1 | initial version |

I first got

```
---> 14 from progress.bar import Bar
15 import pprint
16
ImportError: No module named progress.bar
```

So, i bet that you installed `progress`

from pip, which i did. But then, i got a very different error:

```
A 3-dimensional polyhedron in ZZ^3 defined as the convex hull of 8 vertices
Unfold: 12 faces
[A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices]
Find all length 2 sets from 8 vertices
Find all length 11 sets from 28 edges
Processing | | 0/21474180
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-2-96862f2c002c> in <module>()
263
264 # Unfold
--> 265 planar, G = gray(flatten, all_vertex_pairs)
266 pp = pprint.PrettyPrinter(indent=Integer(4))
267 pp.pprint(planar)
<ipython-input-2-96862f2c002c> in gray(flatten, all_vertex_pairs)
37 s.remove(i)
38 s.add(j)
---> 39 flag, planar, G = test_edges(all_vertex_pairs, s, flatten)
40 if flag:
41 return planar, G
<ipython-input-2-96862f2c002c> in test_edges(all_v_pairs, possible_unfolding, flatten)
169 return False, {}, None
170 test = assign_edges(all_v_pairs, possible_unfolding)
--> 171 planar = planar_representation({}, flatten, test)
172 if planar == {}:
173 return False, {}, None
<ipython-input-2-96862f2c002c> in planar_representation(planar, flatten, test_case)
126 for i in range(len(flatten)):
127 key = flatten[i]
--> 128 cycle = poly2list(key)
129 to_delete = []
130 for j in range(len(cycle)):
<ipython-input-2-96862f2c002c> in poly2list(face)
85 OUTPUT: A numpy integer array of every edge possible inside a face.
86 """
---> 87 converted_face = convert(face)
88 edges = np.array(Combinations(converted_face, Integer(2)).list()).astype(int)
89 return edges
<ipython-input-2-96862f2c002c> in convert(data)
69 s_data = s_data.split(",")
70 for i in range(len(s_data)):
---> 71 s_data[i] = float(s_data[i])
72 return np.array(s_data)
73
ValueError: could not convert string to float: A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
```

2 | No.2 Revision |

**EDIT** : OK got it:

For the graph with a single vertex, the `eulerian_circuit`

method is btoken;

```
sage: G = Graph()
sage: G.add_vertex(0)
sage: G
Graph on 1 vertex
sage: G.eulerian_circuit()
---------------------------------------------------------------------------
StopIteration Traceback (most recent call last)
<ipython-input-5-0c288f8b38d6> in <module>()
----> 1 G.eulerian_circuit()
/opt/sagemath/sage-source/local/lib/python2.7/site-packages/sage/graphs/generic_graph.pyc in eulerian_circuit(self, return_vertices, labels, path)
4001 edges.append(e if labels else (e[0], e[1]))
4002 else:
-> 4003 next_edge = next(g_edge_iter(v))
4004
4005 if next_edge[0] == v: # in the undirected case we want to
StopIteration:
```

Thanks for reporting, this is now trac ticket 28451

[previous answer in trying to reproduce the issue]

I first got

```
---> 14 from progress.bar import Bar
15 import pprint
16
ImportError: No module named progress.bar
```

