#8829 fix docstring typos

src/sage/schemes/elliptic_curves/ell_number_field.py

@@ -3545,7 +3545,8 @@ def has_rational_cm(self, field=None):
     def saturation(self, points, verbose=False,
                    max_prime=0, one_prime=0, odd_primes_only=False,
                    lower_ht_bound=None, reg=None, debug=False):
-        r""" Given a list of rational points on `E` over `K`, compute the
+        r"""
+        Given a list of rational points on `E` over `K`, compute the
         saturation in `E(K)` of the subgroup they generate.
 
         INPUT:
@@ -3657,11 +3658,11 @@ def saturation(self, points, verbose=False,
 
         ALGORITHM:
 
-        For rank 1 subgroups, simply do trial divison up to the maximal
+        For rank 1 subgroups, simply do trial division up to the maximal
         prime divisor. For higher rank subgroups, perform trial divison
         on all linear combinations for small primes, and look for
         projections `E(K) \rightarrow \oplus E(k) \otimes \mathbf{F}_p` which
-        are either full rank or provide `p`-divisble linear combinations,
+        are either full rank or provide `p`-divisible linear combinations,
         where the `k` here are residue fields of `K`.
 
         TESTS::
@@ -3752,7 +3753,8 @@ def saturation(self, points, verbose=False,
 
 
     def gens_quadratic(self, **kwds):
-        """Return generators for the Mordell-Weil group modulo torsion, for a
+        """
+        Return generators for the Mordell-Weil group modulo torsion, for a
         curve which is a base change from `\QQ` to a quadratic field.
 
         EXAMPLES::
@@ -3787,7 +3789,7 @@ def gens_quadratic(self, **kwds):
             raise ValueError("gens_quadratic() requires the base field to be quadratic")
 
         EE = self.descend_to(QQ)
-        if len(EE)==0:
+        if not EE:
             raise ValueError("gens_quadratic() requires the elliptic curve to be a base change from Q")
 
         # In all cases there are exactly two distinct curves /Q whose

src/sage/schemes/elliptic_curves/saturation.py

@@ -11,7 +11,7 @@
 finitely-generated Abelian group.
 
 The process of `p`-saturating a given set of points is implemented
-here.  The naive algirithm simply checks all `(p^r-1)/(p-1)`
+here.  The naive algorithm simply checks all `(p^r-1)/(p-1)`
 projective combinations of the points, testing each to see if it can
 be divided by `p`.  If this occurs then we replace one of the points
 and continue.  The function :meth:`p_saturation` does one step of
@@ -54,20 +54,21 @@
 from sage.rings.all import ZZ
 
 def p_saturation(Plist, p, sieve=True, lin_combs = dict(), verbose=False):
-    r""" Checks whether the list of points is `p`-saturated.
+    r"""
+    Checks whether the list of points is `p`-saturated.
 
     INPUT:
 
-    - ``Plist`` (list) - a list of independent points on one elliptic curve
+    - ``Plist`` (list) - a list of independent points on one elliptic curve.
 
-    - ``p`` (integer) - a prime number
+    - ``p`` (integer) - a prime number.
 
     - ``sieve`` (boolean) - if True, use a sieve (when there are at
       least 2 points); otherwise test all combinations.
 
     - ``lin_combs`` (dict) - a dict, possibly empty, with keys
       coefficient tuples and values the corresponding linear
-      combinations of the points in ``Plist``
+      combinations of the points in ``Plist``.
 
     .. note::
 
@@ -101,7 +102,7 @@ def p_saturation(Plist, p, sieve=True, lin_combs = dict(), verbose=False):
         sage: p_saturation([P,Q,R],3)
         (True, {})
 
-    Here we see an example where 19-aturation is proved, with the
+    Here we see an example where 19-saturation is proved, with the
     verbose flag set to True so that we can see what is going on::
 
         sage: p_saturation([P,Q,R],19, verbose=True)
@@ -352,17 +353,18 @@ def a(pt,g):
 
 
 def full_p_saturation(Plist, p, lin_combs = dict(), verbose=False):
-    r""" Full `p`-saturation of ``Plist``.
+    r"""
+    Full `p`-saturation of ``Plist``.
 
     INPUT:
 
-    - ``Plist`` (list) - a list of independent points on one elliptic curve
+    - ``Plist`` (list) - a list of independent points on one elliptic curve.
 
-    - ``p`` (integer) - a prime number
+    - ``p`` (integer) - a prime number.
 
     - ``lin_combs`` (dict, default null) - a dict, possibly empty,
       with keys coefficient tuples and values the corresponding linear
-      combinations of the points in ``Plist``
+      combinations of the points in ``Plist``.
 
     OUTPUT: