py3: automorphism_group, canonical_label, canonical_form and doctest in MathonPseudocyclicStronglyRegularGraph

[dcoudert]

This ticket fix py3 failing doctest in graphs.MathonPseudocyclicStronglyRegularGraph:

Failed example:
    L = sum(i*(r[a]-r[b]) for i,(a,b) in zip(range(1,len(ff)+1), ff)); L
Expected:
    [ 0  1 -1 -3 -2 -4  3  4  2]
    [-1  0  1 -4 -3 -2  2  3  4]
    [ 1 -1  0 -2 -4 -3  4  2  3]
    [ 3  4  2  0  1 -1 -3 -2 -4]
    [ 2  3  4 -1  0  1 -4 -3 -2]
    [ 4  2  3  1 -1  0 -2 -4 -3]
    [-3 -2 -4  3  4  2  0  1 -1]
    [-4 -3 -2  2  3  4 -1  0  1]
    [-2 -4 -3  4  2  3  1 -1  0]
Got:
    [ 0  1  4  2 -3 -1 -4 -2  3]
    [-1  0  3  4 -4  1 -2 -3  2]
    [-4 -3  0  1  2 -2  4  3 -1]
    [-2 -4 -1  0  4 -3  3  2  1]
    [ 3  4 -2 -4  0  2 -1  1 -3]
    [ 1 -1  2  3 -2  0 -3 -4  4]
    [ 4  2 -4 -3  1  3  0 -1 -2]
    [ 2  3 -3 -2 -1  4  1  0 -4]
    [-3 -2  1 -1  3 -4  2  4  0]

and

Failed example:
    G9.automorphism_group(algorithm="bliss").order() # optional - bliss
Expected:
    9
Got:
    3

in this ticket, we do

• ensure that the ordering with 'sage' and 'bliss' is the same in automorphism_group and canonical_label/canonical_form
• clean bliss to avoid for instance indexing a dictionary with a possibly not hashable key. The new solution is slower but safe.
• specify the partition in the doctest of MathonPseudocyclicStronglyRegularGraph to make the doctest stable with py2 and py3
• pass correct domain to PermutationGroup in bliss.pyx

[dcoudert]

New commits:

​45630b8

trac #27571: fix a doctest in families.py

[dcoudert]

previous branch was not correct (direct modification of develop. oups..)

---

New commits:

​88bde07

trac #27571: fix a doctest in MathonPseudocyclicStronglyRegularGraph

[git]

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

​cedcb22

trac #27571: clean bliss, canonical_form, and automorphism_group

[git]

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

​9006edb

trac #27571: remove not tested tag in petersen_family

[dcoudert]

With py3 I regularly tag has not tested the doctest of pertersen_family. This is a bug reported in #26800...

[git]

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

​7598b52	trac #27571: Merged with 8.8.beta0
​8fcd584	trac #27571: mark a doctest printing a dictionary py2 py3

[dcoudert]

I tried to investigate further on the possible cause of the issues with automorphism_group and the Python3 failing doctests in src/sage/graphs/generators/families.py.

The good news is that we have the same result with 'bliss' and 'sage'

sage: G = graphs.PaleyGraph(9)
sage: a = G.automorphism_group(partition=[sorted(G)])
sage: it = (x for x in a.normal_subgroups() if x.order() == 9)
sage: subg = next(iter(it))
sage: r = [matrix(libgap.PermutationMat(libgap(z), 9).sage())
....:      for z in subg]
sage: ff = list(map(lambda y: (y[0]-1,y[1]-1),
....:          Permutation(map(lambda x: 1+r.index(x^-1), r)).cycle_tuples()[1:]))
sage: L = sum(i*(r[a]-r[b]) for i,(a,b) in zip(range(1,len(ff)+1), ff)); L
[ 0  1 -1 -3 -2 -4  3  4  2]
[-1  0  1 -4 -3 -2  2  3  4]
[ 1 -1  0 -2 -4 -3  4  2  3]
[ 3  4  2  0  1 -1 -3 -2 -4]
[ 2  3  4 -1  0  1 -4 -3 -2]
[ 4  2  3  1 -1  0 -2 -4 -3]
[-3 -2 -4  3  4  2  0  1 -1]
[-4 -3 -2  2  3  4 -1  0  1]
[-2 -4 -3  4  2  3  1 -1  0]

sage: G.relabel()
sage: G3x3=graphs.MathonPseudocyclicStronglyRegularGraph(2,G=G,L=L)
sage: G3x3.is_strongly_regular(parameters=True)
(441, 220, 109, 110)
sage: G3x3.automorphism_group(algorithm="bliss").order() # optional - bliss
3  # <-- expect 27 in Python 2 
sage: G3x3.automorphism_group(algorithm="sage").order() # long time
3  # <-- expect 27 in Python 2 

The issue may come from PermutationGroup that is used in both case...

