Magma padics

src/sage/ext_data/magma/sage/basic.m

@@ -125,7 +125,7 @@ intrinsic Sage(X::RngIntRes) -> MonStgElt, BoolElt
   return Sprintf("Zmod(%o)", Characteristic(X)), false;
 end intrinsic;
 
-/* Approximate fields */
+/* Approximate real and complex fields */
 
 intrinsic Sage(X::FldRe) -> MonStgElt, BoolElt
 {}
@@ -147,6 +147,34 @@ intrinsic Sage(X::FldComElt) -> MonStgElt, BoolElt
   return Sprintf("%o([%o, %o])", Sage(Parent(X)), Sage(Real(X)), Sage(Imaginary(X))), true;
 end intrinsic;
 
+/* p-adic rings and fields */
+
+intrinsic Sage(X::RngPad) -> MonStgElt, BoolElt
+{p-adic rings, either free precision model or exact model}
+    prec := Precision(X);
+    if Type(prec) eq Infty then
+      return Sprintf("Zp(%o, %o, 'relaxed')", Sage(Prime(X)), Sage(Precision(X))), false;
+    else
+      return Sprintf("Zp(%o, %o, 'capped-rel')", Sage(Prime(X)), Sage(Precision(X))), false;
+    end if;
+end intrinsic;
+
+intrinsic Sage(X::FldPad) -> MonStgElt, BoolElt
+{p-adic fields, either free precision model or exact model}
+    prec := Precision(X);
+    if Type(prec) eq Infty then
+      return Sprintf("Qp(%o, %o, 'relaxed')", Sage(Prime(X)), Sage(Precision(X))), false;
+    else
+      return Sprintf("Qp(%o, %o, 'capped-rel')", Sage(Prime(X)), Sage(Precision(X))), false;
+    end if;
+end intrinsic;
+
+intrinsic Sage(X::RngPadRes) -> MonStgElt, BoolElt
+{fixed precision model}
+    return Sprintf("Zp(%o, %o, 'fixed-mod')", Sage(Prime(X)), Sage(Precision(X))), false;
+end intrinsic;
+
+
 /* Polynomials */
 
 intrinsic SageNamesHelper(X::.) -> MonStgElt

src/sage/rings/padics/padic_base_leaves.py

@@ -304,6 +304,19 @@
                 from sage.rings.padics.padic_generic import ResidueLiftingMap
                 return ResidueLiftingMap._create_(R, self)
 
+    def _magma_init_(self, magma):
+        """
+        Conversion to magma.
+
+        EXAMPLES::
+
+            sage: # optional - magma
+            sage: F = Qp(5,7,"capped-rel")
+            sage: magma(F)
+            5-adic field mod 5^7
+        """
+        return f"pAdicRing({self.prime()},{self.precision_cap()})"
+
 
 class pAdicRingCappedAbsolute(pAdicRingBaseGeneric, pAdicCappedAbsoluteRingGeneric):
     r"""
@@ -607,6 +620,19 @@
                 from sage.rings.padics.padic_generic import ResidueLiftingMap
                 return ResidueLiftingMap._create_(R, self)
 
+    def _magma_init_(self, magma):
+        """
+        Conversion to magma.
+
+        EXAMPLES::
+
+            sage: # optional - magma
+            sage: F = Zp(5,7,"fixed-mod")
+            sage: magma(F)
+            Quotient of the 5-adic ring modulo the ideal generated by 5^7
+        """
+        return f"pAdicQuotientRing({self.prime()},{self.precision_cap()})"
+
 
 class pAdicFieldCappedRelative(pAdicFieldBaseGeneric, pAdicCappedRelativeFieldGeneric):
     r"""
@@ -719,6 +745,19 @@
                 from sage.rings.padics.padic_generic import ResidueLiftingMap
                 return ResidueLiftingMap._create_(R, self)
 
+    def _magma_init_(self, magma):
+        """
+        Conversion to magma.
+
+        EXAMPLES::
+
+            sage: # optional - magma
+            sage: F = Qp(5,7,"capped-rel")
+            sage: magma(F)
+            5-adic field mod 5^7
+        """
+        return f"pAdicField({self.prime()},{self.precision_cap()})"
+
     def random_element(self, algorithm='default'):
         r"""
         Return a random element of ``self``, optionally using the ``algorithm``