Trac #20310: change for p-adic rings

Started as a proposal to change precision of rings, this is now a more
general `change` method.

URL: https://trac.sagemath.org/20310
Reported by: caruso
Ticket author(s): David Roe
Reviewer(s): Julian Rüth, Xavier Caruso

src/sage/categories/pushout.py

@@ -2371,7 +2371,7 @@ def __init__(self, p, prec, extras=None):
                     raise ValueError("completion type must be one of %s"%(", ".join(self._real_types)))
             else:
                 if self.type not in self._dvr_types:
-                    raise ValueError("completion type must be one of %s"%(", ".join(self._dvr_types)))
+                    raise ValueError("completion type must be one of %s"%(", ".join(self._dvr_types[1:])))
 
     def _repr_(self):
         """
@@ -2473,7 +2473,7 @@ def __ne__(self, other):
         return not (self == other)
 
     _real_types = ['Interval','Ball','MPFR','RDF','RLF']
-    _dvr_types = [None, 'fixed-mod','capped-abs','capped-rel','lazy']
+    _dvr_types = [None, 'fixed-mod','floating-point','capped-abs','capped-rel','lazy']
 
     def merge(self, other):
         """
@@ -2557,9 +2557,9 @@ def merge(self, other):
                 return CompletionFunctor(self.p, new_prec, {'type':new_type, 'sci_not':new_scinot, 'rnd':new_rnd})
             else:
                 new_type = self._dvr_types[min(self._dvr_types.index(self.type), self._dvr_types.index(other.type))]
-                if new_type == 'fixed-mod':
-                    if self.type != 'fixed-mod' or other.type != 'fixed-mod':
-                        return None # no coercion into fixed-mod
+                if new_type in ('fixed-mod', 'floating-point'):
+                    if self.type != other.type:
+                        return None # no coercion into fixed-mod or floating-point
                     new_prec = min(self.prec, other.prec)
                 else:
                     new_prec = max(self.prec, other.prec) # since elements track their own precision, we don't want to truncate them