So, i bet that you installed `progress`

from pip, which i did. But then, i got a very different error:

```
A 3-dimensional polyhedron in ZZ^3 defined as the convex hull of 8 vertices
Unfold: 12 faces
[A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices]
Find all length 2 sets from 8 vertices
Find all length 11 sets from 28 edges
Processing | | 0/21474180
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-2-96862f2c002c> in <module>()
263
264 # Unfold
--> 265 planar, G = gray(flatten, all_vertex_pairs)
266 pp = pprint.PrettyPrinter(indent=Integer(4))
267 pp.pprint(planar)
<ipython-input-2-96862f2c002c> in gray(flatten, all_vertex_pairs)
37 s.remove(i)
38 s.add(j)
---> 39 flag, planar, G = test_edges(all_vertex_pairs, s, flatten)
40 if flag:
41 return planar, G
<ipython-input-2-96862f2c002c> in test_edges(all_v_pairs, possible_unfolding, flatten)
169 return False, {}, None
170 test = assign_edges(all_v_pairs, possible_unfolding)
--> 171 planar = planar_representation({}, flatten, test)
172 if planar == {}:
173 return False, {}, None
<ipython-input-2-96862f2c002c> in planar_representation(planar, flatten, test_case)
126 for i in range(len(flatten)):
127 key = flatten[i]
--> 128 cycle = poly2list(key)
129 to_delete = []
130 for j in range(len(cycle)):
<ipython-input-2-96862f2c002c> in poly2list(face)
85 OUTPUT: A numpy integer array of every edge possible inside a face.
86 """
---> 87 converted_face = convert(face)
88 edges = np.array(Combinations(converted_face, Integer(2)).list()).astype(int)
89 return edges
<ipython-input-2-96862f2c002c> in convert(data)
69 s_data = s_data.split(",")
70 for i in range(len(s_data)):
---> 71 s_data[i] = float(s_data[i])
72 return np.array(s_data)
73
ValueError: could not convert string to float: A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
```

3 | No.3 Revision |

**EDIT** : OK got it:

For the graph with a single vertex, the `eulerian_circuit`

method is ~~btoken;~~broken;

```
sage: G = Graph()
sage: G.add_vertex(0)
sage: G
Graph on 1 vertex
sage: G.eulerian_circuit()
---------------------------------------------------------------------------
StopIteration Traceback (most recent call last)
<ipython-input-5-0c288f8b38d6> in <module>()
----> 1 G.eulerian_circuit()
/opt/sagemath/sage-source/local/lib/python2.7/site-packages/sage/graphs/generic_graph.pyc in eulerian_circuit(self, return_vertices, labels, path)
4001 edges.append(e if labels else (e[0], e[1]))
4002 else:
-> 4003 next_edge = next(g_edge_iter(v))
4004
4005 if next_edge[0] == v: # in the undirected case we want to
StopIteration:
```

Thanks for reporting, this is now trac ticket 28451

[previous answer in trying to reproduce the issue]

I first got

```
---> 14 from progress.bar import Bar
15 import pprint
16
ImportError: No module named progress.bar
```

So, i bet that you installed `progress`

from pip, which i did. But then, i got a very different error:

```
A 3-dimensional polyhedron in ZZ^3 defined as the convex hull of 8 vertices
Unfold: 12 faces
[A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices]
Find all length 2 sets from 8 vertices
Find all length 11 sets from 28 edges
Processing | | 0/21474180
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-2-96862f2c002c> in <module>()
263
264 # Unfold
--> 265 planar, G = gray(flatten, all_vertex_pairs)
266 pp = pprint.PrettyPrinter(indent=Integer(4))
267 pp.pprint(planar)
<ipython-input-2-96862f2c002c> in gray(flatten, all_vertex_pairs)
37 s.remove(i)
38 s.add(j)
---> 39 flag, planar, G = test_edges(all_vertex_pairs, s, flatten)
40 if flag:
41 return planar, G
<ipython-input-2-96862f2c002c> in test_edges(all_v_pairs, possible_unfolding, flatten)
169 return False, {}, None
170 test = assign_edges(all_v_pairs, possible_unfolding)
--> 171 planar = planar_representation({}, flatten, test)
172 if planar == {}:
173 return False, {}, None
<ipython-input-2-96862f2c002c> in planar_representation(planar, flatten, test_case)
126 for i in range(len(flatten)):
127 key = flatten[i]
--> 128 cycle = poly2list(key)
129 to_delete = []
130 for j in range(len(cycle)):
<ipython-input-2-96862f2c002c> in poly2list(face)
85 OUTPUT: A numpy integer array of every edge possible inside a face.
86 """
---> 87 converted_face = convert(face)
88 edges = np.array(Combinations(converted_face, Integer(2)).list()).astype(int)
89 return edges
<ipython-input-2-96862f2c002c> in convert(data)
69 s_data = s_data.split(",")
70 for i in range(len(s_data)):
---> 71 s_data[i] = float(s_data[i])
72 return np.array(s_data)
73
ValueError: could not convert string to float: A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
```

