r3
-	// gen[1] = r3 * gen[1] * r1
-	// gen[2] = r1 * gen[2] * r2
-	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);
-
-	// gen[3] = gen[0]^{-1}
-	// gen[4] = gen[1]^{-1}
-	// gen[5] = gen[2]^{-1}
-	mat_pseudoinverse(ws, gen[3], gen[0]);
-	mat_pseudoinverse(ws, gen[4], gen[1]);
-	mat_pseudoinverse(ws, gen[5], gen[2]);
-
-	mat_workspace_clear(ws);
-	CLEAR(b1);CLEAR(c1);CLEAR(a2);CLEAR(c2);CLEAR(a3);CLEAR(b3);
-	mpq_clear(sinv);
-	mpq_clear(qinv);
-	mat_clear(r1);
-	mat_clear(r2);
-	mat_clear(r3);
-}
-
-#ifdef QEXT_TRIVIAL
-// p1,p2,p3 are only allowed to be 2,3,4,6
-void generators_triangle_rotation_2346_rational(mat *gen, int p1, int p2, int p3, mpq_t s, mpq_t q)
-{
-	mpq_t rho1, rho2, rho3;
-	mpq_inits(rho1,rho2,rho3,NULL);
-
-	// rho_i = s^2 + 2s cos(2 pi / p_i) + 1
-	// coefficient 2 is the value for p=infinity, not sure if that would even work
-	quartic(rho1, s, 0, 0, 1, p1 == 2 ? -2 : p1 == 3 ? -1 : p1 == 4 ? 0 : p1 == 6 ? 1 : 2, 1);
-	quartic(rho2, s, 0, 0, 1, p2 == 2 ? -2 : p2 == 3 ? -1 : p2 == 4 ? 0 : p2 == 6 ? 1 : 2, 1);
-	quartic(rho3, s, 0, 0, 1, p3 == 2 ? -2 : p3 == 3 ? -1 : p3 == 4 ? 0 : p3 == 6 ? 1 : 2, 1);
-
-	generators_triangle_rotation_generic(gen, rho1, rho2, rho3, s, q);
-
-	mpq_clears(rho1,rho2,rho3,NULL);
-}
-#endif
-
-#ifdef QEXT
-void generators_triangle_rotation_555_barbot(mat *gen, mpq_t s_, mpq_t q_)
-{
-	NUMBER rho, c, one, s;
-	INIT(rho, QT_SQRT5);INIT(c, QT_SQRT5);INIT(one, QT_SQRT5);INIT(s, QT_SQRT5);
-
-	// c = - (1+sqrt(5))/2
-	mpq_set_si(c->a[0], -1, 2);
-	mpq_set_si(c->a[1], -1, 2);
-	SET_ONE(one);
-
-	SET_Q(s, s_);
-
-	// rho = s^2 + cs + 1
-	SET(rho, one);
-	MUL(rho, rho, s);
-	ADD(rho, rho, c);
-	MUL(rho, rho, s);
-	ADD(rho, rho, one);
-
-	generators_triangle_rotation_generic(gen, rho, rho, rho, s_, q_);
-
-	CLEAR(rho);CLEAR(c);CLEAR(one);CLEAR(s);
-}
-#endif
-
-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_triangle_rotation_subgroup(group_t *group, mat *gen, mat *matrices)
-{
-	mat_workspace *ws;
-	mat tmp;
-	char buf[100], buf2[100], buf3[100];
-
-	// allocate stuff
-	TYPE type = GETTYPE(gen[0]->x[0]);
-	ws = mat_workspace_init(3, type);
-	mat_init(tmp, 3, type);
-
-//	initialize_triangle_generators(ws, gen, p1, p2, p3, s, q);
-
-	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;
-		if(!group->elements[i].need_to_compute)
-			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
-	mat_clear(tmp);
-	mat_workspace_clear(ws);
-}
--- a/enumerate_triangle_group.h
+++ b/enumerate_triangle_group.h
@@ -1,30 +0,0 @@
-#ifndef ENUMERATE_TRIANGLE_GROUP_H
-#define ENUMERATE_TRIANGLE_GROUP_H
-
-#include "mat.h"
-#include "coxeter.h"
-
-#include <mps/mps.h>
-
-// rational only functions
-int solve_characteristic_polynomial(mps_context *solv, mps_monomial_poly *poly, mpq_t tr, mpq_t trinv, double *eigenvalues);
-void continued_fraction_approximation(mpq_t out, double in, int level);
-
-// generators
-void generators_triangle_rotation_generic(mat *gen, NUMBER rho1, NUMBER rho2, NUMBER rho3, mpq_t s, mpq_t q);
-
-#ifdef QEXT_TRIVIAL
-void generators_triangle_rotation_2346_rational(mat *gen, int p1, int p2, int p3, mpq_t s, mpq_t q);
-#endif
-
-#ifdef QEXT
-void generators_triangle_rotation_555_barbot(mat *gen, mpq_t s_, mpq_t q_);
-#endif
-
-// general functions
-void quartic(NUMBER out, NUMBER in, int a, int b, int c, int d, int e);
-void discriminant(NUMBER out, NUMBER x, NUMBER y);
-char *print_word(groupelement_t *g, char *str);
-void enumerate_triangle_rotation_subgroup(group_t *group, mat *gen, mat *matrices);
-
-#endif
--- a/generators.c
+++ b/generators.c
@@ -0,0 +1,148 @@
+#include "generators.h"
+#include "mat.h"
+
+#define LOOP(i,n) for(int i = 0; i < (n); i++)
+
+void generators_triangle_reflection_generic(mat *gen, NUMBER sqrho1, NUMBER sqrho2, NUMBER sqrho3, NUMBER t)
+{
+	NUMBER tmp;
+	NUMBER tinv;
+	TYPE type = GETTYPE(sqrho1);
+
+	INIT(tmp, type);
+	INIT(tinv, type);
+	INV(tinv, t);
+
+	LOOP(i, 3) {
+		mat_init(gen[i], 3, type);
+		mat_zero(gen[i]);
+		LOOP(j, 3) {
+			SET_INT(*mat_ref(gen[i], j, j), i == j ? 1 : -1);
+		}
+	}
+
+	MUL(tmp, t, sqrho1);
+	NEG(*mat_ref(gen[2], 1, 2), tmp);
+	NEG(*mat_ref(gen[0], 2, 0), sqrho2);
+	NEG(*mat_ref(gen[1], 0, 1), sqrho3);
+
+	MUL(tmp, tinv, sqrho1);
+	NEG(*mat_ref(gen[1], 2, 1), tmp);
+	NEG(*mat_ref(gen[2], 0, 2), sqrho2);
+	NEG(*mat_ref(gen[0], 1, 0), sqrho3);
+
+	CLEAR(tmp);
+	CLEAR(tinv);
+}
+
+// warning: this is not compatible anymore!
+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;
+		}
+	}
+
+	NUMBER param;
+	INIT(param, type);
+	SET_Q(param, t);
+
+	generators_triangle_reflection_generic(gen, rho[0], rho[1], rho[2], param);
+
+	LOOP(i, 3) CLEAR(rho[i]);
+	CLEAR(param);
+
+	return 1;
+}
+
+int generators_triangle_reflection_group_555_complex(mat *gen, int q1, int q2, int q3, mpq_t treal, mpq_t timag)
+{
+
+	int q[3] = {q1, q2, q3};
+
+	NUMBER sqrho[3];
+	LOOP(i, 3) INIT(sqrho[i], QT_GAUSS_SQRT5);
+
+	// compute sqrho1, sqrho2, sqrho3
+	LOOP(i, 3) {
+		if(q[i] == 1) {
+			// 2cos(pi/5) = 1/2 + 1/2*sqrt(5) = 1/2 + 7/12 a - 1/24 a^3
+			mpq_set_si(sqrho[i]->a[0], 1, 2);
+			mpq_set_si(sqrho[i]->a[1], 7, 12);
+			mpq_set_si(sqrho[i]->a[2], 0, 1);
+			mpq_set_si(sqrho[i]->a[3], -1, 24);
+		} else if(q[i] == 2) {
+			// 2cos(pi/5) = -1/2 + 1/2*sqrt(5)
+			mpq_set_si(sqrho[i]->a[0], -1, 2);
+			mpq_set_si(sqrho[i]->a[1], 7, 12);
+			mpq_set_si(sqrho[i]->a[2], 0, 1);
+			mpq_set_si(sqrho[i]->a[3], -1, 24);
+		} else {
+			return 0;
+		}
+	}
+
+	NUMBER param;
+	INIT(param, QT_GAUSS_SQRT5);
+	mpq_set(param->a[0], treal);
+	mpq_set_si(param->a[1], -1, 6);
+	mpq_mul(param->a[1], param->a[1], timag);
+	mpq_set_si(param->a[2], 0, 1);
+	mpq_set_si(param->a[3], 1, 12);
+	mpq_mul(param->a[3], param->a[3], timag);
+
+	generators_triangle_reflection_generic(gen, sqrho[0], sqrho[1], sqrho[2], param);
+
+	LOOP(i, 3) CLEAR(sqrho[i]);
+	CLEAR(param);
+
+	return 1;
+
+}
--- a/generators.h
+++ b/generators.h
@@ -0,0 +1,13 @@
+#ifndef GENERATORS_H
+#define GENERATORS_H
+
+#include "mat.h"
+
+void generators_triangle_reflection_generic(mat *gen, NUMBER rho1, NUMBER rho2, NUMBER rho3, NUMBER q);
+int generators_triangle_reflection_group(mat *gen, int p1, int p2, int p3, int q1, int q2, int q3, mpq_t q);
+
+#ifdef QEXT
+int generators_triangle_reflection_group_555_complex(mat *gen, int q1, int q2, int q3, mpq_t real, mpq_t imag);
+#endif
+
+#endif
--- a/make_picture.py
+++ b/make_picture.py
@@ -0,0 +1,45 @@
+#!/usr/bin/python
+
+import sys
+import math
+
+f = open(sys.argv[1])
+lines = [x.split() for x in f]
+f.close()
+
+res = int(sys.argv[2]) # pixel per unit
+
+data = {(round(float(l[0])*res), round(float(l[1])*res)) : float(l[5]) for l in lines}
+data[(0,0)] = 2.0
+
+xmin = min([p[0] for p in data.keys()])
+xmax = max([p[0] for p in data.keys()])
+ymin = min([p[1] for p in data.keys()])
+ymax = max([p[1] for p in data.keys()])
+yrange=max([-ymin,ymax])
+
+print("P3")
+print("{dx:d} {dy:d}".format(dx=xmax-xmin+1, dy=2*yrange+1))
+print("255")
+
+for i in range(-yrange,yrange+1):
+	for j in range(xmin,xmax+1):
+		x = j
+		y = i if i >= ymin and i <= ymax else -i
+
+		if not (x,y) in data:
+			value = 0
+		else:
+			value = data[(x,y)]-1
+
+		value = 0 if value < 0 else 1 if value > 1 else value
+
+		r = round(255*value**0.5)
+		g = round(255*(value)**3)
+		b = round(255*(math.sin(2*math.pi*value)))
+
+		r = 0 if r < 0 else 255 if r > 255 else r
+		g = 0 if g < 0 else 255 if g > 255 else g
+		b = 0 if b < 0 else 255 if b > 255 else b
+
+		print("%d %d %d" % (r,g,b))
--- a/mat.h
+++ b/mat.h
@@ -24,7 +24,8 @@
 #define SUB qext_sub
 #define NEG qext_neg
 #define MUL qext_mul
-// #define DIV qext_div
+#define DIV qext_div
+#define INV qext_inv
 #define CMP qext_cmp
 #define PRINT qext_print
 #define SNPRINT qext_snprint
@@ -46,6 +47,7 @@
 #define NEG mpq_neg
 #define MUL mpq_mul
 #define DIV mpq_div
+#define INV mpq_inv
 #define PRINT(x) gmp_printf("%Qd", x)
 #define SNPRINT(out, size, x) gmp_snprintf(out, size, "%Qd", x)
 #define TYPE int
--- a/output/max_slope_picture/colors
+++ b/output/max_slope_picture/colors
@@ -1,14 +0,0 @@
-#a6cee3
-#1f78b4
-#b2df8a
-#33a02c
-#fb9a99
-#e31a1c
-#fdbf6f
-#ff7f00
-#cab2d6
-#6a3d9a
-#ffff99
-#b15928
-#ffff00
-#00ffff
--- a/output/max_slope_picture/combine_images
+++ b/output/max_slope_picture/combine_images
@@ -1,6 +0,0 @@
-#!/bin/bash
-
-convert -size 100x99 canvas:black combined.png
-for a in partition_*.pnm; do
-	composite -compose plus combined.png $a combined.png
-done
--- a/output/max_slope_picture/generate.hs
+++ b/output/max_slope_picture/generate.hs
@@ -1,69 +0,0 @@
-import Text.Printf
-import System.Environment
-import System.Process
-import Data.List
-
-wordlist = ["abacabacbabcbacbcacbac", "abacbabcbacbac", "abacbabcbacbcacbac", "abacbacbacbacbacbacbac", "abacbacbacbacbac", "abacbacbac", "bacabacbabcbacbcacbcac", "bacabacbabcbacbcac", "baca", "bacbabcbacbcac", "bacbacbacbacbacbacbcac", "bacbacbacbacbcac", "bacbacbcac", "bacbac"]
-
-colors = [(0.651,0.808,0.890), (0.122,0.471,0.706), (0.698,0.875,0.541), (0.200,0.627,0.173), (0.984,0.604,0.600), (0.890,0.102,0.110), (0.992,0.749,0.435), (1.000,0.498,0.000), (0.792,0.698,0.839), (0.416,0.239,0.604), (1.000,1.000,0.600), (0.694,0.349,0.157), (1.000,1.000,0.000), (0.000,1.000,1.000)]
