Spelling corrections

A number of spelling corrections as reported by the codespell (see: https://github.com/codespell-project/codespell) program and lists.

Some remarks:
- not considered are grammatical errors
- not considered are names in the code although there are a number that could be improved (like `childs` -> `children`)
- in the documentation it could be made clearer what are variables and what is running text (e.g. by placing variables in running text between backticks)
- some comments are in the French language, I think it would be better to have them in the English (United States version).

5 files changed, 5 insertions, 5 deletions

diff --git a/src/Persistent_cohomology/benchmark/performance_rips_persistence.cpp b/src/Persistent_cohomology/benchmark/performance_rips_persistence.cpp
index 030b072a..3bec8830 100644
--- a/src/Persistent_cohomology/benchmark/performance_rips_persistence.cpp
+++ b/src/Persistent_cohomology/benchmark/performance_rips_persistence.cpp
@@ -49,7 +49,7 @@ void timing_persistence(FilteredComplex & cpx
  * with a Hasse diagram. The Hasse diagram represents explicitly all 
  * codimension 1 incidence relations in the complex, and hence leads to 
  * a faster computation of persistence because boundaries are precomputed. 
- * Hovewer, the simplex tree may be constructed directly from a point cloud and
+ * However, the simplex tree may be constructed directly from a point cloud and
  * is more compact.
  * We compute persistent homology with coefficient fields Z/2Z and Z/1223Z.
  * We present also timings for the computation of multi-field persistent 
diff --git a/src/Persistent_cohomology/example/custom_persistence_sort.cpp b/src/Persistent_cohomology/example/custom_persistence_sort.cpp
index 410cd987..bba0b2f7 100644
--- a/src/Persistent_cohomology/example/custom_persistence_sort.cpp
+++ b/src/Persistent_cohomology/example/custom_persistence_sort.cpp
@@ -33,7 +33,7 @@ using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomolog
       Gudhi::persistent_cohomology::Field_Zp >;
 
 std::vector<Point> random_points() {
-  // Instanciate a random point generator
+  // Instantiate a random point generator
   CGAL::Random rng(0);
 
   // Generate "points_number" random points in a vector
diff --git a/src/Persistent_cohomology/example/persistence_from_simple_simplex_tree.cpp b/src/Persistent_cohomology/example/persistence_from_simple_simplex_tree.cpp
index bffaabdd..3da6771e 100644
--- a/src/Persistent_cohomology/example/persistence_from_simple_simplex_tree.cpp
+++ b/src/Persistent_cohomology/example/persistence_from_simple_simplex_tree.cpp
@@ -95,7 +95,7 @@ int main(int argc, char * const argv[]) {
   SimplexVector = {9, 10, 11};
   st.insert_simplex_and_subfaces(SimplexVector, 0.3);
 
-  // ++ NINETH
+  // ++ NINTH
   std::clog << "   - INSERT (2,10,12)" << std::endl;
   SimplexVector = {2, 10, 12};
   st.insert_simplex_and_subfaces(SimplexVector, 0.3);
diff --git a/src/Persistent_cohomology/example/rips_multifield_persistence.cpp b/src/Persistent_cohomology/example/rips_multifield_persistence.cpp
index 2edf5bc4..d154bcde 100644
--- a/src/Persistent_cohomology/example/rips_multifield_persistence.cpp
+++ b/src/Persistent_cohomology/example/rips_multifield_persistence.cpp
@@ -104,7 +104,7 @@ void program_options(int argc, char * argv[]
       ("min-field-charac,p", po::value<int>(&min_p)->default_value(2),
        "Minimal characteristic p of the coefficient field Z/pZ.")
       ("max-field-charac,q", po::value<int>(&max_p)->default_value(1223),
-       "Minimial characteristic q of the coefficient field Z/pZ.")
+       "Minimal characteristic q of the coefficient field Z/pZ.")
       ("min-persistence,m", po::value<Filtration_value>(&min_persistence),
        "Minimal lifetime of homology feature to be recorded. Default is 0");
 
diff --git a/src/Persistent_cohomology/include/gudhi/Persistent_cohomology.h b/src/Persistent_cohomology/include/gudhi/Persistent_cohomology.h
index d428e497..2301a66b 100644
--- a/src/Persistent_cohomology/include/gudhi/Persistent_cohomology.h
+++ b/src/Persistent_cohomology/include/gudhi/Persistent_cohomology.h
@@ -211,7 +211,7 @@ class Persistent_cohomology {
   /** \brief Update the cohomology groups under the insertion of an edge.
    *
    * The 0-homology is maintained with a simple Union-Find data structure, which
-   * explains the existance of a specific function of edge insertions. */
+   * explains the existence of a specific function of edge insertions. */
   void update_cohomology_groups_edge(Simplex_handle sigma) {
     Simplex_handle u, v;
     boost::tie(u, v) = cpx_->endpoints(sigma);