[git]

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

​15790aa

trac #27571: fix merge conflict with 8.8.beta5

[dcoudert]

Any comment is more than welcome.

[dimpase]

hmm, I don't understand, are you saying there is a discrepancy between Python 2 and Python 3 answers?

[dcoudert]

Yes, the answer in py2 of sage: G3x3.automorphism_group(algorithm="sage").order() is different than in py3. have no clue whats going on.

Here, I try to align the behaviors with sage and bliss, and fix an issue in MathonPseudocyclicStronglyRegularGraph.

[dimpase]

I presume that py2 is giving the correct answer, right?

[dcoudert]

I don't know. We should ask experts in these graph and methods.

[dimpase]

why would you think there is graphs.PasechnikGraph(..) there? you are talking to one of them ;-)

$ git blame src/sage/graphs/generators/families.py
...
4c7cb931a9b (Dima Pasechnik    2015-11-07 17:41:10 +0000 3124) def MathonPseudocyclicStronglyRegularGraph(t, G=None, L=None):
...

you can take canonical forms of G3x3 in py2 and in py3, in py2 compute G3x3.canonical_label().automorphism_group() (of order 27) and check that it is also an automorphism group for G3x3 in py3. (you should also chech that the canonical labellings are the same, naturally)

I guess it's a bug in py3 implementation (or in bliss)

[dcoudert]

you can take canonical forms of G3x3 in py2 and in py3, in py2 compute G3x3.canonical_label().automorphism_group() (of order 27) and check that it is also an automorphism group for G3x3 in py3.

How can I do that ?

(you should also chech that the canonical labellings are the same, naturally)

Since we try to avoid sorting vertices, canonical labels in py2 and py3 have no reason to be the same. And, we use partition = [list(self)]

I guess it's a bug in py3 implementation (or in bliss)

I don't know. I'm having hard time trying to understand this code.

I'll be happy if we could at least finalize this ticket, and possibly let the other issue for another dedicated ticket.

[dimpase]

Replying to dcoudert:

you can take canonical forms of G3x3 in py2 and in py3, in py2 compute G3x3.canonical_label().automorphism_group() (of order 27) and check that it is also an automorphism group for G3x3 in py3.

How can I do that ?

G3x3.canonical_label().automorphism_group() gives the group by a list of generators, so apply each of them to the other graph...

(you should also chech that the canonical labellings are the same, naturally)

Since we try to avoid sorting vertices, canonical labels in py2 and py3 have no reason to be the same. And, we use partition = [list(self)]

well, this is manifestly not true - canonical means lexicographically minimal (or maximal) 0-1 adjacency matrix (converted into a vector). A non-lexicographically optimal "canonical" is not canonical...

[dcoudert]

G3x3.canonical_label().automorphism_group() gives the group by a list of generators, so apply each of them to the other graph...

I really don't know how to do that. I have never studied or used these tools.

[dimpase]

Well, applying a permutation p to a a graph g is just g.relabel(perm=p). E.g.

sage: g=graphs.PetersenGraph()
sage: aut=g.automorphism_group()
sage: amat=g.adjacency_matrix()
sage: g.relabel(perm=aut.gens()[0])
sage: amat==g.adjacency_matrix()  # as expected, as a.gens() are automorphims of g
True
age: p=PermutationGroupElement("(1,2,3,4,5,6,7,8,9,10)")
sage: g.relabel(perm=p)           # but p is not
sage: amat==g.adjacency_matrix()  # so the adjacency matrix gets changed
False

[dcoudert]

I tried this with Python 2 with and without this patch and get the same error:

sage: g = graphs.PetersenGraph()
sage: h = g.canonical_label()
sage: aut = h.automorphism_group()
sage: aut
Permutation Group with generators [(3,6)(4,7)(5,9), (1,4)(2,6)(5,7)(8,9), (0,1)(3,4)(6,7)]
sage: list(aut.gens())
[(3,6)(4,7)(5,9), (1,4)(2,6)(5,7)(8,9), (0,1)(3,4)(6,7)]
sage: amat = h.adjacency_matrix()
sage: p = PermutationGroupElement("(3,6)(4,7)(5,9)")
sage: h.relabel(inplace=False, perm=p).adjacency_matrix() == amat
True
sage: p = PermutationGroupElement("(1,4)(2,6)(5,7)(8,9)")
sage: h.relabel(inplace=False, perm=p).adjacency_matrix() == amat
True
sage: p = PermutationGroupElement("(0,1)(3,4)(6,7)")
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-15-d9b1c60b9f74> in <module>()
----> 1 p = PermutationGroupElement("(0,1)(3,4)(6,7)")