-
-main = sequence $ zipWith (generatePicture "result_20210419_221603.out") wordlist colors
-
-generatePicture :: String -> String -> (Double,Double,Double) -> IO ()
-generatePicture datafile word color = do
-  file1 <- readFile datafile
-  file2 <- readProcess "../special_element" [word] ""
-  let values1 = map (normalize.read.(!!4).words) (lines file1) :: [Double]
-  let values2 = map (normalize.read.(!!3).words) (lines file2) :: [Double]
-  let diff = zipWith (-) values1 values2
-  writeFile (printf "partition_%s.pnm" word) $ drawGrayscalePicture color diff
-  printf "Wrote partition_%s.pnm\n" word
-
-- kind of a failed experiment
-- supersample (width, height) to (factor*width - factor + 1, factor*height - factor + 1)
-- supersample :: Int -> Int -> Int -> [Double] -> [Double]
-- supersample width height factor orig = [pix x y | x <- [0..(width-1)*factor], y <- [0..(height-1)*factor]]
--     where
--       pix x y = xl*yl*a + xl*yr*b + xr*yl*c + xr*yr*d
--           where
--             x_ = x`div`factor
--             y_ = y`div`factor
--             xr = fromIntegral (x`mod`factor)/fromIntegral factor :: Double
--             xl = 1 - xr :: Double
--             yr = fromIntegral (y`mod`factor)/fromIntegral factor :: Double
--             yl = 1 - yr :: Double
--             aoffset = x_*height + y_
--             boffset = x_*height + y_+1
--             coffset = (x_+1)*height + y_
--             doffset = (x_+1)*height + y_+1
--             a = orig!!aoffset
--             b = if boffset < width*height then orig!!boffset else 0
--             c = if coffset < width*height then orig!!coffset else 0
--             d = if doffset < width*height then orig!!doffset else 0
-
-- xl*yl*a + xl*yr*b + xr*yl*c + xr*yr*d
-
-drawGrayscalePicture :: (Double,Double,Double) -> [Double] -> String
-drawGrayscalePicture (r,g,b) values = drawPicture 100 99 $ map color values
-    where
-      color x = (round (255*r*colorscale x), round (255*g*colorscale x), round (255*b*colorscale x))
-
-drawPicture :: Int -> Int -> [(Int,Int,Int)] -> String
-drawPicture w h values = printf "P3\n%d %d\n255\n%s" w h pixels
-    where
-      pixels = concat [printf "%d %d %d\n" r g b | (r,g,b) <- values] :: String
-
-normalize x = if x < 1 then 1/x else x
-
-readDataFile :: String -> IO [(String,Double)]
-readDataFile filename = do
-  f <- readFile filename
-  return $ map process $ map words $ lines f
-      where
-        process (x:y:_:_:z:rest) = (x++" "++y,read z)
-        normalize x = if x < 1 then 1/x else x
-
-colorscale :: Double -> Double
-colorscale x = if cs x < 0 then 1 else if cs x > 1 then 0 else 1 - cs x
-    where
-      cs x = 1e5*x
--- a/output/max_slope_picture/result_20210419_221603.out
+++ b/output/max_slope_picture/result_20210419_221603.out
--- a/output/max_slope_picture_billiards/generate.hs
+++ b/output/max_slope_picture_billiards/generate.hs
@@ -1,14 +0,0 @@
-- resize and convert image with
-- convert max_slope_billiards.pnm -scale 3000x max_slope_billiards.png
-
-import Text.Printf
-
-colors = [(0.651,0.808,0.890), (0.122,0.471,0.706), (0.698,0.875,0.541), (0.200,0.627,0.173), (0.984,0.604,0.600), (0.890,0.102,0.110), (0.992,0.749,0.435), (1.000,0.498,0.000), (0.792,0.698,0.839), (0.416,0.239,0.604), (1.000,1.000,0.600), (0.694,0.349,0.157), (1.000,1.000,0.000), (0.000,1.000,1.000)]
-col = map (\(r,g,b) -> (round $ r*255, round $ g*255, round $ b*255)) colors :: [(Int,Int,Int)]
-
-main = do
-  foo <- readFile "max_slopes_billiard"
-  let dat = map (read.(!!2).words) $ lines foo :: [Int]
-  writeFile "max_slope_billiards.pnm" $ header ++ unlines [printf "%d %d %d" r g b | p <- dat, let (r,g,b) = col !! (p `mod` 14)]
-      where
-        header = "P3\n300\n123\n255\n"
--- a/output/max_slope_picture_billiards/max_slope_highres.plt
+++ b/output/max_slope_picture_billiards/max_slope_highres.plt
@@ -1,15 +0,0 @@
-if(!exists("index")) index = 50
-
-set xrange [0:0.45]
-set yrange [0:1]
-set xyplane at 0
-#plot "max_slopes_billiard" using 1:2:($3 - 10*floor($3/10)) w p pt 7 ps 1.1 lc palette t ""
-plot "max_slopes_billiard" using 1:2:3 w p pt 7 ps 1.1 lc palette t ""
-#splot "max_slopes_billiard" using 1:2:3 w p pt 7 ps 0.3 t ""
-#plot "max_slopes_billiard" using 1:2:4 w p pt 7 ps 1.1 lc palette t ""
-
-pause 10
-#if(MOUSE_KEY == 60) index=index-1
-#if(MOUSE_KEY == 62) index=index+1
-#print MOUSE_KEY
-reread
--- a/output/max_slope_picture_billiards/max_slopes_billiard
+++ b/output/max_slope_picture_billiards/max_slopes_billiard
--- a/output/max_slope_picture_billiards/words
+++ b/output/max_slope_picture_billiards/words
@@ -1,132 +0,0 @@
-bcabca
-bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
-bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
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-baca
-
--- a/output/old/conewidth_5_6_7.png
+++ b/output/old/conewidth_5_6_7.png
--- a/parallel.c
+++ b/parallel.c
@@ -1,409 +0,0 @@
-#include "parallel.h"
-
-#include <mpi.h>
-#include <sys/stat.h>
-#include <sys/mman.h>
-#include <fcntl.h>
-#include <errno.h>
-#include <string.h>
-#include <unistd.h>
-#include <malloc.h>
-#include <stdlib.h>
-
-//#define DEBUG INFO
-#define DEBUG(msg, ...)
-#define INFO(msg, ...) fprintf(stderr, "[%003d%10.3f] " msg, mpi_rank(0), runtime(), ##__VA_ARGS__)
-//#define DEBUG(msg, ...) fprintf(stderr, "[   %10.3f] " msg, runtime(), ##__VA_ARGS__)
-//#define DEBUG_MPI(msg, node, ...) fprintf(stderr, "[%003d%10.3f] " msg, node, runtime(), ##__VA_ARGS__)
-#define DONE(x) *((int*)(x))
-
-enum message_tag {
-	PARALLEL_ORDER = 0,
-	PARALLEL_RESULT,
-	PARALLEL_SHUTDOWN,
-	PARALLEL_GLOBAL_DATA
-};
-
-struct timespec starttime;
-
-int mpi_rank(int activate_mpi)
-{
-	static int active = 0;
-	if(activate_mpi)
-		active = 1;
-
-	if(!active)
-		return 0;
-	else {
-		int rank;
-		MPI_Comm_rank(MPI_COMM_WORLD, &rank);
-		return rank;
-	}
-}
-
-void start_timer()
-{
-	clock_gettime(CLOCK_MONOTONIC, &starttime);
-}
-
-double runtime()
-{
-	struct timespec curtime;
-	double diff;
-	clock_gettime(CLOCK_MONOTONIC, &curtime);
-	return (curtime.tv_sec - starttime.tv_sec) + (curtime.tv_nsec - starttime.tv_nsec) / 1e9;
-}
-
-parallel_context *parallel_init()
-{
-	parallel_context *ctx = malloc(sizeof(parallel_context));
-
-	if(!getenv("OMPI_COMM_WORLD_SIZE")) {
-		ctx->mpi_mode = 0;
-		DEBUG("Running standalone.\n");
-		return ctx;
-	}
-
-	ctx->mpi_mode = 1;
-	int result = MPI_Init(NULL, NULL);
-	MPI_Comm_size(MPI_COMM_WORLD, &ctx->size);
-	MPI_Comm_rank(MPI_COMM_WORLD, &ctx->rank);
-	MPI_Get_processor_name(ctx->processor_name, &ctx->processor_name_len);
-
-	mpi_rank(1); // display the rank in debug output from now on
-
-	if(ctx->rank == 0)
-		DEBUG("Running in mpi mode, %d nodes.\n", ctx->size);
-
-	return ctx;
-}
-
-void parallel_destroy(parallel_context* ctx)
-{
-	if(ctx->mpi_mode) {
-		MPI_Type_free(&ctx->order_datatype);
-		MPI_Type_free(&ctx->result_datatype);
-		MPI_Finalize();
-	}
-
-	free(ctx);
-}
-
-void parallel_set_datasize_and_callbacks(parallel_context *ctx, parallel_callback_init init, parallel_callback_job job, parallel_callback_destroy destroy, int global_data_size, int node_data_size, int input_size, int output_size)
-{
-	ctx->init = init;
-	ctx->destroy = destroy;
-	ctx->job = job;
-	ctx->global_data_size = global_data_size;
-	ctx->node_data_size = node_data_size;
-	ctx->input_size = input_size;
-	ctx->output_size = output_size;
-
-	if(ctx->mpi_mode) {
-		// create a datatype for job orders, consisting of an integer (the job id) and a user-defined section
-		int order_blocklengths[2] = {1, input_size};
-		MPI_Aint order_displacements[2] = {0, sizeof(int)};
-		MPI_Datatype order_types[2] = {MPI_INT, MPI_BYTE};
-		MPI_Type_create_struct(2, order_blocklengths, order_displacements, order_types, &ctx->order_datatype);
-		MPI_Type_commit(&ctx->order_datatype);
-
-		int result_blocklengths[2] = {1, output_size};
-		MPI_Aint result_displacements[2] = {0, sizeof(int)};
-		MPI_Datatype result_types[2] = {MPI_INT, MPI_BYTE};
-		MPI_Type_create_struct(2, result_blocklengths, result_displacements, result_types, &ctx->result_datatype);
-		MPI_Type_commit(&ctx->result_datatype);
-	}
-}
-
-int parallel_job(parallel_context *ctx, const void *global_data, void *node_data, int block)
-{
-	MPI_Status status;
-	double jobtime;
-	void *input_and_job_nr = malloc(ctx->input_size + sizeof(int));
-	void *output_and_job_nr = malloc(ctx->output_size + sizeof(int));
-	void *input = input_and_job_nr + sizeof(int);
-	int *job_nr = (int *)input_and_job_nr;
-	void *output = output_and_job_nr + sizeof(int);
-	int *output_job_nr = (int *)output_and_job_nr;
-	int result = 0;
-	int message_present;
-
-	if(block) {
-		jobtime = -MPI_Wtime();
-		MPI_Probe(0, MPI_ANY_TAG, MPI_COMM_WORLD,
-		          &status);
-		jobtime += MPI_Wtime();
-
-		INFO("TIMING: Probe() took %f seconds\n", jobtime);
-		message_present = 1;
-	} else {
-		MPI_Iprobe(0, MPI_ANY_TAG, MPI_COMM_WORLD,
-		          &message_present, &status);
-	}
-
-//		DEBUG("Message received: source = %d, tag = %d\n", status.MPI_SOURCE, status.MPI_TAG);
