gh-35248: using "change_ring" in quadratic_forms
    
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### 📚 Description

Deprecate the non-standard `base_change_to` in favor of the standard
`change_ring` inside quadratic forms.

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URL: #35248
Reported by: Frédéric Chapoton
Reviewer(s): Matthias Köppe

Author: Release Manager

src/sage/algebras/clifford_algebra.py

@@ -571,8 +571,8 @@ def _coerce_map_from_(self, V):
             Q = self._quadratic_form
             try:
                 return (V.variable_names() == self.variable_names() and
-                        V._quadratic_form.base_change_to(self.base_ring()) == Q)
-            except Exception:
+                        V._quadratic_form.change_ring(self.base_ring()) == Q)
+            except (TypeError, AttributeError):
                 return False
 
         if self.free_module().has_coerce_map_from(V):

src/sage/quadratic_forms/count_local_2.pyx

@@ -88,10 +88,6 @@ def count_modp__by_gauss_sum(n, p, m, Qdet):
     return count
 
 
-
-
-
-
 cdef CountAllLocalTypesNaive_cdef(Q, p, k, m, zvec, nzvec):
     """
     This Cython routine is documented in its Python wrapper method
@@ -102,26 +98,21 @@ cdef CountAllLocalTypesNaive_cdef(Q, p, k, m, zvec, nzvec):
     cdef long ptr     # Used to increment the vector
     cdef long solntype    # Used to store the kind of solution we find
 
-
     # Some shortcuts and definitions
     n = Q.dim()
     R = p ** k
-    Q1 = Q.base_change_to(IntegerModRing(R))
-
+    Q1 = Q.change_ring(IntegerModRing(R))
 
     # Cython Variables
     cdef IntegerMod_gmp zero, one
     zero = IntegerMod_gmp(IntegerModRing(R), 0)
     one = IntegerMod_gmp(IntegerModRing(R), 1)
 
-
-
     # Initialize the counting vector
-    count_vector = [0  for i in range(6)]
+    count_vector = [0 for i in range(6)]
 
     # Initialize v = (0, ... , 0)
-    v = [Mod(0, R)  for i in range(n)]
-
+    v = [Mod(0, R) for i in range(n)]
 
     # Some declarations to speed up the loop
     R_n = R ** n
@@ -140,7 +131,6 @@ cdef CountAllLocalTypesNaive_cdef(Q, p, k, m, zvec, nzvec):
         if (ptr > 0):
             v[ptr-1] += 1
 
-
         # Evaluate Q(v) quickly
         tmp_val = Mod(0, R)
         for a from 0 <= a < n:
@@ -154,7 +144,6 @@ cdef CountAllLocalTypesNaive_cdef(Q, p, k, m, zvec, nzvec):
             if (solntype != 0):
                 count_vector[solntype] += 1
 
-
     # Generate the Bad-type and Total counts
     count_vector[3] = count_vector[4] + count_vector[5]
     count_vector[0] = count_vector[1] + count_vector[2] + count_vector[3]

src/sage/quadratic_forms/quadratic_form.py

@@ -41,6 +41,8 @@
 from sage.quadratic_forms.quadratic_form__evaluate import QFEvaluateVector, QFEvaluateMatrix
 from sage.structure.sage_object import SageObject
 from sage.combinat.integer_lists.invlex import IntegerListsLex
+from sage.misc.superseded import deprecated_function_alias
+
 
 def QuadraticForm__constructor(R, n=None, entries=None):
     """
@@ -1542,7 +1544,7 @@ def Gram_det(self):
         """
         return self.det() / ZZ(2**self.dim())
 
-    def base_change_to(self, R):
+    def change_ring(self, R):
         """
         Alters the quadratic form to have all coefficients
         defined over the new base_ring R.  Here R must be
@@ -1555,10 +1557,12 @@ def base_change_to(self, R):
         arithmetic evaluations.
 
         INPUT:
-            R -- a ring
+        
+        - R -- a ring
 
         OUTPUT:
-            quadratic form
+        
+        quadratic form
 
         EXAMPLES::
 
@@ -1567,16 +1571,13 @@ def base_change_to(self, R):
             [ 1 0 ]
             [ * 1 ]
 
-        ::
-
-            sage: Q1 = Q.base_change_to(IntegerModRing(5)); Q1
+            sage: Q1 = Q.change_ring(IntegerModRing(5)); Q1
             Quadratic form in 2 variables over Ring of integers modulo 5 with coefficients:
             [ 1 0 ]
             [ * 1 ]
 
             sage: Q1([35,11])
             1
-
         """
         # Check that a canonical coercion is possible
         if not is_Ring(R):
@@ -1586,6 +1587,8 @@ def base_change_to(self, R):
         # Return the coerced form
         return QuadraticForm(R, self.dim(), [R(x) for x in self.coefficients()])
 
+    base_change_to = deprecated_function_alias(35248, change_ring)
+
     def level(self):
         r"""
         Determines the level of the quadratic form over a PID, which is a

src/sage/quadratic_forms/quadratic_form__local_field_invariants.py

@@ -223,7 +223,7 @@ def _rational_diagonal_form_and_transformation(self):
     """
     n = self.dim()
     K = self.base_ring().fraction_field()
-    Q = self.base_change_to(K)
+    Q = self.change_ring(K)
     MS = MatrixSpace(K, n, n)
 
     try:

src/sage/quadratic_forms/quadratic_form__mass__Siegel_densities.py

@@ -10,7 +10,7 @@
 #  Copyright by Jonathan Hanke 2007 <[email protected]>
 ########################################################################
 
-import copy
+from copy import deepcopy
 
 from sage.arith.misc import kronecker, legendre_symbol, prime_divisors
 from sage.functions.all import sgn
@@ -191,7 +191,7 @@ def Watson_mass_at_2(self):
 
     """
     # Make a 0-dim'l quadratic form (for initialization purposes)
-    Null_Form = copy.deepcopy(self)
+    Null_Form = deepcopy(self)
     Null_Form.__init__(ZZ, 0)
 
     # Step 0: Compute Jordan blocks and bounds of the scales to keep track of
@@ -230,7 +230,7 @@ def Watson_mass_at_2(self):
     eps_dict = {}
     for j in range(s_min, s_max+3):
         two_form = (diag_dict[j-2] + diag_dict[j] + dim2_dict[j]).scale_by_factor(2)
-        j_form = (two_form + diag_dict[j-1]).base_change_to(IntegerModRing(4))
+        j_form = (two_form + diag_dict[j-1]).change_ring(IntegerModRing(4))
 
         if j_form.dim() == 0:
             eps_dict[j] = 1
@@ -279,7 +279,7 @@ def Kitaoka_mass_at_2(self):
 
     """
     # Make a 0-dim'l quadratic form (for initialization purposes)
-    Null_Form = copy.deepcopy(self)
+    Null_Form = deepcopy(self)
     Null_Form.__init__(ZZ, 0)
 
     # Step 0: Compute Jordan blocks and bounds of the scales to keep track of
@@ -372,7 +372,7 @@ def mass_at_two_by_counting_mod_power(self, k):
         4
     """
     R = IntegerModRing(2**k)
-    Q1 = self.base_change_to(R)
+    Q1 = self.change_ring(R)
     n = self.dim()
     MS = MatrixSpace(R, n)