presentation: add is_rule

Author: james-d-mitchell

docs/source/data-structures/presentations/present-helpers.rst

@@ -49,6 +49,7 @@ Contents
     greedy_reduce_length_and_number_of_gens
     index_rule
     is_normalized
+    is_rule
     is_strongly_compressible
     length
     longest_rule

src/libsemigroups_pybind11/presentation/__init__.py

@@ -55,6 +55,7 @@
     presentation_add_cyclic_conjugates as _add_cyclic_conjugates,
     presentation_index_rule as _index_rule,
     presentation_is_normalized as _is_normalized,
+    presentation_is_rule as _is_rule,
 )
 
 from libsemigroups_pybind11.detail.cxx_wrapper import (
@@ -272,3 +273,4 @@ def __init__(self: _Self, *args, **kwargs) -> None:
 add_cyclic_conjugates = _wrap_cxx_free_fn(_add_cyclic_conjugates)
 index_rule = _wrap_cxx_free_fn(_index_rule)
 is_normalized = _wrap_cxx_free_fn(_is_normalized)
+is_rule = _wrap_cxx_free_fn(_is_rule)

src/present.cpp

@@ -1452,6 +1452,37 @@ This function returns ``True`` if the :any:`Presentation.alphabet` of *p* is
 :rtype: bool
 )pbdoc");
 
+      m.def("presentation_is_rule",
+            &presentation::is_rule<Word>,
+            py::arg("p"),
+            py::arg("lhs"),
+            py::arg("rhs"),
+            R"pbdoc(
+:sig=(p: Presentation, lhs: Word, rhs: Word) -> bool:
+:only-document-once:
+
+Check whether a rule belongs to a presentation.
+
+This function returns ``True`` if *lhs* and *rhs* form a rule in *p*.
+That is, if *lhs* occurs in an even index position in ``p.rules``
+and *rhs* is the next item in ``p.rules``.
+
+:param p: the presentation.
+:type p: Presentation
+
+:param lhs: the left-hand side of the rule.
+:type lhs: :ref:`Word<pseudo_word_type_helper>`
+
+:param rhs: the right-hand side of the rule.
+:type rhs: :ref:`Word<pseudo_word_type_helper>`
+
+:returns: Whether or not *lhs* and *rhs* form a rule in *p*.
+:rtype: bool
+
+:raises LibsemigroupsError:
+  if :any:`Presentation.throw_if_bad_alphabet_or_rules` throws.
+)pbdoc");
+
     }  // bind_present
 
     template <typename Word>

tests/test_present.py

@@ -2213,3 +2213,14 @@ def test_presentation_is_normalized():
     p.contains_empty_word(True)
     p.rules = [[0] * 4, []]
     assert presentation.is_normalized(p)
+
+
+def test_presentation_is_rule():
+    p = Presentation("abc")
+    p.contains_empty_word(True)
+    p.rules = ["aaaa", ""]
+
+    assert not presentation.is_rule(p, "a" * 3, "")
+    assert presentation.is_rule(p, "a" * 4, "")
+    assert not presentation.is_rule(p, "", "a" * 4)
+    assert not presentation.is_rule(p, "ad" * 4, "")