add some typing annotations to gens methods (-> tuple)

src/sage/rings/algebraic_closure_finite_field.py

@@ -53,12 +53,11 @@
 
 - Vincent Delecroix (November 2013): additional methods
 """
-
 from sage.misc.abstract_method import abstract_method
 from sage.misc.fast_methods import WithEqualityById
-
 from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.ring import Field
+from sage.sets.family import AbstractFamily
 from sage.structure.element import Element, FieldElement
 from sage.structure.richcmp import richcmp
 
@@ -833,7 +832,7 @@ def gen(self, n):
         F = self._subfield(n)
         return self(F.gen())
 
-    def gens(self):
+    def gens(self) -> AbstractFamily:
         """
         Return a family of generators of ``self``.
 

src/sage/rings/asymptotic/growth_group.py

@@ -2370,7 +2370,7 @@ def _pushout_(self, other):
             from sage.categories.cartesian_product import cartesian_product
             return cartesian_product([self, other])
 
-    def gens_monomial(self):
+    def gens_monomial(self) -> tuple:
         r"""
         Return a tuple containing monomial generators of this growth
         group.
@@ -2399,9 +2399,9 @@ def gens_monomial(self):
             sage: GrowthGroup('QQ^x').gens_monomial()
             ()
         """
-        return tuple()
+        return ()
 
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return a tuple of all generators of this growth group.
 
@@ -3519,7 +3519,7 @@ def _split_raw_element_(raw_element):
         from sage.functions.other import real, imag
         return real(raw_element), imag(raw_element)
 
-    def gens_monomial(self):
+    def gens_monomial(self) -> tuple:
         r"""
         Return a tuple containing monomial generators of this growth
         group.
@@ -3546,7 +3546,7 @@ def gens_monomial(self):
             return tuple()
         return (self(raw_element=self.base().one()),)
 
-    def gens_logarithmic(self):
+    def gens_logarithmic(self) -> tuple:
         r"""
         Return a tuple containing logarithmic generators of this growth
         group.
@@ -4529,7 +4529,7 @@ def some_elements(self):
         return iter(self.element_class(self, e)
                     for e in self.base().some_elements() if e > 0)
 
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return a tuple of all generators of this exponential growth
         group.
@@ -4543,7 +4543,7 @@ def gens(self):
             sage: E.gens()
             ()
         """
-        return tuple()
+        return ()
 
     def construction(self):
         r"""

src/sage/rings/asymptotic/growth_group_cartesian.py

@@ -836,7 +836,7 @@ def next_custom(self):
         from sage.categories.cartesian_product import cartesian_product
         return pushout(cartesian_product(newS), cartesian_product(newO))
 
-    def gens_monomial(self):
+    def gens_monomial(self) -> tuple:
         r"""
         Return a tuple containing monomial generators of this growth group.
 

src/sage/rings/derivation.py

@@ -649,7 +649,7 @@ def ngens(self):
             raise NotImplementedError("generators are not implemented for this derivation module")
         return len(self._gens)
 
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return the generators of this module of derivations.
 

src/sage/rings/function_field/ideal.py

@@ -723,7 +723,7 @@ def module(self):
         """
         return self._module
 
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return a set of generators of this ideal.
 

src/sage/rings/function_field/ideal_polymod.py

@@ -579,7 +579,7 @@ def module(self):
         return V.span([to(g) for g in self.gens_over_base()], base_ring=O)
 
     @cached_method
-    def gens_over_base(self):
+    def gens_over_base(self) -> tuple:
         """
         Return the generators of this ideal as a module over the maximal order
         of the base rational function field.
@@ -624,7 +624,7 @@ def _gens_over_base(self):
                 for row in self._hnf]
         return gens, self._denominator
 
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return a set of generators of this ideal.
 
@@ -1108,7 +1108,7 @@ def __pow__(self, mod):
 
         return generic_power(self, mod)
 
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return a set of generators of this ideal.
 
