gh-35683: deprecation warning for #34880

    
Per #34962 (comment),
we should first issue deprecation warnings for the change suggested in
#34880.
    
URL: #35683
Reported by: Lorenz Panny
Reviewer(s): Kwankyu Lee

src/sage/algebras/quatalg/quaternion_algebra.py

@@ -1400,8 +1400,8 @@ def __init__(self, A, basis, check=True):
                     raise ValueError("lattice must contain 1")
 
                 # check if multiplicatively closed
-                M1 = basis_for_quaternion_lattice(basis)
-                M2 = basis_for_quaternion_lattice(list(basis) + [x * y for x in basis for y in basis])
+                M1 = basis_for_quaternion_lattice(basis, reverse=False)
+                M2 = basis_for_quaternion_lattice(list(basis) + [x * y for x in basis for y in basis], reverse=False)
                 if M1 != M2:
                     raise ValueError("given lattice must be a ring")
 
@@ -2549,7 +2549,7 @@ def __mul__(self, right):
         # if self.__right_order == right.__left_order:
         #     left_order = self.__left_order
         #     right_order = right.__right_order
-        basis = tuple(basis_for_quaternion_lattice(gens))
+        basis = tuple(basis_for_quaternion_lattice(gens, reverse=False))
         A = self.quaternion_algebra()
         return A.ideal(basis, check=False)
 
@@ -2692,7 +2692,7 @@ def multiply_by_conjugate(self, J):
         """
         Jbar = [b.conjugate() for b in J.basis()]
         gens = [a * b for a in self.basis() for b in Jbar]
-        basis = tuple(basis_for_quaternion_lattice(gens))
+        basis = tuple(basis_for_quaternion_lattice(gens, reverse=False))
         R = self.quaternion_algebra()
         return R.ideal(basis, check=False)
 
@@ -2900,7 +2900,7 @@ def cyclic_right_subideals(self, p, alpha=None):
 #######################################################################
 
 
-def basis_for_quaternion_lattice(gens, reverse=False):
+def basis_for_quaternion_lattice(gens, reverse=None):
     r"""
     Return a basis for the `\ZZ`-lattice in a quaternion algebra
     spanned by the given gens.
@@ -2919,12 +2919,18 @@ def basis_for_quaternion_lattice(gens, reverse=False):
         sage: from sage.algebras.quatalg.quaternion_algebra import basis_for_quaternion_lattice
         sage: A.<i,j,k> = QuaternionAlgebra(-1,-7)
         sage: basis_for_quaternion_lattice([i+j, i-j, 2*k, A(1/3)])
+        doctest:warning ... DeprecationWarning: ...
         [1/3, i + j, 2*j, 2*k]
 
         sage: basis_for_quaternion_lattice([A(1),i,j,k])
         [1, i, j, k]
 
     """
+    if reverse is None:
+        from sage.misc.superseded import deprecation
+        deprecation(34880, 'The default value for the "reverse" argument to basis_for_quaternion_lattice() will'
+                           ' change from False to True. Pass the argument explicitly to silence this warning.')
+        reverse = False
     if not gens:
         return []
     Z, d = quaternion_algebra_cython.integral_matrix_and_denom_from_rational_quaternions(gens, reverse)

src/sage/modular/quatalg/brandt.py

@@ -399,7 +399,7 @@ def basis_for_left_ideal(R, gens):
         sage: sage.modular.quatalg.brandt.basis_for_left_ideal(B.maximal_order(), [3*(i+j),3*(i-j),6*k,A(3)])
         [3/2 + 1/2*i + k, i + 2*k, 3/2*j + 3/2*k, 3*k]
     """
-    return basis_for_quaternion_lattice([b * g for b in R.basis() for g in gens])
+    return basis_for_quaternion_lattice([b * g for b in R.basis() for g in gens], reverse=False)
 
 
 def right_order(R, basis):