/Users/dcoudert/sage/local/lib/python2.7/site-packages/sage/groups/perm_gps/permgroup_element.pyx in sage.groups.perm_gps.permgroup_element.PermutationGroupElement.__init__ (build/cythonized/sage/groups/perm_gps/permgroup_element.c:5853)()
    502 
    503         degree = max([1] + [max(cycle+(1,)) for cycle in v])
--> 504         v = from_cycles(degree, v)
    505 
    506         self.__gap = 'PermList({})'.format(list(v)) # Make sure it is a list

/Users/dcoudert/sage/local/lib/python2.7/site-packages/sage/combinat/permutation.pyc in from_cycles(n, cycles, parent)
   7041     # Only positive elements
   7042     if int(flattened_and_sorted[0]) < 1:
-> 7043         raise ValueError("All elements should be strictly positive "
   7044                          "integers, and I just found a non-positive one.")
   7045 

ValueError: All elements should be strictly positive integers, and I just found a non-positive one.

[dimpase]

probably there must be commas between cycles. check the docs on the function you get the error in.

e.g. [(1,2),(3,4)] should. away from the kbd now, in a train, sorry.

[dcoudert]

The format of the input is ok. I tried PermutationGroupElement([(0,1), (3,4), (6,7)]) with same result (i.e., error).

As I said, this ticket fixes 1 doctest and aligns the behaviors of the implementations bliss and sage. I don't understand the problem with automorphisms, permutation groups, etc. and so I propose to let the resolution of thee issues to another ticket with experts in these questions.

[dimpase]

It is a bug in the constructor of PermutationGroupElement. The code assumes that 0 is not in the domain...

A workaround would be to relabel the graph vertices from 1, to n, not from 0 to n-1. OK, our flight is boarding, need to go :-)

[dcoudert]

Should we open a new ticket for the bug in PermutationGroupElement ?

[dimpase]

Replying to dcoudert:

Should we open a new ticket for the bug in PermutationGroupElement ?

I just opened a ticket for this, see #27881

[dimpase]

To test if automorphisms are OK, one can also convert permutations into matrices.

sage: G3x3=G3x3.canonical_label()
sage: a=G3x3.automorphism_group()
sage: pm=map(lambda t: t.matrix(), a.gens())
sage: am=G3x3.adjacency_matrix()
sage: map(lambda t: t*am==am*t, pm)
[True, True, True]

So one can output matrices in py2 and input in py3, and do the check. (assuming G3x3 is already in canonical label form in both)

[dcoudert]

Running the example with py3 gives [False] with this patch

sage: G = graphs.PaleyGraph(9)
sage: a = G.automorphism_group(partition=[sorted(G)])
sage: it = (x for x in a.normal_subgroups() if x.order() == 9)
sage: subg = next(iter(it))
sage: r = [matrix(libgap.PermutationMat(libgap(z), 9).sage())
....:      for z in subg]
sage: ff = list(map(lambda y: (y[0]-1,y[1]-1),
....:          Permutation(map(lambda x: 1+r.index(x^-1), r)).cycle_tuples()[1:]))
sage: L = sum(i*(r[a]-r[b]) for i,(a,b) in zip(range(1,len(ff)+1), ff)); L
[ 0  1 -1 -3 -2 -4  3  4  2]
[-1  0  1 -4 -3 -2  2  3  4]
[ 1 -1  0 -2 -4 -3  4  2  3]
[ 3  4  2  0  1 -1 -3 -2 -4]
[ 2  3  4 -1  0  1 -4 -3 -2]
[ 4  2  3  1 -1  0 -2 -4 -3]
[-3 -2 -4  3  4  2  0  1 -1]
[-4 -3 -2  2  3  4 -1  0  1]
[-2 -4 -3  4  2  3  1 -1  0]
sage: G.relabel()
sage: G3x3=graphs.MathonPseudocyclicStronglyRegularGraph(2,G=G,L=L)
sage: G3x3 = G3x3.canonical_label()
sage: a = G3x3.automorphism_group()
sage: pm = list(map(lambda t: t.matrix(), a.gens()))
sage: am = G3x3.adjacency_matrix()
sage: list(map(lambda t: t*am==am*t, pm))
[False]

and without this patch, we get

[False, False, False]

[dimpase]

thus, it was broken before the patch, as [False, False, False] is obviously not correct (probably due to incorrect indexing of vertices), and even more broken after the patch, which appears to break either the construction of the graph, or the very computation of the automorphism group. :-(

To rule out that the construction gets broken, can you compare the adjacency matrices of the canonical label computed with py2, with the one computed with py3?

