presentation: add is_normalized

Author: james-d-mitchell

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

@@ -48,6 +48,7 @@ Contents
     greedy_reduce_length
     greedy_reduce_length_and_number_of_gens
     index_rule
+    is_normalized
     is_strongly_compressible
     length
     longest_rule

src/libsemigroups_pybind11/presentation/__init__.py

@@ -54,6 +54,7 @@
     presentation_balance as _balance,
     presentation_add_cyclic_conjugates as _add_cyclic_conjugates,
     presentation_index_rule as _index_rule,
+    presentation_is_normalized as _is_normalized,
 )
 
 from libsemigroups_pybind11.detail.cxx_wrapper import (
@@ -270,3 +271,4 @@ def __init__(self: _Self, *args, **kwargs) -> None:
 balance = _wrap_cxx_free_fn(_balance)
 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)

src/present.cpp

@@ -1431,6 +1431,27 @@ This function returns the minimum index ``i`` of *lhs* such that ``p.rules[i +
 
 :raises LibsemigroupsError:  if ``p.throw_if_bad_alphabet_or_rules()`` throws.
 )pbdoc");
+
+      m.def(
+          "presentation_is_normalized",
+          [](Presentation<Word>& p) { return presentation::is_normalized(p); },
+          py::arg("p"),
+          R"pbdoc(
+:sig=(p: Presentation) -> bool:
+:only-document-once:
+
+Check if the presentation is normalized.
+
+This function returns ``True`` if the :any:`Presentation.alphabet` of *p* is
+``0`` to ``p.alphabet().size() - 1`` and ``False`` otherwise.
+
+:param p: the presentation to check.
+:type p: Presentation
+
+:returns: Whether or not the presentation *p* is normalized.
+:rtype: bool
+)pbdoc");
+
     }  // bind_present
 
     template <typename Word>

tests/test_present.py

@@ -12,7 +12,6 @@
 # pylint: disable=missing-function-docstring, invalid-name
 # pylint: disable=comparison-with-callable, too-many-lines
 
-
 import copy
 import pytest
 from libsemigroups_pybind11 import (
@@ -2200,3 +2199,17 @@ def test_presentation_index_rule():
 
     assert presentation.index_rule(p, "aaaa", "") == 0
     assert presentation.index_rule(p, "a", "") == UNDEFINED
+
+
+def test_presentation_is_normalized():
+    p = Presentation("abc")
+    p.contains_empty_word(True)
+    p.rules = ["aaaa", ""]
+    assert not presentation.is_normalized(p)
+    p.alphabet("bac")
+    assert not presentation.is_normalized(p)
+
+    p = Presentation([0, 1, 2])
+    p.contains_empty_word(True)
+    p.rules = [[0] * 4, []]
+    assert presentation.is_normalized(p)