@@ -1134,10 +1134,9 @@ def gens(self):
         """
         if self._gens_two.is_in_cache():
             return self._gens_two.cache
-        else:
-            return self.gens_over_base()
+        return self.gens_over_base()
 
-    def gens_two(self):
+    def gens_two(self) -> tuple:
         r"""
         Return two generators of this fractional ideal.
 
@@ -1173,7 +1172,7 @@ def gens_two(self):
         return tuple(e / d for e in self._gens_two())
 
     @cached_method
-    def _gens_two(self):
+    def _gens_two(self) -> tuple:
         r"""
         Return a set of two generators of the integral ideal, that is
         the denominator times this fractional ideal.
@@ -1556,7 +1555,7 @@ def _relative_degree(self):
 
         return self._ideal._relative_degree
 
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return a set of generators of this ideal.
 
@@ -1582,7 +1581,7 @@ def gens(self):
         iF, from_iF, to_iF = F._inversion_isomorphism()
         return tuple(from_iF(b) for b in self._ideal.gens())
 
-    def gens_two(self):
+    def gens_two(self) -> tuple:
         """
         Return a set of at most two generators of this ideal.
 
@@ -1608,7 +1607,7 @@ def gens_two(self):
         iF, from_iF, to_iF = F._inversion_isomorphism()
         return tuple(from_iF(b) for b in self._ideal.gens_two())
 
-    def gens_over_base(self):
+    def gens_over_base(self) -> tuple:
         """
         Return a set of generators of this ideal.
 

src/sage/rings/function_field/ideal_rational.py

@@ -252,7 +252,7 @@ def gen(self):
         """
         return self._gen
 
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the tuple of the unique generator of this ideal.
 
@@ -267,7 +267,7 @@ def gens(self):
         """
         return (self._gen,)
 
-    def gens_over_base(self):
+    def gens_over_base(self) -> tuple:
         """
         Return the generator of this ideal as a rank one module over the maximal
         order.
@@ -548,7 +548,7 @@ def gen(self):
         """
         return self._gen
 
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the generator of this principal ideal.
 
@@ -563,7 +563,7 @@ def gens(self):
         """
         return (self._gen,)
 
-    def gens_over_base(self):
+    def gens_over_base(self) -> tuple:
         """
         Return the generator of this ideal as a rank one module
         over the infinite maximal order.

src/sage/rings/ideal.py

@@ -280,7 +280,7 @@ def __init__(self, ring, gens, coerce=True, **kwds):
             gens = [ring(x) for x in gens]
 
         gens = tuple(gens)
-        if len(gens) == 0:
+        if not gens:
             gens = (ring.zero(),)
         self.__gens = gens
         MonoidElement.__init__(self, ring.ideal_monoid())
@@ -622,7 +622,7 @@ def reduce(self, f):
         """
         return f       # default
 
-    def gens(self):
+    def gens(self):  # -> tuple | PolynomialSequence
         """
         Return a set of generators / a basis of ``self``.
 

src/sage/rings/lazy_series_ring.py

@@ -1604,7 +1604,7 @@ def ngens(self):
         return 1
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the generators of ``self``.
 
@@ -2168,7 +2168,7 @@ def ngens(self):
         return len(self.variable_names())
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the generators of ``self``.
 

src/sage/rings/localization.py

@@ -838,7 +838,7 @@ def gen(self, i):
         """
         return self(self.base_ring().gen(i))
 
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return a tuple whose entries are the generators for this
         object, in order.

src/sage/rings/number_field/class_group.py

@@ -303,7 +303,7 @@ def representative_prime(self, norm_bound=1000):
                 return P
         raise RuntimeError("No prime of norm less than %s found in class %s" % (norm_bound, c))
 
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return generators for a representative ideal in this
         (`S`-)ideal class.

src/sage/rings/number_field/number_field_ideal.py

@@ -815,7 +815,7 @@ def gens_reduced(self, proof=None):
         self._cache_bnfisprincipal(proof=proof, gens=True)
         return self._reduced_generators
 