-
-	if(message_present) {
-		if(status.MPI_TAG == PARALLEL_SHUTDOWN) {
-			DEBUG("Shutting down\n");
-			result = 1;
-		} else if(status.MPI_TAG == PARALLEL_ORDER) {
-			MPI_Recv(input_and_job_nr,
-			         1, ctx->order_datatype,
-			         0, PARALLEL_ORDER, MPI_COMM_WORLD,
-			         &status);
-
-			DEBUG("Working on job %d\n", *job_nr);
-
-			jobtime = -MPI_Wtime();
-
-			// do the actual work
-			ctx->job(global_data, node_data, input, output);
-
-			jobtime += MPI_Wtime();
-
-			INFO("TIMING: job %d took %f seconds\n", *job_nr, jobtime);
-
-			*output_job_nr = *job_nr;
-			jobtime = -MPI_Wtime();
-			MPI_Send(output_and_job_nr,
-			         1, ctx->result_datatype,
-			         0, PARALLEL_RESULT, MPI_COMM_WORLD);
-			jobtime += MPI_Wtime();
-
-			INFO("TIMING: Send() took %f seconds\n", jobtime);
-		}
-	} else {
-		result = 2;
-	}
-
-	free(input_and_job_nr);
-	free(output_and_job_nr);
-
-	return result;
-}
-
-int parallel_work(parallel_context *ctx)
-{
-	// do nothing in non-mpi mode
-	if(ctx->mpi_mode == 0)
-		return 0;
-
-	void *global_data = malloc(ctx->global_data_size);
-	void *node_data = malloc(ctx->node_data_size);
-
-	// wait for global data
-	MPI_Bcast(global_data, ctx->global_data_size, MPI_BYTE, 0, MPI_COMM_WORLD);
-
-	DEBUG("Global data received\n");
-
-	// initialize node_data (and do once-per-node computation)
-	ctx->init(global_data, node_data);
-
-	DEBUG("Initialization completed\n");
-
-	int shutdown = 0;
-	while(shutdown != 1) {
-		shutdown = parallel_job(ctx, global_data, node_data, 1);
-	}
-
-	ctx->destroy(global_data, node_data);
-
-	free(global_data);
-	free(node_data);
-
-	return 0;
-}
-
-int parallel_run(parallel_context *ctx, const void *global_data, const void *input_array, void *output_array, unsigned int njobs, const char *_restart_filename)
-{
-	// in non-mpi-mode, just run init, forall(jobs) job
-	if(ctx->mpi_mode == 0) {
-		void *node_data = malloc(ctx->node_data_size);
-		int result = ctx->init(global_data, node_data);
-		if(result != 0)
-			goto cleanup_standalone;
-
-		for(int i = 0; i < njobs; i++) {
-			result = ctx->job(
-				global_data,
-				node_data,
-				input_array + ctx->input_size*i,
-				output_array + ctx->output_size*i);
-			if(result != 0)
-				goto cleanup_standalone;
-		}
-
-	cleanup_standalone:
-		ctx->destroy(global_data, node_data);
-		return result;
-	} else {
-		// if no restart file was specified, pick a filename
-		char *restart_filename;
-		char buffer[128];
-		int restartf;
-		if(_restart_filename == NULL) {
-			time_t t = time(NULL);
-			struct tm *loctm = localtime(&t);
-			strftime(buffer, sizeof(buffer), "restart/restart_%y%m%d_%H%M%S", loctm);
-			restart_filename = buffer;
-		} else {
-			restart_filename = (char *)_restart_filename;
-		}
-
-		// open restart file if it exists, otherwise create it
-		int continuing = 1;
-		restartf = open(restart_filename, O_RDWR);
-		if(restartf == -1 && errno == ENOENT) {
-			restartf = open(restart_filename, O_RDWR | O_CREAT, 0666);
-			continuing = 0;
-		}
-		if(restartf == -1) {
-			DEBUG("Error opening restart file: %s\n", strerror(errno));
-			exit(1);
-		}
-
-		// map restart file
-		int itemsize = (ctx->output_size + sizeof(int)); // for every job, store output, and completed flag
-		ftruncate(restartf, njobs*itemsize);
-		void *alljobs = mmap(0, njobs*itemsize, PROT_READ | PROT_WRITE, MAP_SHARED, restartf, 0);
-		if(alljobs == MAP_FAILED) {
-			DEBUG("Error mapping restart file: %s\n", strerror(errno));
-			exit(1);
-		}
-
-		// count completed jobs, or initialize jobs
-		int completed = 0;
-		if(continuing) {
-			for(int i = 0; i < njobs; i++)
-				if(DONE(alljobs + i*itemsize))
-					completed++;
-		} else {
-			for(int i = 0; i < njobs; i++) {
-				DONE(alljobs + i*itemsize) = 0;
-				memcpy(alljobs + i*itemsize + sizeof(int), input_array + i*ctx->input_size, ctx->input_size); // copy input data
-			}
-		}
-
-		fsync(restartf);
-
-		if(continuing) {
-			INFO("Continuing from restart file, %d/%d jobs completed, %d nodes\n", completed, njobs, ctx->size);
-		} else {
-			INFO("Starting from scratch, %d jobs, %d nodes\n", njobs, ctx->size);
-		}
-
-		if(completed >= njobs)
-			goto cleanup_mpi;
-
-		/* Send global data */
-		MPI_Bcast((void*)global_data, ctx->global_data_size, MPI_BYTE, 0, MPI_COMM_WORLD);
-
-		DEBUG("Global data sent\n");
-
-		// we want to be able to run jobs ourselves, so initialize node_data
-		void *node_data = malloc(ctx->node_data_size);
-		ctx->init(global_data, node_data);
-
-		void *input_message_buffer = malloc(ctx->input_size + sizeof(int));
-		void *output_message_buffer = malloc(ctx->output_size + sizeof(int));
-		int *active_jobs = malloc(sizeof(int)*ctx->size);
-		memset(active_jobs, 0, ctx->size*sizeof(int));
-		int active_worker_nodes = ctx->size - 1;  // we don't count ourselves, since we can't shut ourselves down
-
-		// find next unfinished job
-		int current = 0;
-		while(current < njobs && DONE(alljobs + current*itemsize))
-			current++;
-
-		// assign initial jobs, 2 for each worker thread
-		for(int i = 0; i < 2*ctx->size; i++) {
-			if(current >= njobs) // all jobs are assigned
-				break;
-
-			// send job id and input data
-			// send to all nodes except ourself (node 0)
-			*((int*)input_message_buffer) = current;
-			memcpy(input_message_buffer + sizeof(int), input_array + current*ctx->input_size, ctx->input_size);
-			MPI_Send(input_message_buffer, 1, ctx->order_datatype,
-			         i%ctx->size, PARALLEL_ORDER, MPI_COMM_WORLD);
-
-			DEBUG("Job %d sent to node %d\n", current, i%ctx->size);
-			active_jobs[i%ctx->size]++;
-			current++;
-		}
-
-		MPI_Status status;
-		int message_present;
-		while(active_jobs[0] != 0 || active_worker_nodes != 0) {
-			MPI_Iprobe(MPI_ANY_SOURCE, PARALLEL_RESULT, MPI_COMM_WORLD, &message_present, &status);
-			DEBUG("Message present, tag = %d, source = %d\n", status.MPI_TAG, status.MPI_SOURCE);
-			if(!message_present) {
-				// if there are no more messages to process, we can run a job ourselves before returning to managing
-				DEBUG("Start running job myself\n");
-				int result = parallel_job(ctx, global_data, node_data, 0);
-				DEBUG("Finished running job myself, result = %d\n");
-			} else if(status.MPI_TAG == PARALLEL_RESULT) {
-				MPI_Recv(output_message_buffer, 1, ctx->result_datatype,
-				         MPI_ANY_SOURCE, PARALLEL_RESULT, MPI_COMM_WORLD, &status);
-
-				DEBUG("Got message tag %d from node %d\n", status.MPI_TAG, status.MPI_SOURCE);
-
-				int node = status.MPI_SOURCE;
-				int id = *((int*)output_message_buffer);
-				memcpy(alljobs + id*itemsize + sizeof(int), output_message_buffer + sizeof(int), ctx->output_size);
-				DONE(alljobs + id*itemsize) = 1;
-				active_jobs[node]--;
-
-				// todo: deal with unresponsive nodes
-				// strategy: when no jobs left, go through unfinished list again, incrementing oversubscribe counter
-				// if oversubscribe counter is at limit, shut node down instead
-				//
-
-				if(current >= njobs) { // all jobs are assigned, try to shut down node
-					// don't try to shut down ourselves, and only if it has no other jobs to do
-					if(node != 0 && active_jobs[node] == 0) {
-						MPI_Send(NULL, 0, MPI_BYTE, node, PARALLEL_SHUTDOWN, MPI_COMM_WORLD);
-						active_worker_nodes--;
-						INFO("job %d completed by node %d, shut down, %d workers remaining\n", id, node, active_worker_nodes);
-					}
-				} else {
-					*((int*)input_message_buffer) = current;
-					memcpy(input_message_buffer + sizeof(int), input_array + current*ctx->input_size, ctx->input_size);
-					MPI_Send(input_message_buffer, 1, ctx->order_datatype,
-					         node, PARALLEL_ORDER, MPI_COMM_WORLD);
-					active_jobs[node]++;
-					current++;
-
-					if(active_jobs[node] < 3) {
-						*((int*)input_message_buffer) = current;
-						memcpy(input_message_buffer + sizeof(int), input_array + current*ctx->input_size, ctx->input_size);
-						MPI_Send(input_message_buffer, 1, ctx->order_datatype,
-						          node, PARALLEL_ORDER, MPI_COMM_WORLD);
-						active_jobs[node]++;
-						current++;
-
-						INFO("job %d completed by node %d, continues with %d and %d\n", id, node, current-1, current-2);
-					} else {
-						INFO("job %d completed by node %d, continues with %d\n", id, node, current-1);
-					}
-				}
-			}
-		}
-
-		for(int i = 0; i < njobs; i++) {
-			memcpy(output_array + i*ctx->output_size, alljobs + i*itemsize + sizeof(int), ctx->output_size);
-		}
-
-		free(input_message_buffer);
-		free(output_message_buffer);
-		free(node_data);
-		free(active_jobs);
-
-	cleanup_mpi:
-		munmap(alljobs, njobs*itemsize);
-		close(restartf);
-	}
-
-	return 0;
-}
--- a/parallel.h
+++ b/parallel.h
@@ -1,118 +0,0 @@
-#ifndef PARALLEL_H
-#define PARALLEL_H
-
-/*
-  this is a library to parallelize workloads which can be split up naturally
-  into a sequence of independent jobs, using MPI. A program will usually
-
-  - do precomputation
-  - fill array with input data
-  - do the parallel work
-  - print the output data
-
-  we want to enable restarts, so that only unfinshed jobs need to be repeated.
