Doc fixes 2

src/aho-corasick.cpp

@@ -106,7 +106,7 @@ This function returns the index of the child of the node with index
 :param letter: the edge-label connecting the parent to the desired child.
 :type letter: int
 
-:returns: the index of the child.
+:returns: The index of the child.
 :rtype: int | Undefined
 
 :raises LibsemigroupsError:  if ``throw_if_node_index_not_active(parent)`` raises an exception.
@@ -126,7 +126,7 @@ Calculate the height of a node.
 :param i: the index of the node whose height is sought
 :type i: int
 
-:returns: the height.
+:returns: The height.
 :rtype: int
 
 :raises LibsemigroupsError:  if ``throw_if_node_index_not_active(i)`` raises an exception.

src/cong-common.cpp

@@ -313,7 +313,7 @@ had been newly constructed from *knd* and *p*.
 :param p: the presentation.
 :type p: Presentation
 
-:returns:  *self*.
+:returns: *self*.
 :rtype: {name}
 
 :raises LibsemigroupsError: if *p* is not valid.

src/dot.cpp

@@ -213,7 +213,7 @@ This function adds a node with name *name*.
 :param name: the name of the node to add.
 :type name: str
 
-:returns: a newly created :any:`Dot.Node` object with name *name*.
+:returns: A newly created :any:`Dot.Node` object with name *name*.
 :rtype: Dot.Node
 
 :raises LibsemigroupsError: if there is already a node with name *name*.
@@ -235,7 +235,7 @@ This function adds an edge from the node named *head* to the node named *tail*.
 :param tail: the name of the node at the tail of the edge.
 :type tail: str
 
-:returns: a newly created :any:`Dot.Edge` object.
+:returns: A newly created :any:`Dot.Edge` object.
 :rtype: Dot.Edge
 
 :raises LibsemigroupsError: if there is no node named *head* and/or *tail*.
@@ -326,7 +326,7 @@ the represented graph and ``False`` otherwise.
 :param name: the name of the node.
 :type name: str
 
-:returns: whether or not *name* is the name of a node.
+:returns: Whether or not *name* is the name of a node.
 :rtype: bool
 )pbdoc");
     dot.def("kind",

src/errors.cpp

@@ -87,7 +87,7 @@ emanate from C++. This function returns whether :any:`LibsemigroupsError`
 messages contain a prefix that indicates which C++ function raised the
 exception.
 
-:return: Whether :any:`LibsemigroupsError` messages contain a prefix about the
+:returns: Whether :any:`LibsemigroupsError` messages contain a prefix about the
   C++ function that raised the exception.
 :rtype: bool
 )pbdoc");
@@ -103,7 +103,7 @@ emanate from C++. This function specifies whether :any:`LibsemigroupsError`
 messages should contain a prefix that indicates which C++ function raised the
 exception. By default, this information is not included.
 
-:param val: Whether :any:`LibsemigroupsError` messages should contain a prefix
+:param val: whether :any:`LibsemigroupsError` messages should contain a prefix
   about the C++ function that raised the exception.
 :type val: bool
 

src/forest.cpp

@@ -545,7 +545,7 @@ Get the size of the range.
 
 This function returns the number of paths in the range.
 
-:returns:  the number of paths in the range.
+:returns: The number of paths in the range.
 :rtype: int
 )pbdoc");
 

src/freeband.cpp

@@ -53,7 +53,7 @@ band.
 :param y: the second word to compare in the free band.
 :type y: list[int]
 
-:return:
+:returns:
     ``True`` if both words are the same as elements of the free band and
     ``False`` otherwise.
 :rtype: bool

src/froidure-pin-base.cpp

@@ -34,7 +34,7 @@ namespace libsemigroups {
                                               "FroidurePinBase",
                                               R"pbdoc(
 Base class for :any:`FroidurePin` containing non-element specific data and
-member functions. :any:`FroidurePin` is an abstract class which cannot be
+member functions. :any:`FroidurePinBase` is an abstract class which cannot be
 instantiated directly, only via the derived class :any:`FroidurePin`.)pbdoc");
 
     thing.def(
@@ -67,7 +67,7 @@ Set a new value for the batch size.
 The *batch size* is the number of new elements to be found by any call to
 :any:`Runner.run`. This is used by, for example, :any:`FroidurePin.position` so
 that it is possible to find the position of an element after only partially
-enumerating the semigroup.The default value of the batch size is ``8192``.
+enumerating the semigroup. The default value of the batch size is ``8192``.
 
 :param val: the new value for the batch size.
 :type val: int
@@ -171,7 +171,7 @@ This function return the right Cayley graph of the semigroup as it has been
 enumerated so-far. No enumeration is triggered by calls to this function.
 
 :returns:
-  The (possibly partially enumerated) left Cayley graph.
+  The (possibly partially enumerated) right Cayley graph.
 :rtype:
   WordGraph
 
@@ -292,7 +292,8 @@ first letter of the element.
 Check if the categorical multiplicative identity is an element.
 
 :returns:
-  Whether or not the one of any of the elements belongs to the semigroup.
+  Whether or not the categorical multiplicative identity belongs to the
+  semigroup.
 :rtype:
   bool
 
@@ -310,7 +311,8 @@ Check if the categorical multiplicative identity is an element.
 Check if the categorical multiplicative identity is an element.
 
 :returns:
-  Whether or not the one of any of the elements belongs to the semigroup.
+  Whether or not the categorical multiplicative identity belongs to the
+  semigroup.
 :rtype:
   bool
 
@@ -424,7 +426,7 @@ trigger any enumeration.
 Returns the total number of relations in a presentation defining the semigroup.
 This function triggers a full enumeration of the semigroup.
 
