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Improve PolynomialSequence.connection_graph() implementation #35512

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merged 3 commits into from
Apr 23, 2023
Merged

Improve PolynomialSequence.connection_graph() implementation #35512

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eafa33c
Fix Graph.add_clique() for one vertex
tornaria Apr 8, 2023
8d8289b
Improve PolynomialSequence.connection_graph()
tornaria Apr 8, 2023
850c883
mps.connection_graph(): tests to document behavior
tornaria Apr 16, 2023
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4 changes: 4 additions & 0 deletions src/sage/graphs/generic_graph.py
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Original file line number Diff line number Diff line change
Expand Up @@ -18371,6 +18371,9 @@ def add_clique(self, vertices, loops=False):
True
sage: G.vertices(sort=True)
[0, 1, 2, 3]
sage: G.add_clique({4})
sage: G.vertices(sort=True)
[0, 1, 2, 3, 4]
sage: D = DiGraph(4, loops=True)
sage: D.add_clique(range(4), loops=True)
sage: D.is_clique(directed_clique=True, loops=True)
Expand All @@ -18383,6 +18386,7 @@ def add_clique(self, vertices, loops=False):
else:
self.add_edges(itertools.combinations_with_replacement(vertices, 2))
else:
self.add_vertices(vertices)
if self.is_directed():
self.add_edges(itertools.permutations(vertices, 2))
else:
Expand Down
13 changes: 7 additions & 6 deletions src/sage/rings/polynomial/multi_polynomial_sequence.py
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Original file line number Diff line number Diff line change
Expand Up @@ -907,16 +907,17 @@ def connection_graph(self):
sage: F = Sequence([x*y + y + 1, z + 1])
sage: F.connection_graph()
Graph on 3 vertices
sage: F = Sequence([x*y*z])
sage: F.connection_graph().is_clique()
True
sage: F = Sequence([x*y, y*z])
sage: F.connection_graph().is_clique()
False
"""
V = sorted(self.variables())
from sage.graphs.graph import Graph
g = Graph()
g.add_vertices(sorted(V))
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I do not think it is a good idea to remove this line. The point being that you want vertices to represent the variables of the underlying polynomial ring. With this removal it is not the case

sage: B.<x,y,z> = BooleanPolynomialRing()
sage: F = Sequence([B.one()])
sage: F.connection_graph()   # must be a graph on three vertices and no edges

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No, that's not what this line does, since V = self.variables(). Current behaviour:

$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Using Python 3.11.3. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
sage: B.<x,y,z> = BooleanPolynomialRing()
sage: Sequence([x]).connection_graph()
Graph on 1 vertex

In fact, your example is currently broken:

sage: Sequence([B.one()]).connection_graph()
...
IndexError: tuple index out of range

With my patch:

sage: Sequence([B.one()]).connection_graph()
Graph on 0 vertices

I grant that these two examples should be added to the doctest. The "correct" behaviour depends on interpretation of "Return the graph which has the variables of this system as vertices...".

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I added all of these tests to document behaviour:

            sage: F = Sequence([], B)
            sage: F.connection_graph()
            Graph on 0 vertices
            sage: F = Sequence([1], B)
            sage: F.connection_graph()
            Graph on 0 vertices
            sage: F = Sequence([x])
            sage: F.connection_graph()
            Graph on 1 vertex
            sage: F = Sequence([x, y])
            sage: F.connection_graph()
            Graph on 2 vertices

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@videlec if you are satisfied, please don't forget to approve / positive_review. Thanks!

for f in self:
v = f.variables()
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a,tail = v[0],v[1:]
for b in tail:
g.add_edge((a,b))
g.add_clique(f.variables())
return g

def connected_components(self):
Expand Down