-  Further, we want to be resilient to slow/unreliable network and to losing
-  nodes. There is a main node and a number of workers. The main node does the
-  precomputation and then retires do do administrative work, and the workers
-  do the actual jobs. We also want to switch to serial mode if the program is
-  called without MPI.
-
-  The following data has to be transimitted between nodes:
-  - results of the precomputation (read-only, shared between nodes)
-  - job-specific input data, generated by main node before parallel part
-  - output data for each job
-
-  the parallel work shall be given as a callback function which takes
-  input data and precomputation data as parameter
-
-  the above program will look like this for us:
-
-  - parallel_init
-  - if we are a worker, do parallel_work(init_callback, job_callback), exit
-  - do precomputation
-  - fill array with input data
-  - output_array = parallel_run(input_array)
-  - print the output data
-
-  parallel_init:
-    - check if we're running as an mpi program
-    - init mpi, check what kind of node we are
-
-  parallel_work(init_callback1, init_callback2, job_callback):
-    - receive global_precomp (???)
-    - worker_precomp = init_callback2(global_precomp, worker_precomp)
-    - infinite loop:
-      - wait for job on network, receive input
-      - output = job_callback(global_precomp, worker_precomp, input)
-      - send output on network
-      - exit loop on shutdown signal
-
-  parallel_run(global_precomp, input_array, restart file, callbacks):
-    - check if we're running as an MPI program
-    - send global_precomp to all nodes (if MPI)
-    - if(restart file given and exists) read restart file
-    - else create new restart file
-    - until(all jobs finished):
-      - if MPI:
-        - send next job & input to appropriate node
-        - if all jobs are in work, reassign unfinished ones (up to limit)
-        - collect outputs
-      - if no MPI:
-        - worker_precomp = init_callback1
-        - worker_precomp = init_callback2(global_precomp, worker_precomp)
-        - for(j in jobs)
-          - output(j) = job_callback(global_precomp, worker_precomp, input(j))
-    - delete restart file
-    - return array of outputs
-
-    parallel_destroy():
-    - free everything
-
-    have a context? probably yes: parallel_context
-
-    plan:
-    - make interface
-    - implement no-MPI part
-    - restructure singular_values.c to use interface
-    - implement MPI part
-*/
-
-#include <mpi.h>
-#include <time.h>
-
-typedef void (*parallel_callback_destroy)(const void*, void*);
-typedef int (*parallel_callback_init)(const void*,void*);
-typedef int (*parallel_callback_job)(const void*,void*,const void*,void*);
-
-typedef struct {
-	int mpi_mode;
-	struct timespec starttime;
-	char processor_name[MPI_MAX_PROCESSOR_NAME];
-	int processor_name_len;
-	int rank;
-	int size;
-	MPI_Datatype order_datatype;
-	MPI_Datatype result_datatype;
-	parallel_callback_init init;
-	parallel_callback_job job;
-	parallel_callback_destroy destroy;
-	void *global_data;
-	void *node_data;
-	int global_data_size;
-	int node_data_size;
-	int input_size;
-	int output_size;
-} parallel_context;
-
-parallel_context *parallel_init();
-void parallel_set_datasize_and_callbacks(parallel_context *ctx, parallel_callback_init init, parallel_callback_job job, parallel_callback_destroy destroy, int global_data_size, int node_data_size, int input_size, int output_size);
-int parallel_work(parallel_context *ctx);
-int parallel_run(parallel_context *ctx, const void *global_data, const void *input_array, void *output_array, unsigned int njobs, const char *restart_filename);
-void parallel_destroy(parallel_context* ctx);
-
-int mpi_rank();
-void start_timer();
-double runtime();
-
-
-#endif
--- a/parallelization/allhosts
+++ b/parallelization/allhosts
@@ -1,135 +0,0 @@
-
-
-euler.ma.utexas.edu
-fac1.ma.utexas.edu
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--- a/parallelization/check_hostfile
+++ b/parallelization/check_hostfile
@@ -0,0 +1,6 @@
+#!/bin/bash
+
+for a in $(cat $1 | egrep -o '^[^ ]*'); do
+	echo -n "$a "
+	ssh -o ConnectTimeout=5 $a "cat /proc/cpuinfo | egrep '^processor' | wc -l"
+done
--- a/parallelization/generate_commands.py
+++ b/parallelization/generate_commands.py
@@ -0,0 +1,19 @@
+#!/usr/bin/python
+
+wordlength = 16
+n = 101038
+res = 200
+radius = 1
+q = [1,1,1]
+
+denom = round(res/radius)
+
+cmd = "IDLIST=idlist_{len} ../complex_anosov summary {n} {q1} {q2} {q3} {rnum}/{rden} {inum}/{iden}"
+
+for i in range(-res,res+1):
+	for j in range(0,res+1):
+		if i == 0 and j == 0:
+			continue
+		print(cmd.format(
+			len=wordlength, n=n, q1=q[0], q2=q[1], q3=q[2],
+			rnum=i, inum=j, rden=denom, iden=denom))
--- a/parallelization/hostfile
+++ b/parallelization/hostfile
@@ -1,5 +0,0 @@
-linux50 slots=4
-linux52 slots=4
-linux57 slots=4
-linux110 slots=4
-linux115 slots=4
--- a/parallelization/hostfile_big
+++ b/parallelization/hostfile_big
@@ -1,48 +0,0 @@
-linux100 slots=4
-linux104 slots=4
-linux110 slots=4
-linux122 slots=4
-linux149 slots=4
-linux14 slots=4
-linux15 slots=2
-linux16 slots=4
-linux17 slots=2
-linux180 slots=4
-linux181 slots=2
-linux184 slots=4
-linux18 slots=4
-linux20 slots=4
-linux21 slots=4
-linux24 slots=4
-linux27 slots=4
-linux29 slots=4
-linux2 slots=4
-linux30 slots=4
-linux31 slots=4
-linux32 slots=4
-linux38 slots=2
-linux40 slots=4
-linux41 slots=4
-linux46 slots=4
-linux4 slots=4
-linux50 slots=4
-linux52 slots=4
-linux54 slots=4
-linux57 slots=4
-linux62 slots=2
-linux64 slots=4
-linux68 slots=4
-linux69 slots=4
-linux70 slots=4
-linux71 slots=4
-linux72 slots=4
-linux74 slots=4
-linux76 slots=4
-linux79 slots=4
-linux80 slots=4
-linux83 slots=4
-linux86 slots=4
-linux91 slots=4
-linux92 slots=4
-linux96 slots=4
-linux9 slots=2
--- a/parallelization/instructions
+++ b/parallelization/instructions
@@ -0,0 +1,19 @@
+instructions to run in parallel on a cluster:
+
+the hostfile should look like this:
+host1 slots=2
+host2 slots=4
+host3 slots=4
+host4 slots=8
+...
+
+- git clone
+- fix dependencies
+- compile
+- ./generate_commands.py > commands
+- get hostfile
+- check hostfile, delete entries which don't work
+- get idlist
+- ./sync
+- delete old result and done files
+- execute ./run on server
--- a/parallelization/localnames
+++ b/parallelization/localnames
@@ -1,51 +0,0 @@
-linux100
-linux104
-linux110
-linux115
-linux122
-linux149
-linux14
-linux15
-linux164
-linux169
-linux16
-linux17
-linux180
-linux181
-linux184
-linux18
-linux20
-linux21
-linux24
-linux27
-linux29
-linux2
-linux30
-linux31
-linux32
-linux38
-linux40
-linux41
-linux46
-linux4
-linux50
-linux52
-linux54
-linux57
-linux62
-linux64
-linux68
-linux69
-linux70
-linux71
-linux72
-linux74
-linux76
-linux79
-linux80
-linux83
-linux86
-linux91
-linux92
-linux96
-linux9
--- a/parallelization/run
+++ b/parallelization/run
@@ -0,0 +1,7 @@
+#!/bin/bash
+
+cd /home/stecker/compute/triangle_reflection_complex/parallelization
+
+unset DISPLAY
+
+time mpirun -n 50 -x LD_LIBRARY_PATH=/home/stecker/compute/mps/lib --hostfile hostfile_big python3 runjobs.py
--- a/parallelization/run_local
+++ b/parallelization/run_local
@@ -1,9 +0,0 @@
-#!/bin/bash
-
-# nmax=895882 # up to reflection group word length 22 ( 555 group)
-nmax=700000 # up to reflection group word length 22 ( 444 group)
-# nmax=11575 # up to reflection group word length 14
-
-#time mpirun --mca opal_warn_on_missing_libcuda 0  -x LD_LIBRARY_PATH=/home/stecker/svmpi/libs ./singular_values $nmax ejp_trg_restart test.out
-
-time mpirun --mca opal_warn_on_missing_libcuda 0 --mca mpi_yield_when_idle 1 -np 4 ./singular_values 700000 4 4 4 1 1 100 1 100 100 $1
--- a/parallelization/run_utexas
+++ b/parallelization/run_utexas
@@ -1,14 +0,0 @@
-#!/bin/bash
-
-cd /home/stecker/svmpi/
-
-nmax=895882 # up to reflection group word length 22
-# nmax=11575 # up to reflection group word length 14
-
-outfile=result_$(date +%Y%m%d_%H%M%S).out
-
-
-unset DISPLAY
-
-make singular_values &&
-time mpirun -n 100 -x LD_LIBRARY_PATH=/home/stecker/svmpi/libs --hostfile hostfile_big ./singular_values $nmax utexas_cluster_restart $outfile
--- a/parallelization/runjobs.py
+++ b/parallelization/runjobs.py
@@ -0,0 +1,57 @@
+#!/usr/bin/python
+
+from mpi4py import MPI
+import os
+import re
