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diff --git a/src/cython/doc/source/witness_complex_user.rst b/src/cython/doc/source/witness_complex_user.rst
index 698e5441..604c7357 100644
--- a/src/cython/doc/source/witness_complex_user.rst
+++ b/src/cython/doc/source/witness_complex_user.rst
@@ -6,3 +6,26 @@ Definition
.. include:: witness_complex_sum.rst
+Implementation
+--------------
+
+The principal class of this module is Gudhi::Witness_complex.
+
+In both cases, the constructor for this class takes a {witness}x{closest_landmarks} table, where each row represents a
+witness and consists of landmarks sorted by distance to this witness.
+
+.. todo::
+ This table can be constructed by two additional classes Landmark_choice_by_furthest_point and
+ Landmark_choice_by_random_point also included in the module.
+
+.. figure::
+ img/bench_Cy8.png
+ :align: center
+
+ Running time as function on number of landmarks.
+
+.. figure::
+ img/bench_sphere.png
+ :align: center
+
+ Running time as function on number of witnesses for |L|=300.