is_isomorphic broken with keyword edge_labels=True

[jipilab]

This code led to finding this bug in the is_isomorphic method.

Here is a simple working example:

sage: m1 = matrix(ZZ, [[1, -1, -1], [-1, -1, -1], [1, 0, -1]])
sage: m2 = matrix(ZZ, [[-1, -1, -1], [-1, 1, -1], [-1, 1, 0]])

The two matrices are equal up to permutation of rows and columns:

sage: m1.is_permutation_of(m2)
True

But, not over CyclotomicFields:

sage: CF = CyclotomicField(1)
sage: p1 = matrix(CF, [[1, -1, -1], [-1, -1, -1], [1, 0, -1]])
sage: p2 = matrix(CF, [[-1, -1, -1], [-1, 1, -1], [-1, 1, 0]])
sage: p1.is_permutation_of(p2)
False

Even with 2 is also does not work:

sage: CF = CyclotomicField(2)
sage: p1 = matrix(CF, [[1, -1, -1], [-1, -1, -1], [1, 0, -1]])
sage: p2 = matrix(CF, [[-1, -1, -1], [-1, 1, -1], [-1, 1, 0]])
sage: p1.is_permutation_of(p2)
False

This error is provoked at the level of graphs:

sage: g1 = p1.as_bipartite_graph()
sage: g2 = p2.as_bipartite_graph()
sage: sorted(g1.edge_labels())
[1, -1, -1, -1, -1, -1, 1, 0, -1]
sage: sorted(g2.edge_labels())
[-1, -1, -1, -1, 1, -1, -1, 1, 0]

[jipilab]

Here is the current issue, sorting is broken on the CyclotomicField?:

sage: g1 = p1.as_bipartite_graph()
sage: g2 = p2.as_bipartite_graph()
sage: sorted(g1.edge_labels())
[1, -1, -1, -1, -1, -1, 1, 0, -1]
sage: sorted(g2.edge_labels())
[-1, -1, -1, -1, 1, -1, -1, 1, 0]

[vdelecroix]

This code is crap. How can you assume that the elements of your ring could be sorted with respect to some total order?

[jipilab]

Replying to vdelecroix:

This code is crap. How can you assume that the elements of your ring could be sorted with respect to some total order?

Right! :-S I was quite puzzled when saw that this was done!!

That step in the _is_isomorphic method of graph with the option edge_labels=True should be repaired so that it makes sense...

The above code came up while looking at two character tables coming from two isomorphic groups. They should be equal up to permutation of columns and rows, but it was returns False !!!

[vdelecroix]

This is indeed annoying. Many graphs problem like this one have to be fixed with the switch to Python3 (where comparison might simply throw errors)...

[dcoudert]

Agreed. Many progresses have been done in the graph module and a lot remains to be done. Help fixing problems / reviewing tickets is more than welcome :P

I tried the example with Python 2 and 3 and the answer is False in both cases and it is effectively due to the test if edge_labels and sorted(self.edge_labels()) != sorted(other.edge_labels()): that is False here for the reason explained above (#comment:2).

Do you have any suggestion on how to compare the 2 lists of edge labels knowing that edge labels can be unhashable ?

May be this ticket could be moved to the graph component as it will only touch method is_isomorphic ? Could make it easier to trac changes in the graph module...

[dcoudert]

I tried many stuff today without success. This is really one of the major issue of the graph module.

We can do a simple hack to replace the test sorted(self.edge_labels()) != sorted(other.edge_labels()) in method is_isomorphic of generic_graph.py. This is not nice/efficient but it does the job.

                def same_edge_labels(self_labels, other_labels):
                    """
                    Check that the lists have exactly the same content.
                    This is slower than sorting and checking equality, but safe
                    for Python3.
                    """
                    for label in self_labels:
                        if label in other_labels:
                            other_labels.remove(label)
                        else:
                            return False
                    return not other_labels

However, this is far from enough as method graph_isom_equivalent_non_edge_labeled_graph sorts many times lists of edge labels. I tried to remove these sortings, but I don't have a sufficient understanding of the methods to know what is correct, what is not and more importantly, what is assumed as input/output of other methods like those of sage.groups.perm_gps.partn_ref.refinement_graphs, etc.

I'm pushing in a public branch what I tried to do. Feel free to modify/correct/etc. and even suppress if you believe it is not a good approach to fix the problem. It's breaking doctests in is_isomorphic and canonical_label...

