Trac #33628: Fig bug in graphs.RandomToleranceGraph

Part of #32544:
{{{
sage -t --long --warn-long 291.5 --random-
seed=184268751501867371650794470659094787547
src/sage/graphs/generators/random.py
**********************************************************************
File "src/sage/graphs/generators/random.py", line 1527, in
sage.graphs.generators.random.RandomToleranceGraph
Failed example:
    g = graphs.RandomToleranceGraph(8)
Exception raised:
    Traceback (most recent call last):
      File "/Users/dcoudert/sage/local/var/lib/sage/venv-
python3.9/lib/python3.9/site-packages/sage/doctest/forker.py", line 695,
in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/Users/dcoudert/sage/local/var/lib/sage/venv-
python3.9/lib/python3.9/site-packages/sage/doctest/forker.py", line
1093, in compile_and_execute
        exec(compiled, globs)
      File "<doctest
sage.graphs.generators.random.RandomToleranceGraph[0]>", line 1, in
<module>
        g = graphs.RandomToleranceGraph(Integer(8))
      File "/Users/dcoudert/sage/local/var/lib/sage/venv-
python3.9/lib/python3.9/site-packages/sage/graphs/generators/random.py",
line 1553, in RandomToleranceGraph
        return ToleranceGraph(tolrep)
      File "/Users/dcoudert/sage/local/var/lib/sage/venv-
python3.9/lib/python3.9/site-
packages/sage/graphs/generators/intersection.py", line 351, in
ToleranceGraph
        raise ValueError("Invalid tolerance representation at position
"+str(i)+"; third value must be positive!")
    ValueError: Invalid tolerance representation at position 2; third
value must be positive!
}}}
Method `graphs.ToleranceGraph` raises an error when a tolerance is `<=
0`.

URL: https://trac.sagemath.org/33628
Reported by: dcoudert
Ticket author(s): David Coudert
Reviewer(s): Travis Scrimshaw

src/sage/graphs/generators/intersection.py

@@ -282,12 +282,12 @@ def ToleranceGraph(tolrep):
     Return the graph generated by the tolerance representation ``tolrep``.
 
     The tolerance representation ``tolrep`` is described by the list
-    `((l_0,r_0,t_0), (l_1,r_1,t_1), ..., (l_k,r_k,t_k))` where `I_i = (l_i,r_i)`
-    denotes a closed interval on the real line with `l_i < r_i` and `t_i` a
-    positive value, called tolerance. This representation generates the
-    tolerance graph with the vertex set {0,1, ..., k} and the edge set `{(i,j):
-    |I_i \cap I_j| \ge \min{t_i, t_j}}` where `|I_i \cap I_j|` denotes the
-    length of the intersection of `I_i` and `I_j`.
+    `((l_0,r_0,t_0), (l_1,r_1,t_1), \ldots, (l_k,r_k,t_k))` where `I_i =
+    (l_i,r_i)` denotes a closed interval on the real line with `l_i < r_i` and
+    `t_i` a strictly positive value, called tolerance. This representation
+    generates the tolerance graph with the vertex set `\{0,1, \ldots, k\}` and
+    the edge set `\{(i,j): |I_i \cap I_j| \ge \min\{t_i, t_j\}\}` where `|I_i
+    \cap I_j|` denotes the length of the intersection of `I_i` and `I_j`.
 
     INPUT:
 
@@ -296,9 +296,9 @@ def ToleranceGraph(tolrep):
 
     .. NOTE::
 
-        The vertices are named 0, 1, ..., k. The tolerance representation used
-        to create the graph is saved with the graph and can be recovered using
-        ``get_vertex()`` or ``get_vertices()``.
+        The vertices are named `0, 1, \ldots, k`. The tolerance representation
+        used to create the graph is saved with the graph and can be recovered
+        using ``get_vertex()`` or ``get_vertices()``.
 
     EXAMPLES:
 
@@ -342,24 +342,29 @@ def ToleranceGraph(tolrep):
         sage: g = graphs.ToleranceGraph(tolrep)
         Traceback (most recent call last):
         ...
-        ValueError: Invalid tolerance representation at position 0; third value must be positive!
+        ValueError: Invalid tolerance representation at position 0; third value must be > 0
+        sage: g = graphs.ToleranceGraph([(1, 2, 0)])
+        Traceback (most recent call last):
+        ...
+        ValueError: Invalid tolerance representation at position 0; third value must be  > 0
     """
     n = len(tolrep)
 
     for i in range(n):
         if tolrep[i][2] <= 0:
-            raise ValueError("Invalid tolerance representation at position "+str(i)+"; third value must be positive!")
+            raise ValueError("Invalid tolerance representation at position "
+                             "{}; third value must be > 0".format(i))
 
-    g = Graph(n)
+    g = Graph(n, name="Tolerance Graph")
 
-    for i in range(n-1):
-        li,ri,ti = tolrep[i]
-        for j in range(i+1,n):
-            lj,rj,tj = tolrep[j]
-            if min(ri,rj) - max(li,lj) >= min(ti,tj):
+    for i in range(n):
+        li, ri, ti = tolrep[i]
+        for j in range(i + 1, n):
+            lj, rj, tj = tolrep[j]
+            if min(ri, rj) - max(li, lj) >= min(ti, tj):
                 g.add_edge(i,j)
 
-    rep = dict( zip(range(n),tolrep) )
+    rep = dict(zip(range(n), tolrep))
     g.set_vertices(rep)
 
     return g

src/sage/graphs/generators/random.py

@@ -1548,9 +1548,12 @@ def RandomToleranceGraph(n):
         r = randint(0, W)
         if l > r:
             l, r = r, l
-        tolrep.append((l, r, randint(0, W)))
+        # The tolerance value must be > 0
+        tolrep.append((l, r, randint(1, W)))
 
-    return ToleranceGraph(tolrep)
+    g = ToleranceGraph(tolrep)
+    g.name("Random tolerance graph")
+    return g
 
 
 # uniform random triangulation using Schaeffer-Poulalhon algorithm