Hyperbolic Coxeter type classification added

src/sage/combinat/root_system/coxeter_type.py

@@ -30,6 +30,7 @@
 from sage.structure.sage_object import SageObject
 
 lazy_import('sage.rings.universal_cyclotomic_field', 'UniversalCyclotomicField')
+lazy_import('sage.combinat.root_system.type_hyperbolic', 'CoxeterType_Hyperbolic')
 
 
 class CoxeterType(SageObject, metaclass=ClasscallMetaclass):
@@ -52,6 +53,9 @@
         if isinstance(x, CoxeterType):
             return x
 
+        if isinstance(x, list) and x[0] == "Hyp" or x[0] == "Hyperbolic":
+            return CoxeterType_Hyperbolic(*x)
+
         try:
             return CoxeterTypeFromCartanType(CartanType(x))
         except (ValueError, TypeError):
@@ -63,7 +67,7 @@
         raise NotImplementedError("Coxeter types not from Cartan types not yet implemented")
 
     @classmethod
-    def samples(self, finite=None, affine=None, crystallographic=None):
+    def samples(self, finite=None, affine=None, crystallographic=None, hyperbolic=None):
         """
         Return a sample of the available Coxeter types.
 
@@ -75,13 +79,15 @@
 
         - ``crystallographic`` -- boolean or ``None`` (default: ``None``)
 
+        - ``hyperbolic`` -- boolean or ``None`` (default: ``None``)
+
         The sample contains all the exceptional finite and affine
         Coxeter types, as well as typical representatives of the
         infinite families.
 
         EXAMPLES::
 
             sage: CoxeterType.samples()
             [Coxeter type of ['A', 1], Coxeter type of ['A', 5],
              Coxeter type of ['B', 1], Coxeter type of ['B', 5],
              Coxeter type of ['C', 1], Coxeter type of ['C', 5],
@@ -117,7 +123,7 @@
              Coxeter type of ['E', 8, 1], Coxeter type of ['F', 4, 1],
              Coxeter type of ['G', 2, 1], Coxeter type of ['A', 1, 1]]
 
             sage: CoxeterType.samples(crystallographic=True)
             [Coxeter type of ['A', 1], Coxeter type of ['A', 5],
              Coxeter type of ['B', 1], Coxeter type of ['B', 5],
              Coxeter type of ['C', 1], Coxeter type of ['C', 5],
@@ -130,7 +136,7 @@
              Coxeter type of ['E', 8, 1], Coxeter type of ['F', 4, 1],
              Coxeter type of ['G', 2, 1], Coxeter type of ['A', 1, 1]]
 
             sage: CoxeterType.samples(crystallographic=False)
             [Coxeter type of ['H', 3],
              Coxeter type of ['H', 4],
              Coxeter type of ['I', 10]]
@@ -148,6 +154,8 @@
             result = [t for t in result if t.is_finite() == finite]
         if affine is not None:
             result = [t for t in result if t.is_affine() == affine]
+        if hyperbolic is not None:
+            result = [t for t in result if t.is_hyperbolic() == hyperbolic]
         return result
 
     @cached_method
@@ -161,7 +169,7 @@
 
         EXAMPLES::
 
             sage: CoxeterType._samples()
             [Coxeter type of ['A', 1], Coxeter type of ['A', 5],
              Coxeter type of ['B', 1], Coxeter type of ['B', 5],
              Coxeter type of ['C', 1], Coxeter type of ['C', 5],
@@ -186,7 +194,12 @@
                                            ['E', 7, 1], ['E', 8, 1], ['F', 4, 1],
                                            ['G', 2, 1], ['A', 1, 1]]]
 
-        return finite + affine
+        hyperbolic = [CoxeterType(t) for t in [['Hyp', (141, 1, 3)], ['Hyp', (141, 1, 4)],
+                                               ['Hyp', (141, 2, 5)], ['Hyp', (142, 1, 6)],
+                                               ['Hyp', (142, 1, 7)], ['Hyp', (142, 1, 8)],
+                                               ['Hyp', (144, 1, 3)]]]
+
+        return finite + affine + hyperbolic
 
     @abstract_method
     def rank(self):
@@ -315,6 +328,22 @@
         """
         return False
 
+    def is_hyperbolic(self):
+        """
+        Return whether ``self`` is hyperbolic.
+
+        This returns ``False`` by default. Derived class should override this
+        appropriately.
+
+        EXAMPLES::
+
+            sage: CoxeterType(['A', 3]).is_hyperbolic()
+            False
+            sage: CoxeterType(['Hyp', (141, 1, 3)]).is_hyperbolic()
+            True
+        """
+        return False
+
     def is_simply_laced(self):
         """
         Return whether ``self`` is simply laced.
@@ -663,7 +692,7 @@
         EXAMPLES::
 
             sage: ct = CoxeterType(['A',2])
             sage: ct.relabel({1:-1, 2:-2})
             Coxeter type of ['A', 2] relabelled by {1: -1, 2: -2}
         """
         return CoxeterType(self._cartan_type.relabel(relabelling))

src/sage/combinat/root_system/meson.build

@@ -41,6 +41,7 @@ py.install_sources(
   'type_G.py',
   'type_G_affine.py',
   'type_H.py',
+  'type_hyperbolic.py',
   'type_I.py',
   'type_Q.py',
   'type_affine.py',