Changeset 6031:18e45aa21972

Timestamp:

08/29/07 19:48:16 (6 years ago)

Author:

William Stein <wstein@…>

Branch:

default

Message:

2.8.3.rc1

Location:

sage

Files:

• groups/perm_gps/cubegroup.py (modified) (1 diff)
• rings/integer.pyx (modified) (2 diffs)
• structure/element.pyx (modified) (1 diff)
• version.py (modified) (1 diff)

sage/groups/perm_gps/cubegroup.py

@@ -955 +955 @@
 
         This algorithm
-        (a) constructs the free group on 6 generators then computes a
+        \begin{enumerate}
+        \item constructs the free group on 6 generators then computes a
         reasonable set of relations which they satisfy
-        (b) computes a homomorphism from the cube group to this free
+        \item computes a homomorphism from the cube group to this free
         group quotient
-        (c) takes the cube position, regarded as a group element,
+        \item takes the cube position, regarded as a group element,
         and maps it over to the free group quotient
-        (d) using those relations and tricks from combinatorial group
+        \item using those relations and tricks from combinatorial group
         theory (stabilizer chains), solves the "word problem" for that
         element.
-        (e) uses python string parsing to rewrite that in cube notation.
-        The Rubik's cube group has about 4.3x10^(19) elements, so this
+        \item uses python string parsing to rewrite that in cube notation.
+        \end{enumerate}
+        
+        The Rubik's cube group has about $4.3 \times 10^{19}$ elements, so this
         process is time-consuming.
         See http://www.gap-system.org/Doc/Examples/rubik.html

sage/rings/integer.pyx

@@ -1021 +1021 @@
     def __mod__(self, modulus):
         r"""
-        Returns \code{self % modulus}.
+        Returns self modulo the modulus. 
         
         EXAMPLES:
@@ -1031 +1031 @@
             ...
             ZeroDivisionError: Integer modulo by zero
-        """
+            sage: -5 % 7
+            2
+         """
         cdef Integer _modulus, _self
         _modulus = integer(modulus)

sage/structure/element.pyx

@@ -2718 +2718 @@
 def generic_power(a, n, one=None):
     """
-    Computes a^n, where n is an integer, and a is an object which
+    Computes $a^n$, where $n$ is an integer, and $a$ is an object which
     supports multiplication.  Optionally an additional argument,
     which is used in the case that n == 0:

sage/version.py

@@ -1 +1 @@
 """nodoctests"""
-version='2.8.3.alpha5'; date='2007-08-29'
+version='2.8.3.rc1'; date='2007-08-29'