Ticket #11598: trac_11598-docfixes.patch

sage/modular/arithgroup/arithgroup_perm.py

@@ -2 +2 @@
 Arithmetic subgroups defined by permutations of cosets
 
 A subgroup of finite index `H` of a finitely generated group `G` is completely
-described by the action of the generators of `G` on the right cosets `H
+described by the action of a set of generators of `G` on the right cosets `H
 \backslash G = \{Hg\}_{g \in G}`. After some arbitrary choice of numbering one
 can identify the action of generators as elements of a symmetric group acting
 transitively (and satisfying the relations of the relators in G). As `{\rm
@@ -27 +27 @@
     s_2^2 = s_3^3 = -1, \quad r = s_2^{-1}\ l^{-1}\ s_2.
 
 In particular not all four are needed to generate the whole group `{\rm
-SL}_2(\ZZ)`. Three couples which which generate `{\rm SL}_2(\ZZ)` are of
-particular interest:
-
-- `(l,r)` as the pair is involved in the continued fraction algorithm,
-- `(l,s_2)` similar as the one above because of the relations,
+SL}_2(\ZZ)`. Three couples which generate `{\rm SL}_2(\ZZ)` are of particular
+interest:
+
+- `(l,r)` as they are also semigroup generators for the semigroup of matrices
+  in `{\rm SL}_2(\ZZ)` with non-negative entries,
+- `(l,s_2)` as they are closely related to the continued fraction algorithm,
 - `(s_2,s_3)` as the group `{\rm PSL}_2(\ZZ)` is the free product of the finite
   cyclic groups generated by these two elements.
 
 Part of these functions are based on Chris Kurth's *KFarey* package [Kur08]_.
-For tests see the file :mod:`sage.modular.arithgroup.tests`.
+For tests see the file ``sage.modular.arithgroup.tests``.
 
 REFERENCES: 
 
@@ -474 +475 @@
     A subgroup of `{\rm SL}_2(\ZZ)` defined by the action of generators on its
     coset graph.
 
-    The class stores the action of generators `s_2`,`s_3`,`l`,`r` on right cosets
+    The class stores the action of generators `s_2, s_3, l, r` on right cosets
     `Hg` of a finite index subgroup `H < {\rm SL}_2(\ZZ)`. In particular the action of
     `{\rm SL}_2(\ZZ)` on the cosets is on right.