Trac #19946: rewrite and improve explaination of 1b62954

sagemath · Jan 26, 2016 · 1471336 · 1471336
1 parent 7918417
commit 1471336
Showing 1 changed file with 12 additions and 6 deletions.
diff --git a/src/sage/rings/asymptotic/term_monoid.py b/src/sage/rings/asymptotic/term_monoid.py
@@ -3318,16 +3318,22 @@ def rpow(self, base):
             sage: _.parent()
             Exact Term Monoid QQ^n * n^SR with coefficients in Symbolic Ring
 
-        Above, we get ``QQ^n * n^SR`` since
-        ::
+        Above, we get ``QQ^n * n^SR``. The reason is the following:
+        Since $n = 1_{SR} \cdot (1_{\QQ})^n \cdot n^{1_{\QQ}}$, we have
 
-            sage: (n^SR(1)).parent()
-            Exact Term Monoid QQ^n * n^SR with coefficients in Symbolic Ring
+        .. MATH::
 
-        and that is because of ::
+            2^n = (2_{\QQ})^{1_{SR} \cdot (1_{\QQ})^n \cdot n^{1_{\QQ}}}
+            = \left( (2_{\QQ})^n \cdot n^{0_{\QQ}} \right)^{1_{SR}}
+            = \left((2_{\QQ})^{1_{SR}}\right)^n \cdot n^{0_{\QQ} 1_{SR}}
+            = (2_{\QQ})^n \cdot n^{0_{SR}}
 
-            sage: (QQ(2)^SR(1)).parent(), (QQ(1)*SR(1)).parent()
+        where ::
+
+            sage: (QQ(2)^SR(1)).parent(), (QQ(0)*SR(1)).parent()
             (Rational Field, Symbolic Ring)
+
+        was used.
         """
         P = self.parent()