+import math
+import subprocess
+import time
+
+comm = MPI.COMM_WORLD
+rank = comm.Get_rank()
+nodes = comm.Get_size()
+
+# print(os.path.abspath(os.curdir))
+
+done = set()
+for f in os.listdir('.'):
+	if re.search('^done_[0-9]+', f):
+		fp = open(f, "r")
+		for x in fp:
+			done.add(int(x))
+		fp.close()
+
+f = open("commands", "r")
+idx = 0
+todo = []
+for c in f:
+	if not idx in done:
+		todo.append((idx,c))
+	idx = idx+1
+f.close()
+
+start = math.floor(len(todo)/nodes*rank)
+end = math.floor(len(todo)/nodes*(rank+1))
+if(rank == nodes-1):
+	end = len(todo)
+
+print("{n:d} commands awaiting execution, {nnode:d} of them in node {rank:d}".format(n=len(todo),nnode=end-start,rank=rank))
+
+time.sleep(1) # to make sure all nodes read the status first before more gets done
+
+outfilename = "result_{node:003d}".format(node=rank)
+donefilename = "done_{node:003d}".format(node=rank)
+outfile = open(outfilename, "a")
+donefile = open(donefilename, "a")
+
+for i in range(start, end):
+	result = subprocess.call(todo[i][1], stdout=outfile, shell=True)
+	if result == 0:
+		donefile.write(str(todo[i][0]) + '\n')
+	else:
+		print("Command failed: {cmd}".format(cmd=todo[i][1]))
+	outfile.flush()
+	donefile.flush()
+
+outfile.close()
+donefile.close()
--- a/parallelization/stampede.slurm
+++ b/parallelization/stampede.slurm
@@ -1,20 +0,0 @@
-#!/bin/bash
-
-#SBATCH -J ejp_trg
-#SBATCH -o logs/ejp_trg.o%j
-#SBATCH -e logs/ejp_trg.e%j
-#SBATCH -p skx-dev
-#SBATCH -N 1
-#SBATCH -n 48
-#SBATCH -t 00:05:00
-#SBATCH --mail-user=mail@florianstecker.net
-#SBATCH --mail-type=all
-
-export LD_LIBRARY_PATH=$WORK/mps/lib:$LD_LIBRARY_PATH
-
-d=$(date +%Y%m%d_%H%M%S)
-
-nmax=895882 # up to reflection group word length 22
-# nmax=11575 # up to reflection group word length 1
-
-ibrun ./singular_values $nmax $SCRATCH/ejp_trg_restart $WORK/ejp_trg/output/result_$d
--- a/parallelization/sync
+++ b/parallelization/sync
@@ -0,0 +1,7 @@
+#!/bin/bash
+
+rsync -rvt * utexas:compute/triangle_reflection_complex/parallelization/
+#rsync -lvt /usr/lib/libmps.so* utexas:compute/mps/lib/
+#rsync -rvt /usr/include/mps utexas:compute/mps/include/
+
+# now run it with ssh utexas compute/triangle_reflection_complex/parallelization/run
--- a/parallelization/sync_stampede
+++ b/parallelization/sync_stampede
@@ -1,8 +0,0 @@
-#!/bin/bash
-
-rsync -vt *.c *.h Makefile stampede.slurm stampede:work/ejp_trg/
-#rsync -lvt /usr/lib/libmps.so* /usr/include/mps utexas:work/ejp_trg/libs/
-
-# now run it with a job script
-
-# get MPSolve from https://numpi.dm.unipi.it/_media/software/mpsolve/mpsolve-3.2.1.tar.bz2
--- a/parallelization/sync_utexas
+++ b/parallelization/sync_utexas
@@ -1,7 +0,0 @@
-#!/bin/bash
-
-rsync -vt *.c *.h Makefile hostfile hostfile_big allhosts localnames run_utexas run_local utexas:svmpi/
-rsync -lvt /usr/lib/libmps.so* utexas:svmpi/libs/
-rsync -rvt /usr/include/mps utexas:svmpi/libs/
-
-# now run it with ssh utexas -t ssh linux50 svmpi/run_utexas
--- a/qext.c
+++ b/qext.c
@@ -1,5 +1,7 @@
 #include "qext.h"

+#include <assert.h>
+
 int qext_rank;
 mpq_t *qext_coefficient;

@@ -9,13 +11,20 @@ mpq_t *qext_coefficient;
 #define LOOP(i,n) for(int i = 0; i < (n); i++)
 #define RANK(x) ((x)->type->rank)

-const int qext_type_trivial_coeffs[] = {-1, 1};
-struct qext_type qext_type_trivial_v = {1, qext_type_trivial_coeffs, NULL};
-struct qext_type *QT_TRIVIAL = &qext_type_trivial_v;
+struct qext_type *QT_TRIVIAL = &(struct qext_type) {
+	.rank = 1,
+	.integer_coeffs = (const int[]) {-1, 1}
+};

-const int qext_type_sqrt5_coeffs[] = {-5, 0, 1};
-struct qext_type qext_type_sqrt5_v = {2, qext_type_sqrt5_coeffs, NULL};
-struct qext_type *QT_SQRT5 = &qext_type_sqrt5_v;
+struct qext_type *QT_SQRT5 = &(struct qext_type) {
+	.rank = 2,
+	.integer_coeffs = (const int[]) {-5, 0, 1}
+};
+
+struct qext_type *QT_GAUSS_SQRT5 = &(struct qext_type) {
+	.rank = 4,
+	.integer_coeffs = (const int[]) {36, 0, -8, 0, 1}
+};

 static void qext_init_type(struct qext_type *type)
 {
@@ -28,16 +37,6 @@ static void qext_init_type(struct qext_type *type)
 	}
 }

-struct qext_type *qext_newtype(int rank, const int *coeffs)
-{
-	struct qext_type *type = malloc(sizeof(struct qext_type));
-	type->rank = rank;
-	type->integer_coeffs = coeffs;
-	qext_init_type(type);
-
-	return type;
-}
-
 void qext_init(qext_number x, struct qext_type *type)
 {
 	if(type->coeffs == NULL) // uninitialized default type
@@ -161,7 +160,86 @@ void qext_mul(qext_number out, qext_number x, qext_number y)
 	mpq_clear(tmp);
 }

+void qext_inv(qext_number out, qext_number in)
+{
+	qext_number one;
+	qext_init(one, in->type);
+	qext_set_int(one, 1);
+	qext_div(out, one, in);
+	qext_clear(one);
+}
+
 void qext_div(qext_number out, qext_number x, qext_number y)
 {
-	// todo: implement this by solving a linear system
+	int rk = RANK(x);
+	struct qext_type *type = x->type;
+
+	mpq_t tmp;
+	mpq_t result[rk];
+	mpq_t matrix[rk*rk];
+
+	mpq_init(tmp);
+	LOOP(i, rk) mpq_init(result[i]);
+	LOOP(i, rk*rk) mpq_init(matrix[i]);
+
+	// initialize a matrix which represents multiplication by y
+	// that means the i-th column is y*a^i
+	LOOP(i, rk)
+		mpq_set(matrix[i*rk], y->a[i]);
+	LOOP(j, rk-1) { // columns
+		mpq_mul(matrix[j+1], matrix[(rk-1)*rk+j], type->coeffs[0]);
+		LOOP(i, rk-1) { // rows
+			mpq_mul(matrix[(i+1)*rk+(j+1)], matrix[(rk-1)*rk+j], type->coeffs[i+1]);
+			mpq_add(matrix[(i+1)*rk+(j+1)], matrix[(i+1)*rk+(j+1)], matrix[i*rk+j]);
+		}
+	}
+
+	// initialize result as x
+	LOOP(i, rk) mpq_set(result[i], x->a[i]);
+
+	// use Gaussian elimination to solve the system matrix * out = result
+	LOOP(j, rk)
+	{
+		// find nonzero entry
+		int row = j;
+		while(row < rk && mpq_sgn(matrix[row*rk+j]) == 0) row++;
+
+		// if the entire column is zero, the matrix was not invertible
+		// this could happen if the polynomial is not irreducible / we're not in a field
+		assert(row != rk);
+
+		// permute rows
+		if(row != j) {
+			mpq_swap(result[row], result[j]);
+			LOOP(k, rk) {
+				mpq_swap(matrix[row*rk+k], matrix[j*rk+k]);
+			}
+		}
+
+		// normalize
+		LOOP(k, rk)
+			if(k != j)
+				mpq_div(matrix[j*rk+k], matrix[j*rk+k], matrix[j*rk+j]);
+		mpq_div(result[j], result[j], matrix[j*rk+j]);
+		mpq_set_ui(matrix[j*rk+j], 1, 1);
+
+		// subtract
+		LOOP(i, rk) {
+			if(i == j)
+				continue;
+			mpq_mul(tmp, matrix[i*rk+j], result[j]);
+			mpq_sub(result[i], result[i], tmp);
+			for(int k = j+1; k < rk; k++) {
+				mpq_mul(tmp, matrix[i*rk+j], matrix[j*rk+k]);
+				mpq_sub(matrix[i*rk+k], matrix[i*rk+k], tmp);
+			}
+			mpq_set_ui(matrix[i*rk+j], 0, 1); // it isn't strictly necessary to do this as we won't use this entry again, but helps debugging
+		}
+	}
+
+	LOOP(i, rk) mpq_set(out->a[i], result[i]);
+
+	mpq_clear(tmp);
+	LOOP(i, rk) mpq_clear(result[i]);
+	LOOP(i, rk*rk) mpq_clear(matrix[i]);
 }
--- a/qext.h
+++ b/qext.h
@@ -5,8 +5,8 @@

 struct qext_type {
 	int rank;
-	const int *integer_coeffs;
-	mpq_t *coeffs;
+	const int *integer_coeffs;  // actually the rank+1 coefficients of the polynomial
+	mpq_t *coeffs;  // components of a^rank
 };

 struct qext_number_internal {
@@ -18,8 +18,8 @@ typedef struct qext_number_internal qext_number[1];

 extern struct qext_type *QT_TRIVIAL;
 extern struct qext_type *QT_SQRT5;
+extern struct qext_type *QT_GAUSS_SQRT5;

-struct qext_type *qext_newtype(int rank, const int *coeffs);
 void qext_init(qext_number x, struct qext_type *type);
 void qext_clear(qext_number x);
 void qext_set(qext_number x, qext_number y);
@@ -29,6 +29,7 @@ void qext_add(qext_number result, qext_number x, qext_number y);
 void qext_sub(qext_number result, qext_number x, qext_number y);
 void qext_neg(qext_number result, qext_number x);
 void qext_mul(qext_number out, qext_number x, qext_number y);
+void qext_inv(qext_number out, qext_number in);
 void qext_div(qext_number out, qext_number x, qext_number y);
 int qext_cmp(qext_number x, qext_number y);
 void qext_print(qext_number x);
--- a/singular_values.c
+++ b/singular_values.c
@@ -1,471 +0,0 @@
-#include "coxeter.h"
-#include "linalg.h"
-#include "mat.h"
-#include "enumerate_triangle_group.h"
-#include "parallel.h"
-
-#include <time.h>
-
-#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
-
-//#define DEBUG(msg, ...) fprintf(stderr, "[%003d%10.3f] " msg, mpi_rank(0), runtime(), ##__VA_ARGS__)
-#define DEBUG(msg, ...)
