Trac #12696: rename .rational_reconstruct() to .rational_reconstruction() for consistency

For integers modulo n there is a {{{rational_reconstruction}}} method:
{{{
sage: R = IntegerModRing(97)
sage: a = R(2) / R(3)
sage: a.rational_reconstruction()
2/3
}}}
However for polynomials the corresponding method is named
{{{rational_reconstruct}}}:
{{{
sage: K.<x> = R[]
sage: x.rational_reconstruct(x,4,4)
(0, 1)
}}}
The naming is incoherent.

URL: https://trac.sagemath.org/12696
Reported by: zimmerma
Ticket author(s): Lorenz Panny
Reviewer(s): Kwankyu Lee

Author: Release Manager

src/sage/rings/polynomial/polynomial_element.pyx

@@ -126,7 +126,7 @@ from sage.misc.cachefunc import cached_function
 from sage.categories.map cimport Map
 from sage.categories.morphism cimport Morphism
 
-from sage.misc.superseded import deprecation_cython as deprecation
+from sage.misc.superseded import deprecation_cython as deprecation, deprecated_function_alias
 from sage.misc.cachefunc import cached_method
 
 from sage.rings.number_field.order import is_NumberFieldOrder
@@ -8925,7 +8925,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
         else:
             raise NotImplementedError("%s does not provide an xgcd implementation for univariate polynomials"%self.base_ring())
 
-    def rational_reconstruct(self, m, n_deg=None, d_deg=None):
+    def rational_reconstruction(self, m, n_deg=None, d_deg=None):
         r"""
         Return a tuple of two polynomials ``(n, d)``
         where ``self * d`` is congruent to ``n`` modulo ``m`` and
@@ -8950,7 +8950,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
             sage: z  = PolynomialRing(QQ, 'z').gen()
             sage: p = -z**16 - z**15 - z**14 + z**13 + z**12 + z**11 - z**5 - z**4 - z**3 + z**2 + z + 1
             sage: m = z**21
-            sage: n, d = p.rational_reconstruct(m)
+            sage: n, d = p.rational_reconstruction(m)
             sage: print((n ,d))
             (z^4 + 2*z^3 + 3*z^2 + 2*z + 1, z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1)
             sage: print(((p*d - n) % m ).is_zero())
@@ -8961,7 +8961,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
             sage: z  = PolynomialRing(ZZ, 'z').gen()
             sage: p = -z**16 - z**15 - z**14 + z**13 + z**12 + z**11 - z**5 - z**4 - z**3 + z**2 + z + 1
             sage: m = z**21
-            sage: n, d = p.rational_reconstruct(m)
+            sage: n, d = p.rational_reconstruction(m)
             sage: print((n ,d))
             (z^4 + 2*z^3 + 3*z^2 + 2*z + 1, z^10 + z^9 + z^8 + z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1)
             sage: print(((p*d - n) % m ).is_zero())
@@ -8973,12 +8973,12 @@ cdef class Polynomial(CommutativeAlgebraElement):
             sage: x = P.gen()
             sage: p = 7*x^5 - 10*x^4 + 16*x^3 - 32*x^2 + 128*x + 256
             sage: m = x^5
-            sage: n, d = p.rational_reconstruct(m, 3, 2)
+            sage: n, d = p.rational_reconstruction(m, 3, 2)
             sage: print((n ,d))
             (-32*x^3 + 384*x^2 + 2304*x + 2048, 5*x + 8)
             sage: print(((p*d - n) % m ).is_zero())
             True
-            sage: n, d = p.rational_reconstruct(m, 4, 0)
+            sage: n, d = p.rational_reconstruction(m, 4, 0)
             sage: print((n ,d))
             (-10*x^4 + 16*x^3 - 32*x^2 + 128*x + 256, 1)
             sage: print(((p*d - n) % m ).is_zero())
@@ -8993,7 +8993,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
             sage: # p = (1 + t^2*z + z^4) / (1 - t*z)
             sage: p = (1 + t^2*z + z^4)*(1 - t*z).inverse_mod(z^9)
             sage: m = z^9
-            sage: n, d = p.rational_reconstruct(m)
+            sage: n, d = p.rational_reconstruction(m)
             sage: print((n ,d))
             (-1/t*z^4 - t*z - 1/t, z - 1/t)
             sage: print(((p*d - n) % m ).is_zero())
@@ -9002,7 +9002,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
             sage: n = -10*t^2*z^4 + (-t^2 + t - 1)*z^3 + (-t - 8)*z^2 + z + 2*t^2 - t
             sage: d = z^4 + (2*t + 4)*z^3 + (-t + 5)*z^2 + (t^2 + 2)*z + t^2 + 2*t + 1
             sage: prec = 9
-            sage: nc, dc = Pz((n.subs(z = w)/d.subs(z = w) + O(w^prec)).list()).rational_reconstruct(z^prec)
+            sage: nc, dc = Pz((n.subs(z = w)/d.subs(z = w) + O(w^prec)).list()).rational_reconstruction(z^prec)
             sage: print( (nc, dc) == (n, d) )
             True
 
