rename .rational_reconstruct() to .rational_reconstruction() for consistency

[zimmermann6]

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.

CC: @jpflori

Component: basic arithmetic

Author: Lorenz Panny

Branch/Commit: 47c91ea

Reviewer: Kwankyu Lee

Issue created by migration from https://trac.sagemath.org/ticket/12696

[yyyyx4]

Branch: public/12696

[yyyyx4]

Author: Lorenz Panny

[yyyyx4]

Commit: 08c7631

[kwankyu]

comment:7

The added method

+    def rational_reconstruction(self, *args, **kwargs):
+        r"""
+        Compute a rational reconstruction of this polynomial quotient
+        ring element to its parent.
+
+        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.lift().rational_reconstruction(m, *args, **kwargs)

doesn't work for me. The example fails. Is .lift() necessary?

In the header of the docstring, "to its parent" seems wrong. You meant P for the quotient ring P/m? I think it is called "cover (ring)" but I am not sure. Certainly it is not "parent".

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

2e7e636	remove incorrect call to .lift()
888b4fa	fix terminology in docstring

[sagetrac-git]

Changed commit from 08c7631 to 888b4fa

[yyyyx4]

comment:9

Indeed, thanks. (I'm sure I had fixed the .lift() call at some point, but apparently that change didn't make it into the commit...)

[kwankyu]

comment:10

sage -t src/sage/tests/books/computational-mathematics-with-sagemath/polynomes_doctest.py  # 1 doctest failed
sage -t src/sage/tests/books/computational-mathematics-with-sagemath/sol/polynomes_doctest.py  # 1 doctest failed

[sagetrac-git]

Changed commit from 888b4fa to 47c91ea

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

47c91ea

fix book doctests

[kwankyu]

Reviewer: Kwankyu Lee

[kwankyu]

comment:12

Thanks. LGTM.

[vbraun]

Changed branch from public/12696 to 47c91ea