gh-37835: Optimize DisjointSet

    
The methods `find` and `union` of the class `DisjointSet_of_hashables`
pass through an unnecessary layer of input checks that slow down the
code. I avoided these checks, cythonized more of the code, and edited
the docstrings.

I can attest to the fact that these changes improve speed, and in a
follow-up PR (#37839) I mention a test that confirms this.
    
URL: #37835
Reported by: gmou3
Reviewer(s): gmou3, Martin Rubey, Travis Scrimshaw, Vincent Delecroix

src/sage/groups/perm_gps/partn_ref/data_structures.pxd

@@ -114,7 +114,7 @@ cdef inline int OP_find(OrbitPartition *OP, int n) noexcept:
         OP.parent[n] = OP_find(OP, OP.parent[n])
         return OP.parent[n]
 
-cdef inline int OP_join(OrbitPartition *OP, int m, int n) noexcept:
+cdef inline void OP_join(OrbitPartition *OP, int m, int n) noexcept:
     """
     Join the cells containing m and n, if they are different.
     """

src/sage/sets/disjoint_set.pxd

@@ -11,13 +11,25 @@
 from sage.groups.perm_gps.partn_ref.data_structures cimport OrbitPartition
 from sage.structure.sage_object cimport SageObject
 
+cpdef DisjointSet(arg)
+
 cdef class DisjointSet_class(SageObject):
     cdef OrbitPartition *_nodes
+    cpdef cardinality(self)
+    cpdef number_of_subsets(self)
 
 cdef class DisjointSet_of_integers(DisjointSet_class):
-    pass
+    cpdef int find(self, int i)
+    cpdef void union(self, int i, int j)
+    cpdef root_to_elements_dict(self)
+    cpdef element_to_root_dict(self)
+    cpdef to_digraph(self)
 
 cdef class DisjointSet_of_hashables(DisjointSet_class):
     cdef list _int_to_el
     cdef dict _el_to_int
-    cdef DisjointSet_of_integers _d
+    cpdef find(self, e)
+    cpdef void union(self, e, f)
+    cpdef root_to_elements_dict(self)
+    cpdef element_to_root_dict(self)
+    cpdef to_digraph(self)