Trac #15137: Implement right-angled Artin groups

This patch implements Right-angled Artin groups (RAAG's for short,
a.k.a. graph groups or partially commutative groups).

URL: http://trac.sagemath.org/15137
Reported by: tscrim
Ticket author(s): Travis Scrimshaw
Reviewer(s): Frédéric Chapoton, Miguel Marco

src/doc/en/reference/groups/index.rst

@@ -12,6 +12,7 @@ Groups
    sage/groups/finitely_presented
    sage/groups/finitely_presented_named
    sage/groups/braid
+   sage/groups/raag
    sage/groups/abelian_gps/abelian_group
    sage/groups/abelian_gps/values
    sage/groups/abelian_gps/dual_abelian_group

src/sage/groups/all.py

@@ -21,6 +21,8 @@
 lazy_import('sage.groups.affine_gps.affine_group', 'AffineGroup')
 lazy_import('sage.groups.affine_gps.euclidean_group', 'EuclideanGroup')
 
+lazy_import('sage.groups.raag', 'RightAngledArtinGroup')
+
 lazy_import('sage.groups', 'groups_catalog', 'groups')
 
 lazy_import('sage.groups.semimonomial_transformations.semimonomial_transformation_group',

src/sage/groups/finitely_presented.py

@@ -198,7 +198,7 @@ def __init__(self, parent, x, check=True):
         if not isinstance(x, GapElement):
             F = parent.free_group()
             free_element = F(x)
-            fp_family = parent.one().gap().FamilyObj()
+            fp_family = parent.gap().Identity().FamilyObj()
             x = libgap.ElementOfFpGroup(fp_family, free_element.gap())
         ElementLibGAP.__init__(self, parent, x)
 
@@ -219,10 +219,6 @@ def __reduce__(self):
 
             sage: F.<a,b,c> = FreeGroup('a, b, c')
             sage: G = F.quotient([a*b*c/(b*c*a), a*b*c/(c*a*b)])
-            sage: G.__reduce__()
-            (<class 'sage.groups.finitely_presented.FinitelyPresentedGroup'>,
-             (Free Group on generators {a, b, c},
-             (a*b*c*a^-1*c^-1*b^-1, a*b*c*b^-1*a^-1*c^-1)))
             sage: G.inject_variables()
             Defining a, b, c
             sage: x = a*b*c
@@ -776,32 +772,6 @@ def __init__(self, free_group, relations):
         ParentLibGAP.__init__(self, parent_gap)
         Group.__init__(self)
 
-    def __reduce__(self):
-        """
-        Used in pickling.
-
-        TESTS::
-
-            sage: F = FreeGroup(4)
-            sage: F.inject_variables()
-            Defining x0, x1, x2, x3
-            sage: G = F.quotient([x0*x2, x3*x1*x3, x2*x1*x2])
-            sage: G.__reduce__()
-            (<class 'sage.groups.finitely_presented.FinitelyPresentedGroup'>,
-             (Free Group on generators {x0, x1, x2, x3},
-              (x0*x2, x3*x1*x3, x2*x1*x2)))
-
-            sage: F.<a,b,c> = FreeGroup()
-            sage: F.inject_variables()
-            Defining a, b, c
-            sage: G = F / [a*b*c/(b*c*a), a*b*c/(c*a*b)]
-            sage: G.__reduce__()
-            (<class 'sage.groups.finitely_presented.FinitelyPresentedGroup'>,
-             (Free Group on generators {a, b, c},
-              (a*b*c*a^-1*c^-1*b^-1, a*b*c*b^-1*a^-1*c^-1)))
-        """
-        return (FinitelyPresentedGroup, (self._free_group, self._relations))
-
     def _repr_(self):
         """
         Return a string representation.

src/sage/groups/groups_catalog.py

@@ -62,6 +62,7 @@
   - :func:`groups.misc.Braid <sage.groups.braid.BraidGroup>`
   - :func:`groups.misc.CoxeterGroup <sage.combinat.root_system.coxeter_group.CoxeterGroup>`
   - :func:`groups.misc.Free <sage.groups.free_group.FreeGroup>`
+  - :class:`groups.misc.RightAngledArtin <sage.groups.raag.RightAngledArtinGroup>`
   - :func:`groups.misc.SemimonomialTransformation <sage.groups.semimonomial_transformations.semimonomial_transformation_group.SemimonomialTransformationGroup>`
   - :func:`groups.misc.WeylGroup <sage.combinat.root_system.weyl_group.WeylGroup>`
 

src/sage/groups/misc_gps/misc_groups_catalog.py

@@ -19,3 +19,5 @@
 from sage.groups.semimonomial_transformations.semimonomial_transformation_group import SemimonomialTransformationGroup as SemimonomialTransformation
 from sage.combinat.root_system.coxeter_group import CoxeterGroup
 from sage.combinat.root_system.weyl_group import WeylGroup
+from sage.groups.raag import RightAngledArtinGroup as RightAngledArtin
+