presentation-examples: add braid_group

Author: james-d-mitchell

docs/source/data-structures/presentations/examples.rst

@@ -28,6 +28,7 @@ semigroup or monoid they define.
 
     abacus_jones_monoid
     alternating_group
+    braid_group
     brauer_monoid
     chinese_monoid
     cyclic_inverse_monoid

docs/source/libsemigroups.bib

@@ -1,10 +1,14 @@
-%% This BibTeX bibliography file was created using BibDesk.
-%% https://bibdesk.sourceforge.io/
-
-%% Created for James Mitchell at 2024-02-01 14:50:47 +0000 
-
-
-%% Saved with string encoding Unicode (UTF-8) 
+@inbook{Birman2005aa,
+  title = {Braids},
+  ISBN = {9780444514523},
+  url = {http://dx.doi.org/10.1016/B978-044451452-3/50003-4},
+  DOI = {10.1016/b978-044451452-3/50003-4},
+  booktitle = {Handbook of Knot Theory},
+  publisher = {Elsevier},
+  author = {Birman, Joan S. and Brendle, Tara E.},
+  year = {2005},
+  pages = {19–103}
+}
 
 @misc{Aicardi2025aa,
   title={Framization and Deframization}, 

src/libsemigroups_pybind11/presentation/examples.py

@@ -19,6 +19,7 @@
     presentation_examples_abacus_jones_monoid_AJP25 as _abacus_jones_monoid_AJP25,
     presentation_examples_alternating_group as _alternating_group,
     presentation_examples_alternating_group_Moo97 as _alternating_group_Moo97,
+    presentation_examples_braid_group as _braid_group,
     presentation_examples_brauer_monoid as _brauer_monoid,
     presentation_examples_brauer_monoid_KM07 as _brauer_monoid_KM07,
     presentation_examples_chinese_monoid as _chinese_monoid,
@@ -108,6 +109,7 @@
 alternating_group = _wrap_cxx_free_fn(_alternating_group)
 alternating_group_Moo97 = _wrap_cxx_free_fn(_alternating_group_Moo97)
 brauer_monoid = _wrap_cxx_free_fn(_brauer_monoid)
+braid_group = _wrap_cxx_free_fn(_braid_group)
 brauer_monoid_KM07 = _wrap_cxx_free_fn(_brauer_monoid_KM07)
 chinese_monoid = _wrap_cxx_free_fn(_chinese_monoid)
 chinese_monoid_CEKNH01 = _wrap_cxx_free_fn(_chinese_monoid_CEKNH01)

src/presentation-examples.cpp

@@ -1945,6 +1945,26 @@ defines a monoid of size :math:`C_n\ d ^n` where :math:`C_n` is the
 :rtype: Presentation
 
 :raises LibsemigroupsError:  if ``n < 3`` or if ``d = 0``.
+)pbdoc");
+
+    m.def("presentation_examples_braid_group",
+          &presentation::examples::braid_group,
+          py::arg("n"),
+          R"pbdoc(
+:sig=(n: int) -> Presentation:
+
+A presentation for the Braid group.
+
+This function returns a monoid presentation defining the Braid group with
+:math:`n - 1` generators, as described in Equation (2) of :any:`Birman2005aa`.
+
+:param n: the degree, or equivalently the number of generators plus 1.
+:type n: int
+
+:returns: The specified presentation.
+:rtype: Presentation
+
+:raises LibsemigroupsError:  if ``n < 3``.
 )pbdoc");
   }  // init_presentation_examples
 

tests/test_presentation_examples.py

@@ -19,6 +19,7 @@
     congruence_kind,
     LibsemigroupsError,
     ReportGuard,
+    POSITIVE_INFINITY,
 )
 
 from libsemigroups_pybind11.presentation import examples
@@ -413,3 +414,18 @@ def test_abacus_jones():
     tc = ToddCoxeter(congruence_kind.twosided, p)
     assert tc.number_of_classes() == 40
     assert tc.number_of_classes() == 5 * 2**3
+
+
+def test_braid_group():
+    ReportGuard(False)
+    with pytest.raises(LibsemigroupsError):
+        examples.braid_group(0)
+    with pytest.raises(LibsemigroupsError):
+        examples.braid_group(1)
+    with pytest.raises(LibsemigroupsError):
+        examples.braid_group(2)
+
+    p = examples.braid_group(3)
+    assert len(p.alphabet()) == 4
+    tc = ToddCoxeter(congruence_kind.twosided, p)
+    assert tc.number_of_classes() == POSITIVE_INFINITY