sagemathgh-38671: construct order ideals by default for number-field …

…orders

    
This completes the change begun in sagemath#34806 and sagemath#35762: When constructing
ideals of an order, return an ideal of that order, rather than a
fractional ideal of the ambient number field.
    
URL: sagemath#38671
Reported by: Lorenz Panny
Reviewer(s): Kwankyu Lee

src/doc/en/thematic_tutorials/explicit_methods_in_number_theory/nf_orders.rst

@@ -99,7 +99,6 @@ with ideals in non-maximal orders.
     sage: K.<a> = NumberField(x^3 + 2)
     sage: R = K.order(3*a)
     sage: R.ideal(5)
-    doctest:warning ... FutureWarning: ...
     Ideal (5, 15*a, 45*a^2) of Order generated by 3*a in Number Field in a with defining polynomial x^3 + 2
     sage: R.ideal(5).factor()
     Traceback (most recent call last):

src/sage/modular/dirichlet.py

@@ -2380,7 +2380,8 @@ class DirichletGroupFactory(UniqueFactory):
 
     ::
 
-        sage: r4 = CyclotomicField(4).ring_of_integers()
+        sage: K = CyclotomicField(4)
+        sage: r4 = K.ring_of_integers()
         sage: G = DirichletGroup(60, r4)
         sage: G.gens()
         (Dirichlet character modulo 60 of conductor 4
@@ -2393,8 +2394,7 @@ class DirichletGroupFactory(UniqueFactory):
         zeta4
         sage: parent(val)
         Gaussian Integers generated by zeta4 in Cyclotomic Field of order 4 and degree 2
-        sage: r4_29_0 = r4.residue_field(r4.ideal(29).factor()[0][0]); r4_29_0(val)
-        doctest:warning ... DeprecationWarning: ...
+        sage: r4_29_0 = r4.residue_field(K(29).factor()[0][0]); r4_29_0(val)
         17
         sage: r4_29_0(val) * GF(29)(3)
         22

src/sage/rings/number_field/number_field_element_quadratic.pyx

@@ -2866,7 +2866,7 @@ cdef class OrderElement_quadratic(NumberFieldElement_quadratic):
             -13
             sage: w.inverse_mod(13).parent() == OE
             True
-            sage: w.inverse_mod(2*OE)
+            sage: w.inverse_mod(2)
             Traceback (most recent call last):
             ...
             ZeroDivisionError: w is not invertible modulo Fractional ideal (2)

src/sage/rings/number_field/order.py

@@ -503,21 +503,21 @@ def ideal(self, *args, **kwds):
         """
         Return the integral ideal with given generators.
 
+        .. NOTE::
+
+            This method constructs an ideal of this (not necessarily maximal) order.
+            To construct a fractional ideal in the ambient number field, use
+            :meth:`~sage.rings.number_field.number_field.NumberField_generic.fractional_ideal`.
+
         EXAMPLES::
 
             sage: x = polygen(ZZ, 'x')
             sage: K.<a> = NumberField(x^2 + 7)
             sage: R = K.maximal_order()
-            sage: R.ideal(2/3 + 7*a, a)
-            Traceback (most recent call last):
-            ...
-            ValueError: ideal must be integral;
-            use fractional_ideal to create a non-integral ideal.
-            sage: R.ideal(7*a, 77 + 28*a)
-            Fractional ideal (7)
+            sage: R.ideal([7*a, 77 + 28*a])
+            Ideal (7/2*a + 7/2, 7*a) of Maximal Order generated by 1/2*a + 1/2 in Number Field in a with defining polynomial x^2 + 7
             sage: R = K.order(4*a)
             sage: R.ideal(8)
-            doctest:warning ... FutureWarning: ...
             Ideal (8, 32*a) of Order of conductor 8 generated by 4*a
              in Number Field in a with defining polynomial x^2 + 7
 
@@ -526,36 +526,22 @@ def ideal(self, *args, **kwds):
             sage: R = EquationOrder(x^2 + 2, 'a'); R
             Maximal Order generated by a in Number Field in a with defining polynomial x^2 + 2
             sage: (3,15)*R
-            doctest:warning ... DeprecationWarning: ...
-            Fractional ideal (3)
+            Ideal (3, 3*a) of Maximal Order generated by a in Number Field in a with defining polynomial x^2 + 2
 
