src/sage/graphs/generators: add Golay code graph pytests

The algorithm to construct the Shortened 000 111 extended binary Golay
code graph takes a long time, and we plan to cache its vertices and
edges. To ensure that the cached data continue to agree with the
construction, we add a new pytest file that checks the two for
isomorphism.

Author: orlitzky

src/sage/graphs/generators/generators_test.py

@@ -0,0 +1,33 @@
+import pytest
+
+def test_shortened_000_111_extended_binary_Golay_code_graph():
+    r"""
+    Test that Sage produces a graph isomorphic to the one that we
+    get from this construction.
+
+    The construction itself takes a long time.
+    """
+    from sage.coding import codes_catalog
+    from sage.coding.linear_code import LinearCode
+    from sage.graphs.generators.distance_regular import (
+      shortened_000_111_extended_binary_Golay_code_graph
+    )
+    from sage.matrix.constructor import matrix
+    from sage.rings.finite_rings.finite_field_constructor import FiniteField
+
+    code = codes_catalog.GolayCode(FiniteField(2))
+    C_basis = code.basis()
+
+    # now special shortening
+    v = C_basis[0] + C_basis[1] + C_basis[2]  # v has 111 at the start
+    C_basis = C_basis[3:]
+    C_basis.append(v)
+    C_basis = list(map(lambda x: x[3:], C_basis))
+
+    code = LinearCode(matrix(FiniteField(2), C_basis))
+    G = code.cosetGraph()
+    G.name("Shortened 000 111 extended binary Golay code")
+    assert G.is_distance_regular()
+
+    H = shortened_000_111_extended_binary_Golay_code_graph()
+    assert G.is_isomorphic(H)

src/sage/graphs/generators/meson.build

@@ -6,6 +6,7 @@ py.install_sources(
   'classical_geometries.py',
   'degree_sequence.py',
   'families.py',
+  'generators_test.py',
   'intersection.py',
   'platonic_solids.py',
   'random.py',