@@ -9014,7 +9014,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
             sage: # p = (1 + t^2*z + z^4) / (1 - t*z) mod z^9
             sage: p = (1 + t^2*z + z^4) * sum((t*z)**i for i in range(9))
             sage: m = z^9
-            sage: n, d = p.rational_reconstruct(m,)
+            sage: n, d = p.rational_reconstruction(m,)
             sage: print((n ,d))
             (-z^4 - t^2*z - 1, t*z - 1)
             sage: print(((p*d - n) % m ).is_zero())
@@ -9025,7 +9025,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
             sage: x = PolynomialRing(Qp(5),'x').gen()
             sage: p = 4*x^5 + 3*x^4 + 2*x^3 + 2*x^2 + 4*x + 2
             sage: m = x^6
-            sage: n, d = p.rational_reconstruct(m, 3, 2)
+            sage: n, d = p.rational_reconstruction(m, 3, 2)
             sage: print(((p*d - n) % m ).is_zero())
             True
 
@@ -9036,34 +9036,34 @@ cdef class Polynomial(CommutativeAlgebraElement):
             sage: x = P.gen()
             sage: p = P(exp(z).list())
             sage: m = x^5
-            sage: n, d = p.rational_reconstruct(m, 4, 0)
+            sage: n, d = p.rational_reconstruction(m, 4, 0)
             sage: print((n ,d))
             (1/24*x^4 + 1/6*x^3 + 1/2*x^2 + x + 1, 1)
             sage: print(((p*d - n) % m ).is_zero())
             True
             sage: m = x^3
-            sage: n, d = p.rational_reconstruct(m, 1, 1)
+            sage: n, d = p.rational_reconstruction(m, 1, 1)
             sage: print((n ,d))
             (-x - 2, x - 2)
             sage: print(((p*d - n) % m ).is_zero())
             True
             sage: p = P(log(1-z).list())
             sage: m = x^9
-            sage: n, d = p.rational_reconstruct(m, 4, 4)
+            sage: n, d = p.rational_reconstruction(m, 4, 4)
             sage: print((n ,d))
             (25/6*x^4 - 130/3*x^3 + 105*x^2 - 70*x, x^4 - 20*x^3 + 90*x^2 - 140*x + 70)
             sage: print(((p*d - n) % m ).is_zero())
             True
             sage: p = P(sqrt(1+z).list())
             sage: m = x^6
-            sage: n, d = p.rational_reconstruct(m, 3, 2)
+            sage: n, d = p.rational_reconstruction(m, 3, 2)
             sage: print((n ,d))
             (1/6*x^3 + 3*x^2 + 8*x + 16/3, x^2 + 16/3*x + 16/3)
             sage: print(((p*d - n) % m ).is_zero())
             True
             sage: p = P(exp(2*z).list())
             sage: m = x^7
-            sage: n, d = p.rational_reconstruct(m, 3, 3)
+            sage: n, d = p.rational_reconstruction(m, 3, 3)
             sage: print((n ,d))
             (-x^3 - 6*x^2 - 15*x - 15, x^3 - 6*x^2 + 15*x - 15)
             sage: print(((p*d - n) % m ).is_zero())
@@ -9076,26 +9076,26 @@ cdef class Polynomial(CommutativeAlgebraElement):
             sage: x = P.gen()
             sage: p = P(exp(2*z).list())
             sage: m = x^7
-            sage: n, d = p.rational_reconstruct( m, 3, 3)
+            sage: n, d = p.rational_reconstruction(m, 3, 3)
             sage: print((n ,d)) # absolute tolerance 1e-10
             (-x^3 - 6.0*x^2 - 15.0*x - 15.0, x^3 - 6.0*x^2 + 15.0*x - 15.0)
 
