add tuple typing to gens methods in algebras

src/sage/algebras/askey_wilson.py

@@ -348,7 +348,7 @@ def build_monomial(g):
         return Family(A, build_monomial)
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return the generators of ``self``.
 

src/sage/algebras/clifford_algebra.py

@@ -787,7 +787,7 @@ def gen(self, i):
         """
         return self._from_dict({FrozenBitset((i,)): self.base_ring().one()}, remove_zeros=False)
 
-    def algebra_generators(self):
+    def algebra_generators(self) -> Family:
         """
         Return the algebra generators of ``self``.
 
@@ -801,7 +801,7 @@ def algebra_generators(self):
         d = {x: self.gen(i) for i, x in enumerate(self.variable_names())}
         return Family(self.variable_names(), lambda x: d[x])
 
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return the generators of ``self`` (as an algebra).
 

src/sage/algebras/cluster_algebra.py

@@ -2094,7 +2094,7 @@ def retract(self, x):
         return self(x)
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return the list of initial cluster variables and coefficients of ``self``.
 

src/sage/algebras/down_up_algebra.py

@@ -319,7 +319,7 @@ def algebra_generators(self):
         return Family({'d': d, 'u': u})
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return the generators of ``self``.
 

src/sage/algebras/free_zinbiel_algebra.py

@@ -343,7 +343,7 @@ def change_ring(self, R):
         return FreeZinbielAlgebra(R, n=len(A), names=A, side=self._side)
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the generators of ``self``.
 

src/sage/algebras/hecke_algebras/ariki_koike_algebra.py

@@ -532,7 +532,7 @@ def cyclotomic_parameters(self):
             u = cyclotomic_parameters
 
             @cached_method
-            def gens(self):
+            def gens(self) -> tuple:
                 r"""
                 Return the generators of ``self``.
 

src/sage/algebras/hecke_algebras/cubic_hecke_algebra.py

@@ -1415,7 +1415,7 @@ def algebra_generators(self):
         from sage.sets.family import Family
         return Family(self._cubic_braid_group.gens(), self.monomial)
 
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return the generators of ``self``.
 

src/sage/algebras/jordan_algebra.py

@@ -328,7 +328,7 @@ def basis(self):
     algebra_generators = basis
 
     # TODO: Keep this until we can better handle R.<...> shorthand
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the generators of ``self``.
 
@@ -763,7 +763,7 @@ def basis(self):
 
     algebra_generators = basis
 
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the generators of ``self``.
 
@@ -1316,7 +1316,7 @@ def basis(self):
 
     algebra_generators = basis
 
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the generators of ``self``.
 

src/sage/algebras/letterplace/free_algebra_letterplace.pyx

@@ -348,7 +348,7 @@ cdef class FreeAlgebra_letterplace(Parent):
             p *= self._current_ring.gen(j)
         return FreeAlgebraElement_letterplace(self, p)
 
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the tuple of generators.
 

src/sage/algebras/lie_algebras/classical_lie_algebra.py

@@ -2170,7 +2170,7 @@ def _part_generators(self, positive=False):
         return Family(I, d.__getitem__)
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return the generators of ``self`` in the order of `e_i`, `f_i`,
         and `h_i`.

src/sage/algebras/lie_algebras/free_lie_algebra.py

@@ -419,7 +419,7 @@ def lie_algebra_generators(self):
         """
         return self.Lyndon().lie_algebra_generators()
 
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the generators of ``self`` in the Lyndon basis.
 

src/sage/algebras/lie_algebras/heisenberg.py

@@ -6,15 +6,15 @@
 - Travis Scrimshaw (2013-08-13): Initial version
 """
 
-#*****************************************************************************
+# ***************************************************************************
 #       Copyright (C) 2013-2017 Travis Scrimshaw <tcscrims at gmail.com>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ***************************************************************************
 
 from sage.misc.cachefunc import cached_method
 from sage.structure.indexed_generators import IndexedGenerators
@@ -234,7 +234,7 @@ def n(self):
         return self._n
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the Lie algebra generators of ``self``.
 

src/sage/algebras/lie_algebras/lie_algebra.py

@@ -823,7 +823,7 @@ def lie_algebra_generators(self):
         return Family(self._indices, self.monomial, name="monomial map")
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return a tuple whose entries are the generators for this
         object, in some order.