-#define INFO(msg, ...) fprintf(stderr, "[%003d%10.3f] " msg, mpi_rank(0), runtime(), ##__VA_ARGS__)
-
-struct result {
-	int id;
-	mpq_t tr;
-	mpq_t trinv;
-	double x;
-	double y;
-	double slope;
-};
-
-// we want as much as possible to be node data, except if it is only known to the main node
-// (command line arguments) or should only be computed once (id list)
-
-struct global_data {
-	// command line arguments
-	unsigned int nmax;
-	unsigned int p1, p2, p3;
-	unsigned int sstart, send, sdenom;
-	unsigned int qstart, qend, qdenom;
-
-	unsigned int *id_list;
-	unsigned int id_list_length;
-};
-
-struct node_data {
-	group_t *group;
-	mat* matrices;
-	struct result *invariants;
-	struct result **distinct_invariants;
-	int distinct_invariants_length;
-	mps_context *solver;
-};
-
-struct input_data {
-	unsigned int snum, sden;
-	unsigned int qnum, qden;
-};
-
-struct output_data {
-	int max_slope_id;
-	double max_slope;
-};
-
-static int compare_result(const void *a_, const void *b_)
-{
-	int d = 0;
-
-	struct result **a = (struct result **)a_;
-	struct result **b = (struct result **)b_;
-
-	d = mpq_cmp((*a)->tr,(*b)->tr);
-	if(d == 0) {
-		d = mpq_cmp((*a)->trinv, (*b)->trinv);
-	}
-
-	return d;
-}
-
-static int compare_result_by_id(const void *a_, const void *b_)
-{
-	int d = 0;
-
-	struct result **a = (struct result **)a_;
-	struct result **b = (struct result **)b_;
-
-	return (*a)->id - (*b)->id;
-}
-
-static int compare_result_by_tr_trinv_id(const void *a_, const void *b_)
-{
-	int d = 0;
-
-	struct result **a = (struct result **)a_;
-	struct result **b = (struct result **)b_;
-
-	d = mpq_cmp((*a)->tr,(*b)->tr);
-	if(d == 0) {
-		d = mpq_cmp((*a)->trinv, (*b)->trinv);
-		if(d == 0) {
-			d = (*b)->id - (*a)->id;
-		}
-	}
-
-	return d;
-}
-
-static int compare_result_by_slope(const void *a_, const void *b_)
-{
-	int d = 0;
-
-	struct result **a = (struct result **)a_;
-	struct result **b = (struct result **)b_;
-
-	double slopea = (*a)->x / (*a)->y;
-	double slopeb = (*b)->x / (*b)->y;
-
-	return slopea > slopeb ? -1 : slopea < slopeb ? 1 : 0;
-}
-
-int compute_invariants(group_t *group, mat *matrices, struct result **invariants, int *n, int unique)
-{
-	mpq_t tmp;
-	mps_context *solver;
-	mps_monomial_poly *poly;
-	int index;
-	int ntraces = *n, nuniq;
-	int retval;
-	double evs[3];
-	char buf[100];
-
-//	DEBUG("Compute traces\n");
-	for(int i = 0; i < ntraces; i++) {
-		int id = invariants[i]->id;
-		int invid = group->elements[id].inverse->id;
-		mat_trace(invariants[i]->tr, matrices[id]);
-		mat_trace(invariants[i]->trinv, matrices[invid]);
-	}
-
-	if(!unique)
-		nuniq = ntraces;
-	else {
-//		DEBUG("Get unique traces\n");
-		qsort(invariants, ntraces, sizeof(struct result*), compare_result);
-
-		nuniq = 0;
-		for(int i = 0; i < ntraces; i++) {
-			if(i == 0 || compare_result(&invariants[i], &invariants[nuniq-1]) != 0) {
-				invariants[nuniq] = invariants[i];
-				nuniq++;
-			} else {
-				int oldlength = group->elements[invariants[nuniq-1]->id].length;
-				int newlength = group->elements[invariants[i]->id].length;
-				if(newlength < oldlength)
-					invariants[nuniq-1]->id = invariants[i]->id;
-			}
-		}
-	}
-
-	DEBUG("Solve characteristic polynomials\n");
-	solver = mps_context_new();
-	poly = mps_monomial_poly_new(solver, 3);
-	mps_context_set_output_prec(solver, 20); // relative precision
-	mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
-
-	for(int i = 0; i < nuniq; i++) {
-		retval = solve_characteristic_polynomial(solver, poly, invariants[i]->tr, invariants[i]->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]);
-
-		double x = log(fabs(evs[0]));
-		double y = -log(fabs(evs[2]));
-
-		invariants[i]->x = x;
-		invariants[i]->y = y;
-		invariants[i]->slope = y/x;
-	}
-	mps_context_free(solver);
-
-	qsort(invariants, nuniq, sizeof(struct result*), compare_result_by_id);
-
-	*n = nuniq;
-	return 0;
-}
-
-long check_memory_usage(mat *matrices, int n)
-{
-	mpq_t x;
-	long total;
-
-	for(int i = 0; i < n; i++)
-	{
-		LOOP(j,3) LOOP(k,3) {
-			total += mpq_numref(M(matrices[i], j, k))->_mp_size;
-			total += mpq_denref(M(matrices[i], j, k))->_mp_size;
-		}
-	}
-
-	return total;
-}
-
-
-void destroy_node(const void *_g, void *_n)
-{
-	struct global_data *g = (struct global_data *)_g;
-	struct node_data *n = (struct node_data *)_n;
-
-	for(int i = 0; i < g->nmax; i++) {
-		mpq_clear(n->invariants[i].tr);
-		mpq_clear(n->invariants[i].trinv);
-	}
-	free(n->invariants);
-	free(n->distinct_invariants);
-	for(int i = 0; i < g->nmax; i++)
-		mat_clear(n->matrices[i]);
-	free(n->matrices);
-	coxeter_clear(n->group);
-}
-
-int init_node(const void *_g, void *_n)
-{
-	struct global_data *g = (struct global_data *)_g;
-	struct node_data *n = (struct node_data *)_n;
-
-	DEBUG("Allocate\n");
-	g->id_list = (int*)(g+1);  // pointers get scrambled by transmission, reconstruct
-	n->matrices = malloc(g->nmax*sizeof(mat));
-	for(int i = 0; i < g->nmax; i++)
-		mat_init(n->matrices[i], 3);
-	n->invariants = malloc(g->nmax*sizeof(struct result));
-	n->distinct_invariants = malloc(g->nmax*sizeof(struct result)); // we won't need that many, but just in case
-	for(int i = 0; i < g->nmax; i++) {
-		mpq_init(n->invariants[i].tr);
-		mpq_init(n->invariants[i].trinv);
-		n->invariants[i].id = i;
-	}
-
-	// order of the triangle reflection generators: a, b, c
-	// order of the rotation orders: bc, ac, ab
-	DEBUG("Generate group\n");
-	n->group = coxeter_init_triangle(g->p1, g->p2, g->p3, g->nmax);
-
-	return 0;
-}
-
-int process_output(group_t *group, mat *matrices, struct result **invariants, int invariants_length, struct output_data *out)
-{
-	out->max_slope = 0;
-	for(int i = 0; i < invariants_length; i++) {
-		double x = invariants[i]->x;
-		double y = invariants[i]->y;
-
-		if(y/x > out->max_slope + 1e-12 && (x > 0.1 || y > 0.1)) {
-			out->max_slope_id = invariants[i]->id;
-			out->max_slope = y/x;
-		}
-	}
-}
-
-int do_computation(const void *_g, void *_n, const void *_in, void *_out)
-{
-	struct global_data *g = (struct global_data *)_g;
-	struct node_data *n = (struct node_data *)_n;
-	struct input_data *in = (struct input_data *)_in;
-	struct output_data *out = (struct output_data *)_out;
-
-	mpq_t s, q;
-
-	mpq_inits(s, q, NULL);
-	mpq_set_ui(s, in->snum, in->sden);
-	mpq_set_ui(q, in->qnum, in->qden);
-
-	INFO("Computing max slope element for s = %d/%d and q = %d/%d.\n",
-	      in->snum, in->sden,
-	      in->qnum, in->qden);
-
-	for(int i = 0; i < n->group->size; i++)
-		n->group->elements[i].need_to_compute = 0;
-	n->group->elements[0].need_to_compute = 1;
-
-	int needed_elements = 1;
-	for(int i = 0; i < g->id_list_length; i++)
-	{
-		int id = g->id_list[i];
-		n->distinct_invariants[i] = &n->invariants[id];
-		groupelement_t *cur = &n->group->elements[id];
-		while(cur->need_to_compute == 0) {
-			cur->need_to_compute = 1;
-			needed_elements++;
-			cur = cur->parent->parent;  // also need to compute its even-length ancestors
-		}
-		cur = n->group->elements[id].inverse;
-		while(cur->need_to_compute == 0) {
-			cur->need_to_compute = 1;
-			needed_elements++;
-			cur = cur->parent->parent;
-		}
-	}
-	n->distinct_invariants_length = g->id_list_length;
-
-	DEBUG("Need to compute %d elements to get %d traces up to reflection length %d\n",
-	      needed_elements, g->id_list_length, n->group->elements[n->group->size-1].length);
-
-	DEBUG("Compute matrices\n");
-	enumerate(n->group, n->matrices, g->p1, g->p2, g->p3, s, q);
-
-	DEBUG("Compute invariants\n");
-	compute_invariants(
-		n->group, n->matrices,
-		n->distinct_invariants, &n->distinct_invariants_length, 1);
-
-	DEBUG("Find max slopes\n");
-	process_output(n->group, n->matrices, n->distinct_invariants, n->distinct_invariants_length, out);
-
-	mpq_clears(s, q, NULL);
-
-	return 0;
-}
-
-int main(int argc, char *argv[])
-{
-	char buf[100];
-	char buf2[100];
-	struct global_data *g;
-	struct node_data n;
-
-	start_timer();
-
-	// parse command line arguments
-	if(argc < 11) {
-		fprintf(stderr, "Usage: %s <N> <p1> <p2> <p3> <s start> <s end> <s denom> <q start> <q end> <q denom> [restart]\n", argv[0]);
-		exit(1);
-	}
-	int nmax = atoi(argv[1]);
-	g = (struct global_data*)malloc(sizeof(struct global_data) + nmax*sizeof(int));
-	g->id_list = (int*)(g+1);
-	g->nmax = nmax;
-	g->p1 = atoi(argv[2]);
-	g->p2 = atoi(argv[3]);
-	g->p3 = atoi(argv[4]);
-	g->sstart = atoi(argv[5]);
-	g->send = atoi(argv[6]);
-	g->sdenom = atoi(argv[7]);
-	g->qstart = atoi(argv[8]);
-	g->qend = atoi(argv[9]);
-	g->qdenom = atoi(argv[10]);
-
-	// initialize
-	parallel_context *ctx = parallel_init();
-	parallel_set_datasize_and_callbacks(ctx, init_node, do_computation, destroy_node,
-	                                    sizeof(struct global_data) + g->nmax*sizeof(int),
-	                                    sizeof(struct node_data),
-	                                    sizeof(struct input_data),
-	                                    sizeof(struct output_data));
-	if(ctx->mpi_mode == 1 && ctx->rank != 0) {
-		// worker mode
-		parallel_work(ctx);
-		parallel_destroy(ctx);
-		exit(0);
-	}
-
-	init_node(g, &n);
-
-	// use very generic values for the pilot run unless sstart=send and qstart=qend
-	struct input_data pilot_input;
-	struct output_data pilot_output;
-	if(g->sstart == g->send && g->qstart == g->qend) {
-		pilot_input.snum = g->sstart;
-		pilot_input.sden = g->sdenom;
-		pilot_input.qnum = g->qstart;
-		pilot_input.qden = g->qdenom;
-		DEBUG("Single run for s = %d/%d, q = %d/%d\n", g->sstart, g->sdenom, g->qstart, g->qdenom);
-	} else {
-		pilot_input.snum = 4;
-		pilot_input.sden = 100;
-		pilot_input.qnum = 7;
-		pilot_input.qden = 100;
-		DEBUG("Initial run for s = %d/%d, q = %d/%d\n", 4, 100, 7, 100);
-	}
-
-	g->id_list_length = 0;
-	for(int i = 0; i < n.group->size; i++)
-		if(n.group->elements[i].length % 2 == 0 && n.group->elements[i].inverse)
-			g->id_list[g->id_list_length++] = i;
-
-	do_computation(g, &n, &pilot_input, &pilot_output);
-
-	for(int i = 0; i < n.distinct_invariants_length; i++)
-		g->id_list[i] = n.distinct_invariants[i]->id;
-	g->id_list_length = n.distinct_invariants_length;
-
-	if(g->sstart != g->send || g->qstart != g->qend) {
-
-		struct input_data *inputs = malloc((g->send - g->sstart + 1)*(g->qend - g->qstart + 1)*sizeof(struct input_data));
-		struct output_data *outputs = malloc((g->send - g->sstart + 1)*(g->qend - g->qstart + 1)*sizeof(struct input_data));
-
-		int njobs = 0;
-		for(int sloop = g->sstart; sloop <= g->send; sloop++) {
-			for(int qloop = g->qstart; qloop <= g->qend; qloop++) {
-				inputs[njobs].sden = g->sdenom;
-				inputs[njobs].qden = g->qdenom;
-				inputs[njobs].snum = sloop;
-				inputs[njobs].qnum = qloop;
-				njobs++;
-			}
-		}
-
-		if(argc >= 12)
-			parallel_run(ctx, g, inputs, outputs, njobs, argv[11]);
-		else
-			parallel_run(ctx, g, inputs, outputs, njobs, NULL);
-
-//				DEBUG("Loop for s = %d/%d, q = %d/%d\n", sloop, g->sdenom, qloop, g->qdenom);
-
-		for(int i = 0; i < njobs; i++)
-		{
-			gmp_printf("%d/%d %d/%d %d %s %f\n",
-			           inputs[i].snum, inputs[i].sden, inputs[i].qnum, inputs[i].qden,
-			           outputs[i].max_slope_id,
-			           print_word(&n.group->elements[outputs[i].max_slope_id], buf),
-			           outputs[i].max_slope);
-		}
-
-		free(inputs);
-		free(outputs);
-	} else {
-		// output
-		for(int i = 0; i < n.distinct_invariants_length; i++) {
-			// exclude tr = trinv = 2/1/0/-1/3
-			mpq_t tmp;
-			mpq_init(tmp);
-			mpq_set_si(tmp, 2, 1);
-			if(mpq_cmp(n.distinct_invariants[i]->tr, tmp) == 0 &&
-			   mpq_cmp(n.distinct_invariants[i]->trinv, tmp) == 0)
-				continue;
-			mpq_set_si(tmp, 1, 1);
-			if(mpq_cmp(n.distinct_invariants[i]->tr, tmp) == 0 &&
-			   mpq_cmp(n.distinct_invariants[i]->trinv, tmp) == 0)
-				continue;
-			mpq_set_si(tmp, 0, 1);
-			if(mpq_cmp(n.distinct_invariants[i]->tr, tmp) == 0 &&
-			   mpq_cmp(n.distinct_invariants[i]->trinv, tmp) == 0)
-				continue;
-			mpq_set_si(tmp, -1, 1);
-			if(mpq_cmp(n.distinct_invariants[i]->tr, tmp) == 0 &&
-			   mpq_cmp(n.distinct_invariants[i]->trinv, tmp) == 0)
-				continue;
-			mpq_set_si(tmp, 3, 1);
-			if(mpq_cmp(n.distinct_invariants[i]->tr, tmp) == 0 &&
-			   mpq_cmp(n.distinct_invariants[i]->trinv, tmp) == 0)
-				continue;
-			mpq_clear(tmp);
-
-			double slope = n.distinct_invariants[i]->y/n.distinct_invariants[i]->x;
-
-			gmp_printf("%d %s %f\n",
-			           n.distinct_invariants[i]->id,
-			           print_word(&n.group->elements[n.distinct_invariants[i]->id], buf),
-			           slope);
-		}
-
-	}
-
-	destroy_node(g, &n);
-	free(g);
-	parallel_destroy(ctx);
-}
--- a/singular_values_barbot.c
+++ b/singular_values_barbot.c
@@ -1,559 +0,0 @@
-#include "coxeter.h"
-#include "linalg.h"
-#include "mat.h"
-#include "enumerate_triangle_group.h"
-#include "parallel.h"
-
-#include <time.h>
-
-#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
-
-//#define DEBUG(msg, ...) fprintf(stderr, "[%003d%10.3f] " msg, mpi_rank(0), runtime(), ##__VA_ARGS__)
-#define DEBUG(msg, ...)