         .. SEEALSO::
 
             * :mod:`sage.matrix.berlekamp_massey`,
-            * :meth:`sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.rational_reconstruct`
+            * :meth:`sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.rational_reconstruction`
         """
         P = self.parent()
         if not P.base_ring().is_field():
             if not P.base_ring().is_integral_domain():
-                raise NotImplementedError("rational_reconstruct() "
+                raise NotImplementedError("rational_reconstruction() "
                         "is only implemented when the base ring is a field "
                         "or a integral domain, "
                         "a workaround is to do a multimodular approach")
             Pf = P.base_extend(P.base_ring().fraction_field())
             sF = Pf(self)
             mF = Pf(m)
-            n, d = sF.rational_reconstruct( mF, n_deg, d_deg)
+            n, d = sF.rational_reconstruction(mF, n_deg, d_deg)
             l = lcm([n.denominator(), d.denominator()])
             n *= l
             d *= l
@@ -9135,6 +9135,8 @@ cdef class Polynomial(CommutativeAlgebraElement):
         t1 = t1 / c
         return t1, t0
 
+    rational_reconstruct = deprecated_function_alias(12696, rational_reconstruction)
+
     def variables(self):
         """
         Return the tuple of variables occurring in this polynomial.

src/sage/rings/polynomial/polynomial_quotient_ring_element.py

@@ -714,3 +714,27 @@ def trace(self):
             389
         """
         return self.matrix().trace()
+
+    def rational_reconstruction(self, *args, **kwargs):
+        r"""
+        Compute a rational reconstruction of this polynomial quotient
+        ring element to its cover ring.
+
+        This method is a thin convenience wrapper around
+        :meth:`Polynomial.rational_reconstruction`.
+
+        EXAMPLES::
+
+            sage: R.<x> = GF(65537)[]
+            sage: m = x^11 + 25345*x^10 + 10956*x^9 + 13873*x^8 + 23962*x^7 + 17496*x^6 + 30348*x^5 + 7440*x^4 + 65438*x^3 + 7676*x^2 + 54266*x + 47805
+            sage: f = 20437*x^10 + 62630*x^9 + 63241*x^8 + 12820*x^7 + 42171*x^6 + 63091*x^5 + 15288*x^4 + 32516*x^3 + 2181*x^2 + 45236*x + 2447
+            sage: f_mod_m = R.quotient(m)(f)
+            sage: f_mod_m.rational_reconstruction()
+            (51388*x^5 + 29141*x^4 + 59341*x^3 + 7034*x^2 + 14152*x + 23746,
+             x^5 + 15208*x^4 + 19504*x^3 + 20457*x^2 + 11180*x + 28352)
+        """
+        m = self.parent().modulus()
+        R = m.parent()
+        f = R(self._polynomial)
+        return f.rational_reconstruction(m, *args, **kwargs)
+

src/sage/rings/polynomial/polynomial_zmod_flint.pxd

@@ -14,4 +14,4 @@ cdef class Polynomial_zmod_flint(Polynomial_template):
     cdef int _set_list(self, x) except -1
     cdef int _set_fmpz_poly(self, fmpz_poly_t) except -1
     cpdef Polynomial _mul_trunc_opposite(self, Polynomial_zmod_flint other, length)
-    cpdef rational_reconstruct(self, m, n_deg=?, d_deg=?)
+    cpdef rational_reconstruction(self, m, n_deg=?, d_deg=?)

src/sage/rings/polynomial/polynomial_zmod_flint.pyx

@@ -45,6 +45,8 @@ from sage.structure.element cimport parent
 from sage.structure.element import coerce_binop
 from sage.rings.polynomial.polynomial_integer_dense_flint cimport Polynomial_integer_dense_flint
 
+from sage.misc.superseded import deprecated_function_alias
+
 # We need to define this stuff before including the templating stuff
 # to make sure the function get_cparent is found since it is used in
 # 'polynomial_template.pxi'.
@@ -585,7 +587,7 @@ cdef class Polynomial_zmod_flint(Polynomial_template):
         nmod_poly_pow_trunc(&ans.x, &self.x, n, prec)
         return ans
 