-:returns: The number of rules so-far found.
+:returns: The total number of rules.
 :rtype: int
 
 :complexity:
@@ -632,7 +634,7 @@ Returns an iterator yielding the so-far enumerated normal forms (if any).
 This function returns an iterator yielding the normal forms of the semigroup
 represented by *fp* instance (if any). This function does not perform any
 enumeration of *fp*. If you want to obtain the
-complete set of rules, then use :any:`normal_forms` instead.
+complete set of normal forms, then use :any:`normal_forms` instead.
 
 :param fp:
    the :any:`FroidurePin` object.
@@ -753,7 +755,7 @@ Returns an iterator yielding the rules.
 
 This function returns an iterator yielding the rules in a confluent terminating
 rewriting system defining a semigroup isomorphic to the one defined by
-*fp*. This function performs a full enumeration of *fp* If you want to
+*fp*. This function performs a full enumeration of *fp*. If you want to
 obtain the current set of rules without triggering any enumeration, then
 use :any:`current_rules` instead.
 

src/froidure-pin.cpp

@@ -91,7 +91,7 @@ Copy a :any:`FroidurePin` object.
           R"pbdoc(
 :sig=(self: FroidurePin, i: int) -> int:
 
-Returns the position in of the generator with specified index.
+Returns the position of the generator with specified index.
 
 In many cases :any:`FroidurePin.current_position` called with argument *i* will
 return *i*, examples of when this will not be the case are:
@@ -148,7 +148,7 @@ better to just multiply the transformations together.
 :rtype: int
 
 :raises LibsemigroupsError:
-    if the values *i* and *j* are greater than or equal to
+    if *i* or *j* is greater than or equal to
     :any:`FroidurePin.current_size`.
 )pbdoc");
 
@@ -283,7 +283,7 @@ elements are sorted, or :any:`UNDEFINED` if *i* is greater than
 
 Returns the position corresponding to a word.
 
-This function returns the position in *fp* corresponding to the the word
+This function returns the position in *fp* corresponding to the word
 *w* (in the generators). No enumeration is performed, and :any:`UNDEFINED`
 is returned if the position of the element corresponding to *w* cannot be
 determined.
@@ -365,7 +365,7 @@ is that the resulting factorisation may not be minimal.
 :param x: a possible element, or index of element, to factorise.
 :type x: Element | int
 
-:returns: Returns a word in the generators which evaluates to *x*.
+:returns: A word in the generators which evaluates to *x*.
 :rtype: list[int]
 
 :raises LibsemigroupsError:
@@ -548,7 +548,7 @@ Add a copy of an element to the generators.
 This function can be used to add new generators to an existing
 :any:`FroidurePin` instance in such a way that any previously enumerated data
 is preserved and not recomputed, or copied. This can be faster than recomputing
-the semigroup generated by the old generators and the new generators.This
+the semigroup generated by the old generators and the new generators. This
 function changes the semigroup in-place, thereby invalidating possibly
 previously known data about the semigroup, such as the left or right Cayley
 graphs, number of idempotents, and so on.
@@ -863,7 +863,7 @@ in the same state as if it had just been constructed from *gens*.
 
 Find the position of an element with enumeration if necessary.
 
-This function the position of *x* in a :any:`FroidurePin` instance, or
+This function returns the position of *x* in a :any:`FroidurePin` instance, or
 :any:`UNDEFINED` if *x* is not an element.
 
 :param x: a possible element.

src/gabow.cpp

@@ -102,7 +102,7 @@ This function constructs a :any:`Gabow` object from a :any:`WordGraph` *wg*.
 
 Returns a list containing the strongly connected component with given index.
 
-This function returns a list containing the strongly connected components with
+This function returns a list containing the strongly connected component with
 index *i* of the :any:`WordGraph` (returned by :any:`Gabow.word_graph`) used
 to construct the :any:`Gabow` instance.
 
@@ -113,7 +113,7 @@ to construct the :any:`Gabow` instance.
 :rtype: list[int]
 
 :raises LibsemigroupsError:
-  if there is *i* is greater than or equal to
+  if *i* is greater than or equal to
   :any:`number_of_components`.
 
 .. note::
@@ -131,8 +131,8 @@ to construct the :any:`Gabow` instance.
 
 Returns a list containing the strongly connected component of a given node.
 
-This function returns a list containing the strongly connected components of
-the node *n* of the :any:`WordGraph` (returned by :any:`Gabow.word_graph` ) used to
+This function returns a list containing the strongly connected component of
+the node *n* of the :any:`WordGraph` (returned by :any:`Gabow.word_graph`) used to
 construct the :any:`Gabow` instance.
 
 :param n: the node.
@@ -210,7 +210,7 @@ underlying graph of a :any:`Gabow` instance.
 This function re-initializes a :any:`Gabow` object so that it is in the same
 state as if it had just been constructed from *wg*.
 
-:param wg: The word graph.
+:param wg: the word graph.
 :type wg: WordGraph
 
 :returns: *self*.
@@ -262,8 +262,8 @@ Returns the root of the strongly connected component containing a given node.
 
 This function returns the root of the strongly connected component containing
 the node *n* of the underlying :any:`WordGraph`. Two nodes ``a`` and ``b``
-belong to the same strongly connected component if and only if ``root_of(a) ==
-root_of(b)``.
+belong to the same strongly connected component if and only if
+``root_of(a) == root_of(b)``.
 
 :param n: the node.
 :type n: int