-    def gens_two(self):
+    def gens_two(self) -> tuple:
         r"""
         Express this ideal using exactly two generators, the first of
         which is a generator for the intersection of the ideal with `\QQ`.
@@ -861,8 +861,8 @@ def gens_two(self):
             HNF = self.pari_hnf()
             # Check whether the ideal is generated by an integer, i.e.
             # whether HNF is a multiple of the identity matrix
-            if HNF.gequal(HNF[0,0]):
-                a = HNF[0,0]
+            if HNF.gequal(HNF[0, 0]):
+                a = HNF[0, 0]
                 alpha = 0
             else:
                 a, alpha = K.pari_nf().idealtwoelt(HNF)

src/sage/rings/number_field/number_field_rel.py

@@ -493,7 +493,7 @@ def is_absolute(self):
         """
         return False
 
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the generators of this relative number field.
 

src/sage/rings/number_field/order_ideal.py

@@ -399,7 +399,7 @@ def conjugate(self):
         conj_gens = [g.conjugate() for g in self.gens()]
         return NumberFieldOrderIdeal(self.ring(), conj_gens)
 
-    def gens_two(self):
+    def gens_two(self) -> tuple:
         r"""
         Express this ideal using exactly two generators, the first of
         which is a generator for the intersection of the ideal with `\ZZ`.
@@ -506,7 +506,7 @@ def is_principal(self):
             sol = f.solve_integer(-1)
         return sol is not None
 
-    def gens_reduced(self):
+    def gens_reduced(self) -> tuple:
         r"""
         Express this ideal in terms of at most two generators,
         and one if possible (i.e., if the ideal is principal).
@@ -550,7 +550,7 @@ def gens_reduced(self):
             sol = f.solve_integer(-1)
         if sol is None:
             return self.gens_two()
-        gen = sum(c*g for c,g in zip(sol, bas))
+        gen = sum(c * g for c, g in zip(sol, bas))
         assert NumberFieldOrderIdeal(self.ring(), gen) == self
         return (gen,)
 

src/sage/rings/padics/padic_generic.py

@@ -145,20 +145,20 @@ def ngens(self):
         """
         return 1
 
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
-        Return a list of generators.
+        Return a tuple of generators.
 
         EXAMPLES::
 
             sage: R = Zp(5); R.gens()
-            [5 + O(5^21)]
+            (5 + O(5^21),)
             sage: Zq(25,names='a').gens()                                               # needs sage.libs.ntl
-            [a + O(5^20)]
+            (a + O(5^20),)
             sage: S.<x> = ZZ[]; f = x^5 + 25*x -5; W.<w> = R.ext(f); W.gens()           # needs sage.libs.ntl
-            [w + O(w^101)]
+            (w + O(w^101),)
         """
-        return [self.gen()]
+        return (self.gen(),)
 
     def __richcmp__(self, other, op):
         r"""
@@ -195,14 +195,6 @@ def __richcmp__(self, other, op):
 
         return self._printer.richcmp_modes(other._printer, op)
 
-    # def ngens(self):
-    #     return 1
-
-    # def gen(self, n=0):
-    #     if n != 0:
-    #         raise IndexError, "only one generator"
-    #     return self(self.prime())
-
     def print_mode(self):
         r"""
         Return the current print mode as a string.

src/sage/rings/polynomial/infinite_polynomial_ring.py

@@ -1265,7 +1265,7 @@ def _first_ngens(self, n):
         return self.gens()[-n:]
 
     @cached_method
-    def gens_dict(self):
+    def gens_dict(self) -> GenDictWithBasering:
         """
         Return a dictionary-like object containing the infinitely many
         ``{var_name:variable}`` pairs.

src/sage/rings/polynomial/laurent_polynomial_ideal.py

@@ -211,7 +211,7 @@ def __contains__(self, f):
             g = f.__reduce__()[1][0]
         return (g in self.polynomial_ideal())
 
-    def gens_reduced(self):
+    def gens_reduced(self) -> tuple:
         """
         Return a reduced system of generators.