4 | No.4 Revision |

**EDIT** : OK got it:

For the graph with a single vertex, the `eulerian_circuit`

method is broken;

```
sage: G = Graph()
sage: G.add_vertex(0)
sage: G
Graph on 1 vertex
sage: G.eulerian_circuit()
---------------------------------------------------------------------------
StopIteration Traceback (most recent call last)
<ipython-input-5-0c288f8b38d6> in <module>()
----> 1 G.eulerian_circuit()
/opt/sagemath/sage-source/local/lib/python2.7/site-packages/sage/graphs/generic_graph.pyc in eulerian_circuit(self, return_vertices, labels, path)
4001 edges.append(e if labels else (e[0], e[1]))
4002 else:
-> 4003 next_edge = next(g_edge_iter(v))
4004
4005 if next_edge[0] == v: # in the undirected case we want to
StopIteration:
```

Or more generally graphs with vertices but no edges;

```
sage: G = Graph()
sage: G.add_vertices(range(10))
sage: G.eulerian_circuit()
---------------------------------------------------------------------------
StopIteration Traceback (most recent call last)
<ipython-input-27-0c288f8b38d6> in <module>()
----> 1 G.eulerian_circuit()
/opt/sagemath/sage-source/local/lib/python2.7/site-packages/sage/graphs/generic_graph.pyc in eulerian_circuit(self, return_vertices, labels, path)
4001 edges.append(e if labels else (e[0], e[1]))
4002 else:
-> 4003 next_edge = next(g_edge_iter(v))
4004
4005 if next_edge[0] == v: # in the undirected case we want to
StopIteration:
```

Thanks for reporting, this is now trac ticket 28451

[previous answer in trying to reproduce the issue]

I first got

```
---> 14 from progress.bar import Bar
15 import pprint
16
ImportError: No module named progress.bar
```

So, i bet that you installed `progress`

from pip, which i did. But then, i got a very different error:

```
A 3-dimensional polyhedron in ZZ^3 defined as the convex hull of 8 vertices
Unfold: 12 faces
[A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices]
Find all length 2 sets from 8 vertices
Find all length 11 sets from 28 edges
Processing | | 0/21474180
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-2-96862f2c002c> in <module>()
263
264 # Unfold
--> 265 planar, G = gray(flatten, all_vertex_pairs)
266 pp = pprint.PrettyPrinter(indent=Integer(4))
267 pp.pprint(planar)
<ipython-input-2-96862f2c002c> in gray(flatten, all_vertex_pairs)
37 s.remove(i)
38 s.add(j)
---> 39 flag, planar, G = test_edges(all_vertex_pairs, s, flatten)
40 if flag:
41 return planar, G
<ipython-input-2-96862f2c002c> in test_edges(all_v_pairs, possible_unfolding, flatten)
169 return False, {}, None
170 test = assign_edges(all_v_pairs, possible_unfolding)
--> 171 planar = planar_representation({}, flatten, test)
172 if planar == {}:
173 return False, {}, None
<ipython-input-2-96862f2c002c> in planar_representation(planar, flatten, test_case)
126 for i in range(len(flatten)):
127 key = flatten[i]
--> 128 cycle = poly2list(key)
129 to_delete = []
130 for j in range(len(cycle)):
<ipython-input-2-96862f2c002c> in poly2list(face)
85 OUTPUT: A numpy integer array of every edge possible inside a face.
86 """
---> 87 converted_face = convert(face)
88 edges = np.array(Combinations(converted_face, Integer(2)).list()).astype(int)
89 return edges
<ipython-input-2-96862f2c002c> in convert(data)
69 s_data = s_data.split(",")
70 for i in range(len(s_data)):
---> 71 s_data[i] = float(s_data[i])
72 return np.array(s_data)
73
ValueError: could not convert string to float: A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
```

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