-#define INFO(msg, ...) fprintf(stderr, "[%003d%10.3f] " msg, mpi_rank(0), runtime(), ##__VA_ARGS__)
-
-struct result {
-	int id;
-	NUMBER tr;
-	NUMBER trinv;
-	int disc_sign;
-};
-
-// we want as much as possible to be node data, except if it is only known to the main node
-// (command line arguments) or should only be computed once (id list)
-
-struct global_data {
-	// command line arguments
-	unsigned int nmax;
-	unsigned int p1, p2, p3;
-	unsigned int sstart, send, sdenom;
-	unsigned int qstart, qend, qdenom;
-
-	unsigned int *id_list;
-	unsigned int id_list_length;
-};
-
-struct node_data {
-	group_t *group;
-	mat* matrices;
-	struct result *invariants;
-	struct result **distinct_invariants;
-	int distinct_invariants_length;
-	mps_context *solver;
-};
-
-struct input_data {
-	unsigned int snum, sden;
-	unsigned int qnum, qden;
-};
-
-struct output_data {
-	int n_non_loxodromic;
-	int min_wordlength;
-	int elements[10];
-};
-
-static int compare_result(const void *a_, const void *b_)
-{
-	int d = 0;
-
-	struct result **a = (struct result **)a_;
-	struct result **b = (struct result **)b_;
-
-	d = CMP((*a)->tr,(*b)->tr);
-	if(d == 0) {
-		d = CMP((*a)->trinv, (*b)->trinv);
-	}
-
-	return d;
-}
-
-static int compare_result_by_id(const void *a_, const void *b_)
-{
-	int d = 0;
-
-	struct result **a = (struct result **)a_;
-	struct result **b = (struct result **)b_;
-
-	return (*a)->id - (*b)->id;
-}
-
-static int compare_result_by_tr_trinv_id(const void *a_, const void *b_)
-{
-	int d = 0;
-
-	struct result **a = (struct result **)a_;
-	struct result **b = (struct result **)b_;
-
-	d = CMP((*a)->tr,(*b)->tr);
-	if(d == 0) {
-		d = CMP((*a)->trinv, (*b)->trinv);
-		if(d == 0) {
-			d = (*b)->id - (*a)->id;
-		}
-	}
-
-	return d;
-}
-
-/*
-static int compare_result_by_slope(const void *a_, const void *b_)
-{
-	int d = 0;
-
-	struct result **a = (struct result **)a_;
-	struct result **b = (struct result **)b_;
-
-	double slopea = (*a)->x / (*a)->y;
-	double slopeb = (*b)->x / (*b)->y;
-
-	return slopea > slopeb ? -1 : slopea < slopeb ? 1 : 0;
-}
-*/
-
-int invariants_trace_loxodromic(group_t *group, mat *matrices, struct result **invariants, int *n, int unique)
-{
-	int ntraces = *n, nuniq; // ntraces is the number of traces we are asked to compute, nuniq is the number of unique ones after we eliminate duplicates
-
-	// compute the traces
-	for(int i = 0; i < ntraces; i++) {
-		int id = invariants[i]->id;
-		int invid = group->elements[id].inverse->id;
-		mat_trace(invariants[i]->tr, matrices[id]);
-		mat_trace(invariants[i]->trinv, matrices[invid]);
-	}
-
-	// throw out duplicates if unique == 1
-	if(!unique)
-		nuniq = ntraces;
-	else {
-		qsort(invariants, ntraces, sizeof(struct result*), compare_result);
-
-		nuniq = 0;
-		for(int i = 0; i < ntraces; i++) {
-			if(i == 0 || compare_result(&invariants[i], &invariants[nuniq-1]) != 0) {
-				invariants[nuniq] = invariants[i];
-				nuniq++;
-			} else {
-				int oldlength = group->elements[invariants[nuniq-1]->id].length;
-				int newlength = group->elements[invariants[i]->id].length;
-				if(newlength < oldlength)
-					invariants[nuniq-1]->id = invariants[i]->id;
-			}
-		}
-	}
-
-	// check if loxodromic
-	NUMBER disc, zero;
-	double disc_real;
-	INIT(disc, QT_SQRT5);
-	INIT(zero, QT_SQRT5);
-	SET_ZERO(zero);
-	for(int i = 0; i < nuniq; i++) {
-		discriminant(disc, invariants[i]->tr, invariants[i]->trinv);
-		disc_real = mpq_get_d(disc->a[0]) + sqrt(5)*mpq_get_d(disc->a[1]);
-		gmp_printf("%Qd %Qd %f\n", disc->a[0], disc->a[1], disc_real);
-		invariants[i]->disc_sign = disc_real > 0 ? 1 : disc_real < 0 ? -1 : 0;
-	}
-	CLEAR(disc);
-	CLEAR(zero);
-
-	// sort by ID again
-	qsort(invariants, nuniq, sizeof(struct result*), compare_result_by_id);
-
-	*n = nuniq;
-	return 0;
-}
-
-/*
-int invariants_trace_slope(group_t *group, mat *matrices, struct result **invariants, int *n, int unique)
-{
-	mpq_t tmp;
-	mps_context *solver;
-	mps_monomial_poly *poly;
-	int index;
-	int ntraces = *n, nuniq;
-	int retval;
-	double evs[3];
-	char buf[100];
-
-//	DEBUG("Compute traces\n");
-	for(int i = 0; i < ntraces; i++) {
-		int id = invariants[i]->id;
-		int invid = group->elements[id].inverse->id;
-		mat_trace(invariants[i]->tr, matrices[id]);
-		mat_trace(invariants[i]->trinv, matrices[invid]);
-	}
-
-	if(!unique)
-		nuniq = ntraces;
-	else {
-//		DEBUG("Get unique traces\n");
-		qsort(invariants, ntraces, sizeof(struct result*), compare_result);
-
-		nuniq = 0;
-		for(int i = 0; i < ntraces; i++) {
-			if(i == 0 || compare_result(&invariants[i], &invariants[nuniq-1]) != 0) {
-				invariants[nuniq] = invariants[i];
-				nuniq++;
-			} else {
-				int oldlength = group->elements[invariants[nuniq-1]->id].length;
-				int newlength = group->elements[invariants[i]->id].length;
-				if(newlength < oldlength)
-					invariants[nuniq-1]->id = invariants[i]->id;
-			}
-		}
-	}
-
-	DEBUG("Solve characteristic polynomials\n");
-	solver = mps_context_new();
-	poly = mps_monomial_poly_new(solver, 3);
-	mps_context_set_output_prec(solver, 20); // relative precision
-	mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
-
-	for(int i = 0; i < nuniq; i++) {
-		retval = solve_characteristic_polynomial(solver, poly, invariants[i]->tr, invariants[i]->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]);
-
-		double x = log(fabs(evs[0]));
-		double y = -log(fabs(evs[2]));
-
-		invariants[i]->x = x;
-		invariants[i]->y = y;
-		invariants[i]->slope = y/x;
-	}
-	mps_context_free(solver);
-
-	qsort(invariants, nuniq, sizeof(struct result*), compare_result_by_id);
-
-	*n = nuniq;
-	return 0;
-}
-*/
-
-/*
-long check_memory_usage(mat *matrices, int n)
-{
-	mpq_t x;
-	long total;
-
-	for(int i = 0; i < n; i++)
-	{
-		LOOP(j,3) LOOP(k,3) {
-			total += mpq_numref(M(matrices[i], j, k))->_mp_size;
-			total += mpq_denref(M(matrices[i], j, k))->_mp_size;
-		}
-	}
-
-	return total;
-}
-*/
-
-
-void destroy_node(const void *_g, void *_n)
-{
-	struct global_data *g = (struct global_data *)_g;
-	struct node_data *n = (struct node_data *)_n;
-
-	for(int i = 0; i < g->nmax; i++) {
-		CLEAR(n->invariants[i].tr);
-		CLEAR(n->invariants[i].trinv);
-	}
-	free(n->invariants);
-	free(n->distinct_invariants);
-	for(int i = 0; i < g->nmax; i++)
-		mat_clear(n->matrices[i]);
-	free(n->matrices);
-	coxeter_clear(n->group);
-}
-
-int init_node(const void *_g, void *_n)
-{
-	struct global_data *g = (struct global_data *)_g;
-	struct node_data *n = (struct node_data *)_n;
-
-	DEBUG("Allocate\n");
-	g->id_list = (int*)(g+1);  // pointers get scrambled by transmission, reconstruct
-	n->matrices = malloc(g->nmax*sizeof(mat));
-	for(int i = 0; i < g->nmax; i++)
-		mat_init(n->matrices[i], 3, QT_SQRT5);
-	n->invariants = malloc(g->nmax*sizeof(struct result));
-	n->distinct_invariants = malloc(g->nmax*sizeof(struct result)); // we won't need that many, but just in case
-	for(int i = 0; i < g->nmax; i++) {
-		INIT(n->invariants[i].tr, QT_SQRT5);
-		INIT(n->invariants[i].trinv, QT_SQRT5);
-		n->invariants[i].id = i;
-	}
-
-	// order of the triangle reflection generators: a, b, c
-	// order of the rotation orders: bc, ac, ab
-	DEBUG("Generate group\n");
-	n->group = coxeter_init_triangle(g->p1, g->p2, g->p3, g->nmax);
-
-	return 0;
-}
-
-int process_output(group_t *group, mat *matrices, struct result **invariants, int invariants_length, struct output_data *out)
-{
-	out->n_non_loxodromic = 0;
-	out->min_wordlength = INT_MAX;
-	for(int i = 0; i < invariants_length; i++) {
-		if(invariants[i]->disc_sign <= 0 && invariants[i]->id != 0 && invariants[i]->id != 4 && invariants[i]->id != 22) {
-			if(out->n_non_loxodromic < 10)
-				out->elements[out->n_non_loxodromic] = invariants[i]->id;
-			out->n_non_loxodromic++;
-			if(group->elements[invariants[i]->id].length < out->min_wordlength)
-				out->min_wordlength = group->elements[invariants[i]->id].length;
-		}
-	}
-}
-
-int do_computation(const void *_g, void *_n, const void *_in, void *_out)
-{
-	struct global_data *g = (struct global_data *)_g;
-	struct node_data *n = (struct node_data *)_n;
-	struct input_data *in = (struct input_data *)_in;
-	struct output_data *out = (struct output_data *)_out;
-
-	mpq_t s, q;
-
-	mpq_inits(s, q, NULL);
-	mpq_set_ui(s, in->snum, in->sden);
-	mpq_set_ui(q, in->qnum, in->qden);
-
-	INFO("Computing represention with s = %d/%d and q = %d/%d.\n",