         The zero ideal is handled properly::
 
             sage: R.ideal(0)
-            Ideal (0) of Number Field in a with defining polynomial x^2 + 2
-        """
-        if kwds.get('future', False) or not self.is_maximal():
-            if 'future' in kwds:
-                del kwds['future']
-            from sage.rings.number_field.order_ideal import NumberFieldOrderIdeal
-            return NumberFieldOrderIdeal(self, *args, **kwds)
-        if kwds.get('warn', True):
-            if 'warn' in kwds:
-                del kwds['warn']
-            from sage.misc.superseded import deprecation
-            deprecation(34198, 'In the future, constructing an ideal of the ring of '
-                               'integers of a number field will use an implementation '
-                               'compatible with ideals of other (non-maximal) orders, '
-                               'rather than returning an integral fractional ideal of '
-                               'its containing number field. Use .fractional_ideal(), '
-                               'together with an .is_integral() check if desired, to '
-                               'emulate the current behavior.\nSet warn=0 to silence '
-                               'this warning, and future=1 to activate the upcoming '
-                               'behavior already.')
-        I = self.number_field().ideal(*args, **kwds)
-        if not I.is_integral():
-            raise ValueError("ideal must be integral; use fractional_ideal to create a non-integral ideal.")
-        return I
+            Ideal (0) of Maximal Order generated by a in Number Field in a with defining polynomial x^2 + 2
+        """
+        # these keyword arguments are ignored since there used to be optional
+        # arguments with these names for controlling deprecated/future behavior;
+        # see #34806 and #35762
+        if 'warn' in kwds:
+            del kwds['warn']
+        if 'future' in kwds:
+            del kwds['future']
+        from sage.rings.number_field.order_ideal import NumberFieldOrderIdeal
+        return NumberFieldOrderIdeal(self, *args, **kwds)
 
     def _coerce_map_from_(self, R):
         """
@@ -587,10 +573,9 @@ def __mul__(self, right):
             sage: Ok = k.maximal_order(); Ok
             Maximal Order generated by a in Number Field in a with defining polynomial x^2 + 5077
             sage: Ok * (11, a + 7)
-            doctest:warning ... DeprecationWarning: ...
-            Fractional ideal (11, a + 7)
+            Ideal (8*a + 1, 11*a) of Maximal Order generated by a in Number Field in a with defining polynomial x^2 + 5077
             sage: (11, a + 7) * Ok
-            Fractional ideal (11, a + 7)
+            Ideal (8*a + 1, 11*a) of Maximal Order generated by a in Number Field in a with defining polynomial x^2 + 5077
         """
         return self.ideal(right)
 
@@ -610,7 +595,7 @@ def __rmul__(self, left):
             sage: (6, 1/2*a + 11/2)*Ok    # random output
             Fractional ideal (6, 1/2*a + 11/2)
             sage: 17*Ok
-            Fractional ideal (17)
+            Ideal (17/2*a + 17/2, 17*a) of Maximal Order generated by 1/2*a + 1/2 in Number Field in a with defining polynomial x^2 + 431
         """
         return self.ideal(left)
 

src/sage/rings/number_field/order_ideal.py

@@ -9,13 +9,6 @@
     ideals of non-maximal orders (compared to the maximal case).
     This should hopefully change in the future.
 
-TESTS:
-
-This module is currently experimental::
-
-    sage: import sage.rings.number_field.order_ideal
-    doctest:warning ...
-
 EXAMPLES::
 
     sage: O = QuadraticField(-1).order(5*i)
@@ -75,9 +68,6 @@
 from sage.rings.polynomial.polynomial_ring import polygens
 from sage.rings.ideal import Ideal_generic
 
-from sage.misc.superseded import experimental_warning
-experimental_warning(34198, 'Ideals of non-maximal orders are an experimental feature. Be wary of bugs.')
-
 import sage.rings.number_field.order
 
 #TODO I*u works when u lies in I.ring().number_field(), but u*I doesn't