gh-41148: some typing annotations for contains in rings
    
another one, adding some typing annotations in rings

one of the modified files also received a full pep8 cleanup

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: #41148
Reported by: Frédéric Chapoton
Reviewer(s):

Author: Release Manager

src/sage/rings/complex_arb.pyx

@@ -360,7 +360,7 @@ class ComplexBallField(UniqueRepresentation, sage.rings.abc.ComplexBallField):
         """
         return super().__classcall__(cls, precision)
 
-    def __init__(self, long precision=53):
+    def __init__(self, long precision=53) -> None:
         r"""
         Initialize the complex ball field.
 
@@ -1399,7 +1399,7 @@ cdef class ComplexBall(RingElement):
         """
         acb_clear(self.value)
 
-    def __init__(self, parent, x=None, y=None):
+    def __init__(self, parent, x=None, y=None) -> None:
         """
         Initialize the :class:`ComplexBall`.
 
@@ -1529,7 +1529,7 @@ cdef class ComplexBall(RingElement):
         else:
             raise TypeError("unsupported initializer")
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         """
         TESTS::
 
@@ -2333,7 +2333,7 @@ cdef class ComplexBall(RingElement):
         return (arb_is_nonzero(acb_realref(self.value))
                 or arb_is_nonzero(acb_imagref(self.value)))
 
-    def __bool__(self):
+    def __bool__(self) -> bool:
         """
         Return ``True`` iff this complex ball is not the zero ball, i.e. if the
         midpoint and radius of its real and imaginary parts are not all zero.
@@ -2590,7 +2590,7 @@ cdef class ComplexBall(RingElement):
             if _do_sig(prec(self)): sig_off()
         return res
 
-    def __contains__(self, other):
+    def __contains__(self, other) -> bool:
         """
         Return ``True`` if ``other`` can be verified to be contained in ``self``.
 

src/sage/rings/complex_interval.pyx

@@ -125,7 +125,7 @@ cdef class ComplexIntervalFieldElement(FieldElement):
         mpfi_init2(self.__re, self._prec)
         mpfi_init2(self.__im, self._prec)
 
-    def __init__(self, parent, real, imag=None, int base=10):
+    def __init__(self, parent, real, imag=None, int base=10) -> None:
         """
         Initialize a complex number (interval).
 
@@ -168,7 +168,7 @@ cdef class ComplexIntervalFieldElement(FieldElement):
         """
         return self.str(10)
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         """
         Return the hash value of ``self``.
 
@@ -664,7 +664,7 @@ cdef class ComplexIntervalFieldElement(FieldElement):
 
         return center
 
-    def __contains__(self, other):
+    def __contains__(self, other) -> bool:
         """
         Test whether ``other`` is totally contained in ``self``.
 
@@ -1406,7 +1406,7 @@ cdef class ComplexIntervalFieldElement(FieldElement):
         return complex(self.real().n(self._prec),
                        self.imag().n(self._prec))
 
-    def __bool__(self):
+    def __bool__(self) -> bool:
         """
         Return ``True`` if ``self`` is not known to be exactly zero.
 

src/sage/rings/ideal.py

@@ -31,7 +31,7 @@
 from sage.categories.rings import Rings
 from sage.categories.fields import Fields
 from sage.structure.element import MonoidElement
-from sage.structure.richcmp import rich_to_bool, richcmp, op_NE
+from sage.structure.richcmp import rich_to_bool, op_NE
 from sage.structure.sequence import Sequence
 
 
@@ -253,7 +253,7 @@ class Ideal_generic(MonoidElement):
 
     See :func:`Ideal()`.
     """
-    def __init__(self, ring, gens, coerce=True, **kwds):
+    def __init__(self, ring, gens, coerce=True, **kwds) -> None:
         """
         Initialize this ideal.
 
@@ -318,7 +318,7 @@ def _repr_short(self):
             s = repr(x)
             if '\n' in s:
                 has_return = True
-                s = s.replace('\n','\n  ')
+                s = s.replace('\n', '\n  ')
             L.append(s)
         if has_return:
             return '\n(\n  %s\n)\n' % (',\n\n  '.join(L))
@@ -395,7 +395,7 @@ def _richcmp_(self, other, op):
             return rich_to_bool(op, +1)
         raise NotImplementedError(f'ideal comparison in {self.ring()} is not implemented')
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Check if ``x`` is in ``self``.
 