-	      in->snum, in->sden,
-	      in->qnum, in->qden);
-
-	// we need to compute all the elements pointed to in id_list, and all their suffixes or prefixes
-	// I can imagine a smarter way of doing this which checks if there is a shorter route to the element
-	for(int i = 0; i < n->group->size; i++)
-		n->group->elements[i].need_to_compute = 0;
-	n->group->elements[0].need_to_compute = 1;
-
-	int needed_elements = 1;
-	for(int i = 0; i < g->id_list_length; i++)
-	{
-		int id = g->id_list[i];
-		n->distinct_invariants[i] = &n->invariants[id];
-		groupelement_t *cur = &n->group->elements[id];
-		while(cur->need_to_compute == 0) {
-			cur->need_to_compute = 1;
-			needed_elements++;
-			cur = cur->parent->parent;  // also need to compute its even-length ancestors
-		}
-		cur = n->group->elements[id].inverse;
-		while(cur->need_to_compute == 0) {
-			cur->need_to_compute = 1;
-			needed_elements++;
-			cur = cur->parent->parent;
-		}
-	}
-	n->distinct_invariants_length = g->id_list_length;
-
-	DEBUG("Need to compute %d elements to get %d traces up to reflection length %d\n",
-	      needed_elements, g->id_list_length, n->group->elements[n->group->size-1].length);
-
-	DEBUG("Compute matrices\n");
-	mat gen[6];
-	for(int i = 0; i < 6; i++)
-		mat_init(gen[i], 3, QT_SQRT5);
-
-	generators_triangle_rotation_555_barbot(gen, s, q);
-	enumerate_triangle_rotation_subgroup(n->group, gen, n->matrices);
-
-	for(int i = 0; i < 6; i++)
-		mat_clear(gen[i]);
-
-	DEBUG("Compute invariants\n");
-	invariants_trace_loxodromic(
-		n->group, n->matrices,
-		n->distinct_invariants, &n->distinct_invariants_length, 1);
-
-//	DEBUG("Find max slopes\n");
-	process_output(n->group, n->matrices, n->distinct_invariants, n->distinct_invariants_length, out);
-
-	mpq_clears(s, q, NULL);
-
-	return 0;
-}
-
-int main(int argc, char *argv[])
-{
-	char buf[1000];
-	char buf2[1000];
-	char buf3[1000];
-	struct global_data *g;
-	struct node_data n;
-
-	start_timer();
-
-	// parse command line arguments
-	if(argc < 11) {
-		fprintf(stderr, "Usage: %s <N> <p1> <p2> <p3> <s start> <s end> <s denom> <q start> <q end> <q denom> [restart]\n", argv[0]);
-		exit(1);
-	}
-	int nmax = atoi(argv[1]);
-	g = (struct global_data*)malloc(sizeof(struct global_data) + nmax*sizeof(int));
-	g->id_list = (int*)(g+1);
-	g->nmax = nmax;
-	g->p1 = atoi(argv[2]);
-	g->p2 = atoi(argv[3]);
-	g->p3 = atoi(argv[4]);
-	g->sstart = atoi(argv[5]);
-	g->send = atoi(argv[6]);
-	g->sdenom = atoi(argv[7]);
-	g->qstart = atoi(argv[8]);
-	g->qend = atoi(argv[9]);
-	g->qdenom = atoi(argv[10]);
-
-	// initialize
-	parallel_context *ctx = parallel_init();
-	parallel_set_datasize_and_callbacks(ctx, init_node, do_computation, destroy_node,
-	                                    sizeof(struct global_data) + g->nmax*sizeof(int),
-	                                    sizeof(struct node_data),
-	                                    sizeof(struct input_data),
-	                                    sizeof(struct output_data));
-	if(ctx->mpi_mode == 1 && ctx->rank != 0) {
-		// worker mode
-		parallel_work(ctx);
-		parallel_destroy(ctx);
-		exit(0);
-	}
-
-	init_node(g, &n);
-
-	// use very generic values for the pilot run unless sstart=send and qstart=qend
-	struct input_data pilot_input;
-	struct output_data pilot_output;
-	if(g->sstart == g->send && g->qstart == g->qend) {
-		pilot_input.snum = g->sstart;
-		pilot_input.sden = g->sdenom;
-		pilot_input.qnum = g->qstart;
-		pilot_input.qden = g->qdenom;
-		DEBUG("Single run for s = %d/%d, q = %d/%d\n", g->sstart, g->sdenom, g->qstart, g->qdenom);
-	} else {
-		pilot_input.snum = 4;
-		pilot_input.sden = 100;
-		pilot_input.qnum = 7;
-		pilot_input.qden = 100;
-		DEBUG("Initial run for s = %d/%d, q = %d/%d\n", 4, 100, 7, 100);
-	}
-
-	g->id_list_length = 0;
-	for(int i = 0; i < n.group->size; i++)
-		if(n.group->elements[i].length % 2 == 0 && n.group->elements[i].inverse)
-			g->id_list[g->id_list_length++] = i;
-
-	do_computation(g, &n, &pilot_input, &pilot_output);
-
-	for(int i = 0; i < n.distinct_invariants_length; i++)
-		g->id_list[i] = n.distinct_invariants[i]->id;
-	g->id_list_length = n.distinct_invariants_length;
-
-	if(g->sstart != g->send || g->qstart != g->qend) {
-
-		struct input_data *inputs = malloc((g->send - g->sstart + 1)*(g->qend - g->qstart + 1)*sizeof(struct input_data));
-		struct output_data *outputs = malloc((g->send - g->sstart + 1)*(g->qend - g->qstart + 1)*sizeof(struct output_data));
-
-		int njobs = 0;
-		for(int sloop = g->sstart; sloop <= g->send; sloop++) {
-			for(int qloop = g->qstart; qloop <= g->qend; qloop++) {
-				inputs[njobs].sden = g->sdenom;
-				inputs[njobs].qden = g->qdenom;
-				inputs[njobs].snum = sloop;
-				inputs[njobs].qnum = qloop;
-				njobs++;
-			}
-		}
-
-		if(argc >= 12)
-			parallel_run(ctx, g, inputs, outputs, njobs, argv[11]);
-		else
-			parallel_run(ctx, g, inputs, outputs, njobs, NULL);
-
-//				DEBUG("Loop for s = %d/%d, q = %d/%d\n", sloop, g->sdenom, qloop, g->qdenom);
-
-		for(int i = 0; i < njobs; i++)
-		{
-			/*
-			gmp_printf("%d/%d %d/%d %d %s %f\n",
-			           inputs[i].snum, inputs[i].sden, inputs[i].qnum, inputs[i].qden,
-			           outputs[i].max_slope_id,
-			           print_word(&n.group->elements[outputs[i].max_slope_id], buf),
-			           outputs[i].max_slope);
-			*/
-
-
-			printf("%d/%d %d/%d %d %d",
-			       inputs[i].snum, inputs[i].sden, inputs[i].qnum, inputs[i].qden,
-			       outputs[i].n_non_loxodromic, outputs[i].min_wordlength);
-			for(int j = 0; j < 10 && j < outputs[i].n_non_loxodromic; j++)
-				printf(" %s", print_word(&n.group->elements[outputs[i].elements[j]], buf));
-			printf("\n");
-
-		}
-
-		free(inputs);
-		free(outputs);
-	} else {
-		// output
-		for(int i = 0; i < n.distinct_invariants_length; i++) {
-			// exclude tr = trinv = 2/1/0/-1/3
-
-			/*
-			mpq_t tmp;
-			mpq_init(tmp);
-			mpq_set_si(tmp, 2, 1);
-			if(mpq_cmp(n.distinct_invariants[i]->tr, tmp) == 0 &&
-			   mpq_cmp(n.distinct_invariants[i]->trinv, tmp) == 0)
-				continue;
-			mpq_set_si(tmp, 1, 1);
-			if(mpq_cmp(n.distinct_invariants[i]->tr, tmp) == 0 &&
-			   mpq_cmp(n.distinct_invariants[i]->trinv, tmp) == 0)
-				continue;
-			mpq_set_si(tmp, 0, 1);
-			if(mpq_cmp(n.distinct_invariants[i]->tr, tmp) == 0 &&
-			   mpq_cmp(n.distinct_invariants[i]->trinv, tmp) == 0)
-				continue;
-			mpq_set_si(tmp, -1, 1);
-			if(mpq_cmp(n.distinct_invariants[i]->tr, tmp) == 0 &&
-			   mpq_cmp(n.distinct_invariants[i]->trinv, tmp) == 0)
-				continue;
-			mpq_set_si(tmp, 3, 1);
-			if(mpq_cmp(n.distinct_invariants[i]->tr, tmp) == 0 &&
-			   mpq_cmp(n.distinct_invariants[i]->trinv, tmp) == 0)
-				continue;
-			mpq_clear(tmp);
-			*/
-
-			SNPRINT(buf, sizeof(buf), n.distinct_invariants[i]->tr);
-			SNPRINT(buf2, sizeof(buf2), n.distinct_invariants[i]->trinv);
-			printf("%d %s %d\n",
-			       n.distinct_invariants[i]->id,
-			       print_word(&n.group->elements[n.distinct_invariants[i]->id], buf3),
-//			       mpq_get_d(n.distinct_invariants[i]->tr[0])+sqrt(5)*mpq_get_d(n.distinct_invariants[i]->tr[1]),
-//			       mpq_get_d(n.distinct_invariants[i]->trinv[0])+sqrt(5)*mpq_get_d(n.distinct_invariants[i]->trinv[1]),
-			       n.distinct_invariants[i]->disc_sign);
-
-		}
-
-	}
-
-	destroy_node(g, &n);
-	free(g);
-	parallel_destroy(ctx);
-}
Author	SHA1	Message	Date
Florian Stecker	f89545e995	simplify image generation	2022-06-18 14:54:50 +02:00
Florian Stecker	920a530385	remove unnecessary function qext_newtype()	2022-06-16 15:43:19 +02:00
Florian Stecker	cfc13d2ba7	add useful help text	2022-06-15 18:47:55 +02:00
Florian Stecker	979cbe7922	parallelization scripts	2022-06-15 18:04:42 +02:00
Florian Stecker	ec34567ace	Makefile fix	2022-06-15 15:27:08 +02:00
Florian Stecker	575c310cd3	remove irrelevant files	2022-06-15 15:19:38 +02:00
Florian Stecker	ac80bc9f3f	new simpler approach to parallalization	2022-06-15 15:17:54 +02:00
Florian Stecker	429f0890d6	generate beautiful pictures of the complex Anosov set	2022-06-15 12:20:45 +02:00
Florian Stecker	729d1a10b7	add simple CLI interface	2022-06-14 16:03:40 +02:00
Florian Stecker	0763056ccb	compute complex max slope	2022-06-14 15:41:43 +02:00
Florian Stecker	244784794d	compute complex traces	2022-06-14 14:22:22 +02:00
Florian Stecker	15681c308b	import enumerate.c and generators.c, prepare Makefile	2022-06-13 12:05:34 +02:00