sage.rings.bern*: rst fixes

src/sage/rings/bernmm.pyx

@@ -2,6 +2,7 @@ r"""
 Cython wrapper for bernmm library
 
 AUTHOR:
+
     - David Harvey (2008-06): initial version
 """
 
@@ -34,14 +35,17 @@ def bernmm_bern_rat(long k, int num_threads = 1):
     (Wrapper for bernmm library.)
 
     INPUT:
-        k -- non-negative integer
-        num_threads -- integer >= 1, number of threads to use
+
+    - k -- non-negative integer
+    - num_threads -- integer >= 1, number of threads to use
 
     COMPLEXITY:
-        Pretty much quadratic in $k$. See the paper ``A multimodular algorithm
-        for computing Bernoulli numbers'', David Harvey, 2008, for more details.
 
-    EXAMPLES:
+        Pretty much quadratic in $k$. See the paper "A multimodular algorithm
+        for computing Bernoulli numbers", David Harvey, 2008, for more details.
+
+    EXAMPLES::
+
         sage: from sage.rings.bernmm import bernmm_bern_rat
 
         sage: bernmm_bern_rat(0)
@@ -57,7 +61,8 @@ def bernmm_bern_rat(long k, int num_threads = 1):
         sage: bernmm_bern_rat(100, 3)
         -94598037819122125295227433069493721872702841533066936133385696204311395415197247711/33330
 
-    TESTS:
+    TESTS::
+
         sage: lst1 = [ bernoulli(2*k, algorithm='bernmm', num_threads=2) for k in [2932, 2957, 3443, 3962, 3973] ]
         sage: lst2 = [ bernoulli(2*k, algorithm='pari') for k in [2932, 2957, 3443, 3962, 3973] ]
         sage: lst1 == lst2
@@ -87,13 +92,16 @@ def bernmm_bern_modp(long p, long k):
     If $B_k$ is not $p$-integral, returns -1.
 
     INPUT:
+
         p -- a prime
         k -- non-negative integer
 
     COMPLEXITY:
+
         Pretty much linear in $p$.
 
-    EXAMPLES:
+    EXAMPLES::
+
         sage: from sage.rings.bernmm import bernmm_bern_modp
 
         sage: bernoulli(0) % 5, bernmm_bern_modp(5, 0)

src/sage/rings/bernoulli_mod_p.pyx

@@ -2,11 +2,12 @@ r"""
 Bernoulli numbers modulo p
 
 AUTHOR:
-    - David Harvey (2006-07-26): initial version
-    - William Stein (2006-07-28): some touch up.
-    - David Harvey (2006-08-06): new, faster algorithm, also using faster NTL interface
-    - David Harvey (2007-08-31): algorithm for a single Bernoulli number mod p
-    - David Harvey (2008-06): added interface to bernmm, removed old code
+
+- David Harvey (2006-07-26): initial version
+- William Stein (2006-07-28): some touch up.
+- David Harvey (2006-08-06): new, faster algorithm, also using faster NTL interface
+- David Harvey (2007-08-31): algorithm for a single Bernoulli number mod p
+- David Harvey (2008-06): added interface to bernmm, removed old code
 """
 
 #*****************************************************************************
@@ -46,12 +47,15 @@ def verify_bernoulli_mod_p(data):
     (see "Irregular Primes to One Million", Buhler et al)
 
     INPUT:
+
         data -- list, same format as output of bernoulli_mod_p function
 
     OUTPUT:
+
         bool -- True if checksum passed
 
-    EXAMPLES:
+    EXAMPLES::
+
         sage: from sage.rings.bernoulli_mod_p import verify_bernoulli_mod_p
         sage: verify_bernoulli_mod_p(bernoulli_mod_p(next_prime(3)))
         True
@@ -62,7 +66,8 @@ def verify_bernoulli_mod_p(data):
         sage: verify_bernoulli_mod_p([1, 2, 3, 4, 5])
         False
 
-    This one should test that long longs are working:
+    This one should test that long longs are working::
+
         sage: verify_bernoulli_mod_p(bernoulli_mod_p(next_prime(20000)))
         True
 
@@ -91,19 +96,24 @@ def bernoulli_mod_p(int p):
     Returns the bernoulli numbers `B_0, B_2, ... B_{p-3}` modulo `p`.
 
     INPUT:
+
         p -- integer, a prime
 
     OUTPUT:
+
         list -- Bernoulli numbers modulo `p` as a list
                 of integers [B(0), B(2), ... B(p-3)].
 
     ALGORITHM:
+
         Described in accompanying latex file.
 
     PERFORMANCE:
+
         Should be complexity `O(p \log p)`.
 
     EXAMPLES:
+
     Check the results against PARI's C-library implementation (that
     computes exact rationals) for `p = 37`::
 
@@ -112,11 +122,13 @@ def bernoulli_mod_p(int p):
         sage: [bernoulli(n) % 37 for n in xrange(0, 36, 2)]
          [1, 31, 16, 15, 16, 4, 17, 32, 22, 31, 15, 15, 17, 12, 29, 2, 0, 2]
 
-    Boundary case:
+    Boundary case::
+
         sage: bernoulli_mod_p(3)
          [1]
 
     AUTHOR:
+
         -- David Harvey (2006-08-06)
 
     """
@@ -219,13 +231,16 @@ def bernoulli_mod_p_single(long p, long k):
     If `B_k` is not `p`-integral, an ArithmeticError is raised.
 
     INPUT:
+
         p -- integer, a prime
         k -- non-negative integer
 
     OUTPUT:
+
         The `k`-th bernoulli number mod `p`.
 
-    EXAMPLES:
+    EXAMPLES::
+
         sage: bernoulli_mod_p_single(1009, 48)
         628
         sage: bernoulli(48) % 1009
@@ -254,7 +269,7 @@ def bernoulli_mod_p_single(long p, long k):
         ...
         ValueError: k must be non-negative
 
-    Check results against bernoulli_mod_p:
+    Check results against bernoulli_mod_p::
 
         sage: bernoulli_mod_p(37)
          [1, 31, 16, 15, 16, 4, 17, 32, 22, 31, 15, 15, 17, 12, 29, 2, 0, 2]
@@ -282,6 +297,7 @@ def bernoulli_mod_p_single(long p, long k):
          [1, 6, 3]
 
     AUTHOR:
+
         -- David Harvey (2007-08-31)
         -- David Harvey (2008-06): rewrote to use bernmm library