src/sage/algebras/lie_algebras/subalgebra.py

@@ -646,7 +646,7 @@ def retract(self, X):
 
         return self.element_class(self, X)
 
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return the generating set of ``self``.
 

src/sage/algebras/lie_algebras/verma_module.py

@@ -356,7 +356,7 @@ def highest_weight_vector(self):
         return self._from_dict({self._indices.one(): one},
                                remove_zeros=False, coerce=False)
 
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return the generators of ``self`` as a `U(\mathfrak{g})`-module.
 

src/sage/algebras/octonion_algebra.pyx

@@ -952,7 +952,7 @@ class OctonionAlgebra(UniqueRepresentation, Parent):
         return 0
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return the generators of ``self``.
 

src/sage/algebras/q_commuting_polynomials.py

@@ -147,7 +147,7 @@ def gen(self, i):
         return self.monomial(self._indices.gen(i))
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return the generators of ``self``.
 

src/sage/algebras/q_system.py

@@ -382,7 +382,7 @@ def algebra_generators(self):
         d = {a: self.Q(a, 1) for a in I}
         return Family(I, d.__getitem__)
 
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the generators of ``self``.
 

src/sage/algebras/quantum_clifford.py

@@ -301,7 +301,7 @@ def algebra_generators(self):
         return Family(sorted(d), lambda i: d[i])
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return the generators of ``self``.
 

src/sage/algebras/quantum_groups/quantum_group_gap.py

@@ -500,7 +500,7 @@ def zero(self):
         return self.element_class(self, self._libgap.ZeroImmutable())
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the generators of ``self``.
 

src/sage/algebras/quantum_matrix_coordinate_algebra.py

@@ -188,7 +188,7 @@ def one_basis(self):
         return self._indices.one()
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         r"""
         Return the generators of ``self`` as a tuple.
 
@@ -586,7 +586,7 @@ def m(self):
         return self._m
 
     @cached_method
-    def algebra_generators(self):
+    def algebra_generators(self) -> Family:
         """
         Return the algebra generators of ``self``.
 

src/sage/algebras/quatalg/quaternion_algebra.py

@@ -1694,7 +1694,7 @@ def one(self):
         """
         return self.quaternion_algebra().one()
 
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return generators for ``self``.
 

src/sage/algebras/steenrod/steenrod_algebra.py

@@ -452,12 +452,13 @@
 #  Distributed under the terms of the GNU General Public License (GPL)
 # ****************************************************************************
 
-from sage.combinat.free_module import CombinatorialFreeModule
-from sage.misc.lazy_attribute import lazy_attribute
-from sage.misc.cachefunc import cached_method
+from sage.categories.homset import Hom
 from sage.categories.modules_with_basis import ModulesWithBasis
 from sage.categories.tensor import tensor
-from sage.categories.homset import Hom
+from sage.combinat.free_module import CombinatorialFreeModule
+from sage.misc.cachefunc import cached_method
+from sage.misc.lazy_attribute import lazy_attribute
+from sage.sets.family import Family
 
 ######################################################
 # the main class
@@ -2619,7 +2620,7 @@ def ngens(self):
             return sum(self._profile)
         return sum(self._profile[0]) + len([a for a in self._profile[1] if a == 2])
 
-    def gens(self):
+    def gens(self) -> Family:
         r"""
         Family of generators for this algebra.
 
@@ -2676,7 +2677,6 @@ def gens(self):
             sage: SteenrodAlgebra(p=5, profile=[[2,1], [2,2,2]]).algebra_generators()
             Family (Q_0, P(1), P(5))
         """
-        from sage.sets.family import Family
         from sage.sets.non_negative_integers import NonNegativeIntegers
         from sage.rings.infinity import Infinity
         n = self.ngens()

src/sage/algebras/yangian.py

@@ -832,13 +832,13 @@ def gen(self, r, i=None, j=None):
             0
         """
         if i is None and j is None:
-            r,i,j = r
+            r, i, j = r
         if r > self._level:
             return self.zero()
         return Yangian.gen(self, r, i, j)
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the generators of ``self``.
 

src/sage/algebras/yokonuma_hecke_algebra.py

@@ -252,7 +252,7 @@ def algebra_generators(self):
         return Family(sorted(d), lambda i: d[i])
 
     @cached_method
-    def gens(self):
+    def gens(self) -> tuple:
         """
         Return the generators of ``self``.