adding conversions towards magma

Author: fchapoton

src/sage/interfaces/magma.py

@@ -10,7 +10,7 @@
    You must have Magma installed on your
    computer for this interface to work. Magma is not free, so it is
    not included with Sage, but you can obtain it from
-   http://magma.maths.usyd.edu.au/.
+   https://magma.maths.usyd.edu.au/.
 
 The Magma interface offers three pieces of functionality:
 

src/sage/rings/laurent_series_ring.py

@@ -407,6 +407,29 @@ def _repr_(self):
             s = 'Sparse ' + s
         return s
 
+    def _magma_init_(self, magma):
+        """
+        Used in converting this ring to the corresponding ring in MAGMA.
+
+        EXAMPLES::
+
+            sage: # optional - magma
+            sage: R = LaurentSeriesRing(QQ, 'y')
+            sage: R._magma_init_(magma)
+            'SageCreateWithNames(LaurentSeriesRing(_sage_ref...),["y"])'
+            sage: S = magma(R)
+            sage: S
+            Laurent series field in y over Rational Field
+            sage: S.1
+            y
+            sage: magma(LaurentSeriesRing(GF(7), 'x'))                                     # needs sage.rings.finite_rings
+            Laurent series field in x over GF(7)
+        """
+        B = magma(self.base_ring())
+        Bref = B._ref()
+        s = 'LaurentSeriesRing(%s)' % (Bref)
+        return magma._with_names(s, self.variable_names())
+
     def _element_constructor_(self, x, n=0, prec=infinity):
         r"""
         Construct a Laurent series from `x`.

src/sage/rings/power_series_ring.py

@@ -722,6 +722,29 @@ def _coerce_map_from_(self, S):
                 and self.variable_names() == S.variable_names()):
             return True
 
+    def _magma_init_(self, magma):
+        """
+        Used in converting this ring to the corresponding ring in MAGMA.
+
+        EXAMPLES::
+
+            sage: # optional - magma
+            sage: R = QQ[['y']]
+            sage: R._magma_init_(magma)
+            'SageCreateWithNames(PowerSeriesRing(_sage_ref...),["y"])'
+            sage: S = magma(R)
+            sage: S
+            Power series ring in y over Rational Field
+            sage: S.1
+            y
+            sage: magma(PowerSeriesRing(GF(7), 'x'))                                     # needs sage.rings.finite_rings
+            Power series ring in x over GF(7)
+        """
+        B = magma(self.base_ring())
+        Bref = B._ref()
+        s = 'PowerSeriesRing(%s)' % (Bref)
+        return magma._with_names(s, self.variable_names())
+
     def _element_constructor_(self, f, prec=infinity, check=True):
         """
         Coerce object to this power series ring.

src/sage/rings/puiseux_series_ring.py

@@ -277,6 +277,29 @@ def uniformizer(self):
 
     Element = PuiseuxSeries
 
+    def _magma_init_(self, magma):
+        """
+        Used in converting this ring to the corresponding ring in MAGMA.
+
+        EXAMPLES::
+
+            sage: # optional - magma
+            sage: R = PuiseuxSeriesRing(QQ, 'y')
+            sage: R._magma_init_(magma)
+            'SageCreateWithNames(PuiseuxSeriesRing(_sage_ref...),["y"])'
+            sage: S = magma(R)
+            sage: S
+            Puiseux series field in y over Rational Field
+            sage: S.1
+            y
+            sage: magma(PuiseuxSeriesRing(GF(7), 'x'))                                     # needs sage.rings.finite_rings
+            Puiseux series field in x over GF(7)
+        """
+        B = magma(self.base_ring())
+        Bref = B._ref()
+        s = 'PuiseuxSeriesRing(%s)' % (Bref)
+        return magma._with_names(s, self.variable_names())
+
     def _element_constructor_(self, x, e=1, prec=infinity):
         r"""
         Construct a Puiseux series from ``x``.