-    cpdef rational_reconstruct(self, m, n_deg=0, d_deg=0):
+    cpdef rational_reconstruction(self, m, n_deg=0, d_deg=0):
         """
         Construct a rational function n/d such that `p*d` is equivalent to `n`
         modulo `m` where `p` is this polynomial.
@@ -594,7 +596,7 @@ cdef class Polynomial_zmod_flint(Polynomial_template):
 
             sage: P.<x> = GF(5)[]
             sage: p = 4*x^5 + 3*x^4 + 2*x^3 + 2*x^2 + 4*x + 2
-            sage: n, d = p.rational_reconstruct(x^9, 4, 4); n, d
+            sage: n, d = p.rational_reconstruction(x^9, 4, 4); n, d
             (3*x^4 + 2*x^3 + x^2 + 2*x, x^4 + 3*x^3 + x^2 + x)
             sage: (p*d % x^9) == n
             True
@@ -638,6 +640,8 @@ cdef class Polynomial_zmod_flint(Polynomial_template):
 
         return t1, t0
 
+    rational_reconstruct = deprecated_function_alias(12696, rational_reconstruction)
+
     @cached_method
     def is_irreducible(self):
         """

src/sage/rings/power_series_poly.pyx

@@ -1119,7 +1119,7 @@ cdef class PowerSeries_poly(PowerSeries):
         .. SEEALSO::
 
             * :mod:`sage.matrix.berlekamp_massey`,
-            * :meth:`sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.rational_reconstruct`
+            * :meth:`sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.rational_reconstruction`
 
         EXAMPLES::
 
@@ -1172,7 +1172,7 @@ cdef class PowerSeries_poly(PowerSeries):
         polyring = self.parent()._poly_ring()
         z = polyring.gen()
         c = self.polynomial()
-        u, v = c.rational_reconstruct(z**(n + m + 1), m, n)
+        u, v = c.rational_reconstruction(z**(n + m + 1), m, n)
         return u / v
 
     def _symbolic_(self, ring):

src/sage/tests/books/computational-mathematics-with-sagemath/polynomes_doctest.py

@@ -267,7 +267,7 @@
   sage: A = Integers(101); R.<x> = A[]
   sage: f6 = sum( (i+1)^2 * x^i for i in (0..5) ); f6
   36*x^5 + 25*x^4 + 16*x^3 + 9*x^2 + 4*x + 1
-  sage: num, den = f6.rational_reconstruct(x^6, 1, 3); num/den
+  sage: num, den = f6.rational_reconstruction(x^6, 1, 3); num/den
   (100*x + 100)/(x^3 + 98*x^2 + 3*x + 100)
 
 Sage example in ./polynomes.tex, line 1611::
@@ -283,7 +283,7 @@
 
 Sage example in ./polynomes.tex, line 1677::
 
-  sage: num, den = ZpZx(s).rational_reconstruct(ZpZx(x)^10,4,5)
+  sage: num, den = ZpZx(s).rational_reconstruction(ZpZx(x)^10,4,5)
   sage: num/den
   (1073741779*x^3 + 105*x)/(x^4 + 1073741744*x^2 + 105)
 
@@ -304,7 +304,7 @@
 
   sage: def mypade(pol, n, k):
   ....:     x = ZpZx.gen();
-  ....:     n,d = ZpZx(pol).rational_reconstruct(x^n, k-1, n-k)
+  ....:     n,d = ZpZx(pol).rational_reconstruction(x^n, k-1, n-k)
   ....:     return Qx(list(map(lift_sym, n)))/Qx(list(map(lift_sym, d)))
 
 Sage example in ./polynomes.tex, line 1813::

src/sage/tests/books/computational-mathematics-with-sagemath/sol/polynomes_doctest.py

@@ -91,7 +91,7 @@
 
 Sage example in ./sol/polynomes.tex, line 428::
 
-  sage: s.rational_reconstruct(mul(x-i for i in range(4)), 1, 2)
+  sage: s.rational_reconstruction(mul(x-i for i in range(4)), 1, 2)
   (15*x + 2, x^2 + 11*x + 15)
 
 Sage example in ./sol/polynomes.tex, line 454::