wrap at 80

Author: grhkm21

src/sage/rings/polynomial/polynomial_ring.py

@@ -281,7 +281,6 @@ def __init__(self, base_ring, name=None, sparse=False, implementation=None,
 
             sage: GF(7)['x']['y'].is_finite()
             False
-
         """
         # We trust that, if category is given, it is useful and does not need to be joined
         # with the default category
@@ -1626,8 +1625,8 @@ def karatsuba_threshold(self):
 
     def set_karatsuba_threshold(self, Karatsuba_threshold):
         """
-        Changes the default threshold for this ring in the method :meth:`_mul_karatsuba`
-        to fall back to the schoolbook algorithm.
+        Changes the default threshold for this ring in the method
+        :meth:`_mul_karatsuba` to fall back to the schoolbook algorithm.
 
         .. warning::
 
@@ -1948,37 +1947,43 @@ def __init__(self, base_ring, name="x", sparse=False, implementation=None,
     @cached_method(key=lambda self, d, q, sign, lead: (d, q, sign, tuple([x if isinstance(x, (tuple, list)) else (x, 0) for x in lead]) if isinstance(lead, (tuple, list)) else ((lead, 0))))
     def weil_polynomials(self, d, q, sign=1, lead=1):
         r"""
-        Return all integer polynomials whose complex roots all have a specified absolute value.
+        Return all integer polynomials whose complex roots all have a specified
+        absolute value.
 
         Such polynomials `f` satisfy a functional equation
 
         .. MATH::
 
             T^d f(q/T) = s q^{d/2} f(T)
 
-        where `d` is the degree of `f`, `s` is a sign and `q^{1/2}` is the absolute value
-        of the roots of `f`.
+        where `d` is the degree of `f`, `s` is a sign and `q^{1/2}` is the
+        absolute value of the roots of `f`.
 
         INPUT:
 
         - ``d`` -- integer, the degree of the polynomials
 
-        - ``q`` -- integer, the square of the complex absolute value of the roots
+        - ``q`` -- integer, the square of the complex absolute value of the
+          roots
 
-        - ``sign`` -- integer (default `1`), the sign `s` of the functional equation
+        - ``sign`` -- integer (default `1`), the sign `s` of the functional
+          equation
 
-        - ``lead`` -- integer, list of integers or list of pairs of integers (default `1`),
-          constraints on the leading few coefficients of the generated polynomials.
-          If pairs `(a, b)` of integers are given, they are treated as a constraint
-          of the form `\equiv a \pmod{b}`; the moduli must be in decreasing order by
-          divisibility, and the modulus of the leading coefficient must be 0.
+        - ``lead`` -- integer, list of integers or list of pairs of integers
+          (default `1`), constraints on the leading few coefficients of the
+          generated polynomials. If pairs `(a, b)` of integers are given, they
+          are treated as a constraint of the form `\equiv a \pmod{b}`; the
+          moduli must be in decreasing order by divisibility, and the modulus
+          of the leading coefficient must be 0.
 
         .. SEEALSO::
 
-            More documentation and additional options are available using the iterator
+            More documentation and additional options are available using the
+            iterator
             :class:`sage.rings.polynomial.weil.weil_polynomials.WeilPolynomials`
-            directly. In addition, polynomials have a method :meth:`is_weil_polynomial` to
-            test whether or not the given polynomial is a Weil polynomial.
+            directly. In addition, polynomials have a method
+            :meth:`is_weil_polynomial` to test whether or not the given
+            polynomial is a Weil polynomial.
 
         EXAMPLES::
 
@@ -2013,7 +2018,8 @@ def weil_polynomials(self, d, q, sign=1, lead=1):
 
         TESTS:
 
-        We check that products of Weil polynomials are also listed as Weil polynomials::
+        We check that products of Weil polynomials are also listed as Weil
+        polynomials::
 
             sage: all((f * g) in R.weil_polynomials(6, q) for q in [3, 4]                                               # needs sage.libs.flint
             ....:     for f in R.weil_polynomials(2, q) for g in R.weil_polynomials(4, q))
@@ -2028,13 +2034,15 @@ def weil_polynomials(self, d, q, sign=1, lead=1):
             ....:                          for j in range(1, (3+i)//2 + 1))
             ....:          for i in range(4)]) for f in simples]
 
-        Check that every polynomial in this list has 3 real roots between `-2 \sqrt{3}` and `2 \sqrt{3}`::
+        Check that every polynomial in this list has 3 real roots between `-2
+        \sqrt{3}` and `2 \sqrt{3}`::
 
             sage: roots = [f.roots(RR, multiplicities=False) for f in reals]                                            # needs sage.libs.flint
             sage: all(len(L) == 3 and all(x^2 <= 12 for x in L) for L in roots)                                         # needs sage.libs.flint
             True
 
-        Finally, check that the original polynomials are reconstructed as CM polynomials::
+        Finally, check that the original polynomials are reconstructed as CM
+        polynomials::
 
             sage: all(f == T^3*r(T + 3/T) for (f, r) in zip(simples, reals))                                            # needs sage.libs.flint
             True
@@ -2190,7 +2198,8 @@ def _element_class():
 
     def _ideal_class_(self, n=0):
         """
-        Returns the class representing ideals in univariate polynomial rings over fields.
+        Returns the class representing ideals in univariate polynomial rings
+        over fields.
 
         EXAMPLES::