[dimpase]

even quicker might be to compare G3x3.graph6_string() here is what I get with py2

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[dcoudert]

py3 without this patch and no canonical labeling

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py3 without this patch but with canonical labeling

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py3 with this patch but no canonical labeling

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py3 with this patch and canonical labeling

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[dimpase]

OK, I checked these 4 graphs, and it appears that the 1st two are not isomorphic to the 2nd two (assuming we trust our py2 implementations of automorphism computations - the 1st two have groups of order 27, teh 2nd two of order 3). Quite unexpectedly to me, the 2nd two are strongly regular with the same parameters as the 1st two (this explains why it takes forever to try to compute isomorphisms).

So this invalidates my claim that the automorphism computation broke, it's the construction of this particular graph that broke (a bit).

[dcoudert]

I can not help for checking the validity of MathonPseudocyclicStronglyRegularGraph...

[dimpase]

The fact is that this doctest the latter produces different results in py2 and py3.

I understand that there is a way to skip a test for py3, so this can be done here, and another py3-specific ticket opened to deal with the discrepancy.

[dcoudert]

You mean that we should hide the py3 failing doctest ? Is it really useful ?

Currently, this ticket align the behaviors of the 2 methods ('sage' and 'bliss'), do some cleaning and fix 1 doctest for py3. The other issues for which further work is needed are not touched.

[dimpase]

Replying to dcoudert:

I tried to investigate further on the possible cause of the issues with automorphism_group and the Python3 failing doctests in src/sage/graphs/generators/families.py.

The good news is that we have the same result with 'bliss' and 'sage'

sage: G = graphs.PaleyGraph(9)
sage: a = G.automorphism_group(partition=[sorted(G)])
sage: it = (x for x in a.normal_subgroups() if x.order() == 9)
sage: subg = next(iter(it))
sage: r = [matrix(libgap.PermutationMat(libgap(z), 9).sage())
....:      for z in subg]
sage: ff = list(map(lambda y: (y[0]-1,y[1]-1),
....:          Permutation(map(lambda x: 1+r.index(x^-1), r)).cycle_tuples()[1:]))
sage: L = sum(i*(r[a]-r[b]) for i,(a,b) in zip(range(1,len(ff)+1), ff))
sage: G.relabel()
sage: G3x3=graphs.MathonPseudocyclicStronglyRegularGraph(2,G=G,L=L)
sage: G3x3.is_strongly_regular(parameters=True)
(441, 220, 109, 110)
sage: G3x3.automorphism_group(algorithm="bliss").order() # optional - bliss
3  # <-- expect 27 in Python 2 
sage: G3x3.automorphism_group(algorithm="sage").order() # long time
3  # <-- expect 27 in Python 2 

The issue may come from PermutationGroup that is used in both case...

I'm checking this example in Py3, comparing with Py2, and I see that G.relabel() is the place where the first discrepancy occurs. Namely, the order of the new vertices in Py3 differs from the one in Py2, where the order is the same as in the output of G.vertices() before relabeling.

In Py2 the edge (0,1), where 0,1 are elements of the finite field GF(9), and they also come the 1st in G.vertices(), is mapped by relabeling to (0,1), but in Py3 this edge is gone.

Is there a way to force G.relabel() to keep the order of G.vertices()?

[dimpase]

In fact, this looks like a Py3-bug to me.

sage: G = graphs.PaleyGraph(9); G.relabel() 
sage: graphs.PaleyGraph(9).adjacency_matrix()==G.adjacency_matrix() # Py3 -in Py2 it's True
False

It is really totally unexpected that G.relabel() breaks the ordering. Imagine G being in the canonical form, and then G.relabel() breaking it.

I think G.relabel() must leave the adjacency matrix of G intact.

[dcoudert]

I disagree with that. The only way to preserve the ordering is to sort vertex labels, and we want to avoid sorting as much as possible in py3. If a user wants a specific ordering, it is possible to use G.relabel(perm=G.vertices()). Similarly for the adjacency matrix, we can now specify the ordering of the vertices.

Now, for the canonical labeling, the labeling is not unique. It depends on the algorithm used ('sage' and 'bliss' can give different answers), and also on vertex labels.

So we need to find another solution.

[git]

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

​ad9b46f

relabel with an identity perm

[dimpase]

this commit should do the trick, at least this fixes the two failing doctest in src/sage/graphs/generators/families.py for this branch on Py3.

[dimpase]

OK

[chapoton]

failing patchbot is not compatible with positive review :

sage -t --long src/sage/geometry/polyhedron/ppl_lattice_polytope.py
**********************************************************************
File "src/sage/geometry/polyhedron/ppl_lattice_polytope.py", line 986, in sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class.restricted_automorphism_group
Failed example:
    set(G.domain()) == set(Z3square.vertices())
Expected:
    True
Got:
    False

[dimpase]

indeed, None in the domain of the group G below, due to something wrong in this branch.

sage: from sage.geometry.polyhedron.ppl_lattice_polytope import LatticePolytope_PPL
sage: Z3square = LatticePolytope_PPL((0,0), (1,2), (2,1), (3,3))
sage: Z3square.restricted_automorphism_group(vertex_labels=(1,2,3,4)) == PermutationGroup([[(2,3)],[(1,2),(3,4)]])
True
sage: G = Z3square.restricted_automorphism_group()
sage: G == PermutationGroup([[((1,2),(2,1))],[((0,0),(1,2)),((2,1),(3,3))],[((0,0),(3,3))]])
True
sage: G.domain()
{(0, 0), (1, 2), (2, 1), (3, 3), None, None, None, None}
sage: Z3square.vertices()
((0, 0), (1, 2), (2, 1), (3, 3))
sage: set(G.domain())
{None, (0, 0), (1, 2), (2, 1), (3, 3)}

[dimpase]

to narrow this None nonsense down; in this branch one gets:

sage: G=Graph([(0, 1, 1/4), (0, 2, 1/4), (0, 3, -1/4), (1, 2, -1/4), (1, 3, 1/4), (2, 3, 1/4)])
sage: a=G.automorphism_group(edge_labels=True)
sage: a.domain()
{0, 1, 2, 3, None, None, None, None}

[dimpase]

even more specifically, the problem is in bliss interface:

sage: a=G.automorphism_group(edge_labels=True, algorithm="sage")
sage: a.domain()
{0, 1, 2, 3}
sage: a=G.automorphism_group(edge_labels=True, algorithm="bliss")
sage: a.domain()
{0, 1, 2, 3, None, None, None, None}

[dimpase]

OK, so the bug is here in src/sage/graphs/bliss.pyx:

     gens = automorphism_group_gens_from_edge_list(Vnr, Vout, Vin, Lnr, labels, int2vert, partition, directed)
 
     from sage.groups.perm_gps.permgroup import PermutationGroup
-    return PermutationGroup(gens, domain=list(G))
+    return PermutationGroup(gens, domain=int2vert)

this change does not take into account that automorphism_group_gens_from_edge_list modifies int2vert for edge-labelled graphs (bliss cannot do edge-labelled graphs directly, and so a bunch of axiliary vertices and edges is created to deal with them). (Specifically, adds stuff to the end of the list; so one can return the original slice of int2vert).

88bde074188 (David Coudert     2019-03-30 15:45:07 +0100 741)     return PermutationGroup(gens, domain=int2vert)

David, can you fix this?

[git]

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

​a4fb23b	trac #27571: Merged with 8.8.beta7
​50a69e8	trac #27571: give correct domain

[dcoudert]

Thank you Dima for identifying this issue. Fixed.

[chapoton]

green bot. back to needs review ?

[dcoudert]

Yes, forgot to set it back. Thanks.

[dcoudert]

I have updated the ticket description as this ticket fix all doctests in families.py.

[dimpase]

Could you rather chop off the extra tail grown in automorphism_group_gens_from_edge_list rather than creating yet another list?

[git]

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

​93a2a53	trac #27571: Merged with 8.8.rc0
​2136e19	trac #27571: avoid creating an extra variable for the domain

[dcoudert]

Done.

[dimpase]

IMHO the latest commit creates a memory leak. These extra entries for the domain need to be explicitly deallocated in automorphism_group_gens_from_edge_list, no?

[dcoudert]

Are you sure ? int2vert[:G.order()] gives a new sublist (a copy?) to PermutationGroup, no? and then variable int2vert is deallocated.

[dimpase]

OK. It's fine, I didn't pay attention to int2vert being a Python list.

[dcoudert]

Thank you.

[embray]

Not in Sage 8.8. Let's please to try keep tickets' milestones related to the release in which we actually intend to include them, and in particular the release in which they were actually included, especially when closing tickets.