@@ -439,7 +439,7 @@ def _contains_(self, x):
         """
         raise NotImplementedError
 
-    def __bool__(self):
+    def __bool__(self) -> bool:
         r"""
         Return ``True`` if this ideal is not `(0)`.
 
@@ -1081,7 +1081,7 @@ def __mul__(self, other):
             try:
                 if self.ring().has_coerce_map_from(other):
                     return self
-            except (TypeError,ArithmeticError,ValueError):
+            except (TypeError, ArithmeticError, ValueError):
                 pass
             other = self.ring().ideal(other)
         return self._mul_(other)
@@ -1107,7 +1107,8 @@ def _mul_(self, other):
             sage: I._mul_(J)
             Ideal (x^3*y, x^2*y^2, x^3*z, x^2*y*z, x^4, x^3*y) of Multivariate Polynomial Ring in x, y, z over Rational Field
         """
-        return self.ring().ideal([z for z in [x*y for x in self.gens() for y in other.gens()] if z])
+        return self.ring().ideal([z for x in self.gens() for y in other.gens()
+                                  if (z := x * y)])
 
     def __rmul__(self, other):
         """
@@ -1124,10 +1125,11 @@ def __rmul__(self, other):
             try:
                 if self.ring().has_coerce_map_from(other):
                     return self
-            except (TypeError,ArithmeticError,ValueError):
+            except (TypeError, ArithmeticError, ValueError):
                 pass
             other = self.ring().ideal(other)
-        return self.ring().ideal([z for z in [y*x for x in self.gens() for y in other.gens()] if z])
+        return self.ring().ideal([z for x in self.gens() for y in other.gens()
+                                  if (z := y * x)])
 
     def norm(self):
         """
@@ -1284,7 +1286,7 @@ class Ideal_principal(Ideal_generic):
     See :func:`Ideal()`.
     """
     # now Ideal_principal takes a list.
-    #def __init__(self, ring, gen):
+    # def __init__(self, ring, gen):
     #    Ideal_generic.__init__(self, ring, [gen])
 
     def _repr_(self):
@@ -1366,7 +1368,7 @@ def gen(self, i=0):
             raise ValueError(f"i (={i}) must be 0")
         return self.gens()[0]
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Return ``True`` if ``x`` is in ``self``.
 
@@ -1388,7 +1390,7 @@ def __contains__(self, x):
         except NotImplementedError:
             return self._contains_(self.ring()(x))
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         r"""
         Very stupid constant hash function!
 
@@ -1622,10 +1624,10 @@ def is_prime(self):
             sage: RR.ideal(7).is_prime()
             False
         """
-        if self.is_zero(): # PIDs are integral domains by definition
+        if self.is_zero():  # PIDs are integral domains by definition
             return True
         g = self.gen()
-        if g.is_one():     # The ideal (1) is never prime
+        if g.is_one():      # The ideal (1) is never prime
             return False
         if hasattr(g, 'is_irreducible'):
             return g.is_irreducible()
@@ -1819,7 +1821,7 @@ def Cyclic(R, n=None, homog=False, singular=None):
     if not homog:
         I = singular.cyclic(n)
     else:
-        I = singular.cyclic(n).homog(R2.gen(n-1))
+        I = singular.cyclic(n).homog(R2.gen(n - 1))
     return R2.ideal(I).change_ring(R)
 
 
@@ -1870,7 +1872,7 @@ def Katsura(R, n=None, homog=False, singular=None):
     if not homog:
         I = singular.katsura(n)
     else:
-        I = singular.katsura(n).homog(R2.gen(n-1))
+        I = singular.katsura(n).homog(R2.gen(n - 1))
     return R2.ideal(I).change_ring(R)
 
 

src/sage/rings/polynomial/laurent_polynomial_ideal.py

@@ -28,7 +28,7 @@
 
 
 class LaurentPolynomialIdeal( Ideal_generic ):
-    def __init__(self, ring, gens, coerce=True, hint=None):
+    def __init__(self, ring, gens, coerce=True, hint=None) -> None:
         r"""
         Create an ideal in a Laurent polynomial ring.
 
@@ -184,7 +184,7 @@ def _richcmp_(self, right_r, op):
         else:
             raise ValueError("invalid comparison")
 
-    def __contains__(self, f):
+    def __contains__(self, f) -> bool:
         """
         Implement containment testing (in) for Laurent polynomial ideals.