PS: The cost to pay for accepting anything as an edge label is really high :(

---

New commits:

​a1f9014

trac #27232: first trial

[vdelecroix]

There is indeed a general problem with labels (not only for graphs). Ideally, when one has a structure with labels, one should be able to specify

1. whether labels have a total order (and provide a comparison function)
2. whether labels are hashable (and provide a hash function)
3. if neither 1. nor 2. applies, be prepared for costly checks

In the current situation, if 1. applies, you can use sort and if 2. applies you can use Python set.

[jipilab]

Replying to vdelecroix:

There is indeed a general problem with labels (not only for graphs). Ideally, when one has a structure with labels, one should be able to specify

1. whether labels have a total order (and provide a comparison function)
2. whether labels are hashable (and provide a hash function)
3. if neither 1. nor 2. applies, be prepared for costly checks

In the current situation, if 1. applies, you can use sort and if 2. applies you can use Python set.

That sounds like a reasonable ideal. It does not sound too idealistic either.

[dcoudert]

I pushed a new branch to fix the issues with is_isomorphic, and in particular with graph_isom_equivalent_non_edge_labeled_graph. It seems to fix all remaining failing doctests in generic_graph.py in Python 3.

It took me some time to understand the method, and in particular why and when sort is needed. I reduced the number of places where sort is used, and used sorted(..., key=str) to sort hazardous objects (i.e., list of edge labels). For sure some users will invent another kind of edge labels for which this will not work, but unless we implement everywhere the remarks of #comment:7, and so force the user to specify the sort method, I don't see how we can magically answer all requirements.

Help needed: I use method filterfalse from itertools, but it'ss called ifilterfalse in Python 2 and filterfalse in Python 3. I used a try .. except to import it, but there is certainly a smarter way.

Please review, check, double check, do some tests, etc.

---

New commits:

​27ca32d

trac #27232: fix **morphism**

[tscrim]

Replying to dcoudert:

Help needed: I use method filterfalse from itertools, but it'ss called ifilterfalse in Python 2 and filterfalse in Python 3. I used a try .. except to import it, but there is certainly a smarter way.

Get rid of filterfalse:

-    for label in filterfalse(edge_labels.__contains__, G.edge_labels()):
+    for label in G.edge_labels():
+        if label in edge_labels:
+            continue

Although I might also unroll G.edge_labels() and do

    for _,_,label in G.edge_iterator():
        if label in edge_labels:
            continue

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​1b9879a

trac #27232: get rid of filterfalse

[dcoudert]

done.

There is this doctest error:

sage -t --long src/sage/combinat/root_system/coxeter_matrix.py
**********************************************************************
File "src/sage/combinat/root_system/coxeter_matrix.py", line 1041, in sage.combinat.root_system.coxeter_matrix.recognize_coxeter_type_from_matrix
Failed example:
    CoxeterMatrix(CoxeterType(['A',10,1]).coxeter_graph()).coxeter_type()
Expected:
    Coxeter type of ['A', 10, 1]
Got:
    Coxeter type of ['A', 10, 1] relabelled by {0: 2, 1: 3, 2: 4, 3: 5, 4: 6, 5: 7, 6: 8, 7: 9, 8: 10, 9: 0, 10: 1}

Can anyone tell if it's something serious or if it is sufficient to replace the expected output or the example.

[tscrim]

You should not update the output for this test. Here there is an implicit ordering on the vertices and it is not detecting that they should match (instead it is a rotation of the cycle graph by 2 steps). This might be a case where we should force the isomorphism test to (attempt to) sort the output as we need this labeling to be canonical (as there are generally non-trivial automorphisms as in this example).

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​0df542d	trac #27232: Merged with 8.7.beta7
​c4e8db7	trac #27232: fix issue in coxeter_matrix

[dcoudert]

Right, we need a method returning a total ordering of hashable (vertices) or unhashable (labels) objects. It's the only way to ensure the correctness of the methods here. But how to write something reasonably fast ? and where to put it ?

[dimpase]

Maybe functools.cmp_to_key(func) from ​https://docs.python.org/3/library/functools.html ?

[dcoudert]

Replying to dimpase:

Maybe functools.cmp_to_key(func) from ​https://docs.python.org/3/library/functools.html ?

But what should be the function ?

[dimpase]

Replying to dcoudert:

Replying to dimpase:

Maybe functools.cmp_to_key(func) from ​https://docs.python.org/3/library/functools.html ?

But what should be the function ?

the comparison used in Python2, I gather.

[dcoudert]

the comparison used in Python2, I gather.

But we don't have it, right ?

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​4637581

trac #27232: pyflakes

[embray]

Ticket retargeted after milestone closed (if you don't believe this ticket is appropriate for the Sage 8.8 release please retarget manually)