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diff --git a/src/python/test/test_simplex_generators.py b/src/python/test/test_simplex_generators.py
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+""" This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+    Author(s):       Marc Glisse
+
+    Copyright (C) 2020 Inria
+
+    Modification(s):
+      - YYYY/MM Author: Description of the modification
+"""
+
+import gudhi
+import numpy as np
+
+
+def test_flag_generators():
+    pts = np.array([[0, 0], [0, 1.01], [1, 0], [1.02, 1.03], [100, 0], [100, 3.01], [103, 0], [103.02, 3.03]])
+    r = gudhi.RipsComplex(points=pts, max_edge_length=4)
+    st = r.create_simplex_tree(max_dimension=50)
+    st.persistence()
+    g = st.flag_persistence_generators()
+    assert np.array_equal(g[0], [[2, 2, 0], [1, 1, 0], [3, 3, 1], [6, 6, 4], [5, 5, 4], [7, 7, 5]])
+    assert len(g[1]) == 1
+    assert np.array_equal(g[1][0], [[3, 2, 2, 1]])
+    assert np.array_equal(g[2], [0, 4])
+    assert len(g[3]) == 1
+    assert np.array_equal(g[3][0], [[7, 6]])
+    # Compare trivial cases (where the simplex is the generator) with persistence_pairs.
+    # This still makes assumptions on the order of vertices in a simplex and could be more robust.
+    pairs = st.persistence_pairs()
+    assert {tuple(i) for i in g[0]} == {(i[0][0],) + tuple(i[1]) for i in pairs if len(i[0]) == 1 and len(i[1]) != 0}
+    assert {(i[0], i[1]) for i in g[1][0]} == {tuple(i[0]) for i in pairs if len(i[0]) == 2 and len(i[1]) != 0}
+    assert set(g[2]) == {i[0][0] for i in pairs if len(i[0]) == 1 and len(i[1]) == 0}
+    assert {(i[0], i[1]) for i in g[3][0]} == {tuple(i[0]) for i in pairs if len(i[0]) == 2 and len(i[1]) == 0}
+
+
+def test_lower_star_generators():
+    st = gudhi.SimplexTree()
+    st.insert([0, 1, 2], -10)
+    st.insert([0, 3], -10)
+    st.insert([1, 3], -10)
+    st.assign_filtration([2], -1)
+    st.assign_filtration([3], 0)
+    st.assign_filtration([0], 1)
+    st.assign_filtration([1], 2)
+    st.make_filtration_non_decreasing()
+    st.persistence(min_persistence=-1)
+    g = st.lower_star_persistence_generators()
+    assert len(g[0]) == 2
+    assert np.array_equal(g[0][0], [[0, 0], [3, 0], [1, 1]])
+    assert np.array_equal(g[0][1], [[1, 1]])
+    assert len(g[1]) == 2
+    assert np.array_equal(g[1][0], [2])
+    assert np.array_equal(g[1][1], [1])
+
+
+def test_empty():
+    st = gudhi.SimplexTree()
+    st.persistence()
+    assert st.lower_star_persistence_generators() == ([], [])
+    g = st.flag_persistence_generators()
+    assert np.array_equal(g[0], np.empty((0, 3)))
+    assert g[1] == []
+    assert np.array_equal(g[2], [])
+    assert g[3] == []