convert magma power series rings

Author: fchapoton

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

@@ -8,7 +8,7 @@ function PreparseElts(R)
 end function;
 
 intrinsic Sage(X::.) -> MonStgElt, BoolElt
-{Default way to convert a Magma object to Sage if we haven't
+{Default way to convert a Magma object to Sage if we have not
 written anything better.}
     return Sprintf("%o", X), true;
 end intrinsic;
@@ -153,16 +153,19 @@ intrinsic SageNamesHelper(X::.) -> MonStgElt
 {}
   /* XXX */
   i := NumberOfNames(X);
-  if i ge 2 then
-      return (&* [ Sprintf("%o, ", X.j) : j in [ 1..i-1 ] ]) * Sprintf("%o", X.i);
+  if "$" in Sprint(X.i) then
+    /* unnamed variables */
+    return "(" * (&* [ Sprintf("'x%o', ", j) : j in [ 1..i ] ]) * ")"
   else
-      return Sprintf("%o", X.i);
-  end if;
+    /* named variables */
+    return "(" * (&* [ Sprintf("'%o', ", X.j) : j in [ 1..i ] ]) * ")"
+  end if:
 end intrinsic;
 
 intrinsic Sage(X::RngUPol) -> MonStgElt, BoolElt
 {}
-  return Sprintf("%o['%o'.replace('$.', 'x').replace('.', '')]", Sage(BaseRing(X)), SageNamesHelper(X)), false;
+  txt := "PolynomialRing(%o, %o)";
+  return Sprintf(txt, Sage(BaseRing(X)), SageNamesHelper(X)), false;
 end intrinsic;
 
 intrinsic Sage(X::RngUPolElt) -> MonStgElt, BoolElt
@@ -173,7 +176,8 @@ intrinsic Sage(X::RngUPolElt) -> MonStgElt, BoolElt
 
 intrinsic Sage(X::RngMPol) -> MonStgElt, BoolElt
 {}
-  return Sprintf("%o['%o'.replace('$.', 'x').replace('.', '')]", Sage(BaseRing(X)), SageNamesHelper(X)), false;
+  txt := "PolynomialRing(%o, %o)";
+  return Sprintf(txt, Sage(BaseRing(X)), SageNamesHelper(X)), false;
 end intrinsic;
 
 intrinsic Sage(X::RngMPolElt) -> MonStgElt, BoolElt
@@ -264,3 +268,23 @@ intrinsic Sage(X::ModTupRngElt) -> MonStgElt, BoolElt
 {}
     return Sprintf("%o(%o)", Sage(Parent(X)), Sage(ElementToSequence(X))), true;
 end intrinsic;
+
+/* Power series rings */
+
+intrinsic Sage(X::RngSerPow) -> MonStgElt, BoolElt
+{}
+  txt := "PowerSeriesRing(%o, %o)";
+  return Sprintf(txt, Sage(BaseRing(X)), SageNamesHelper(X)), false;
+end intrinsic;
+
+intrinsic Sage(X::RngSerLaur) -> MonStgElt, BoolElt
+{}
+  txt := "LaurentSeriesRing(%o, %o)";
+  return Sprintf(txt, Sage(BaseRing(X)), SageNamesHelper(X)), false;
+end intrinsic;
+
+intrinsic Sage(X::RngSerPuis) -> MonStgElt, BoolElt
+{}
+  txt := "PuiseuxSeriesRing(%o, %o)";
+  return Sprintf(txt, Sage(BaseRing(X)), SageNamesHelper(X)), false;
+end intrinsic;

src/sage/interfaces/magma.py

@@ -221,27 +221,28 @@
 
 from sage.structure.parent import Parent
 from .expect import Expect, ExpectElement, ExpectFunction, FunctionElement
-PROMPT = ">>>"
-
-SAGE_REF = "_sage_ref"
-SAGE_REF_RE = re.compile(r'%s\d+' % SAGE_REF)
-
 from sage.env import SAGE_EXTCODE, DOT_SAGE
 import sage.misc.misc
 import sage.misc.sage_eval
 import sage.interfaces.abc
 from sage.interfaces.tab_completion import ExtraTabCompletion
 from sage.misc.instancedoc import instancedoc
 
+PROMPT = ">>>"
+
+SAGE_REF = "_sage_ref"
+SAGE_REF_RE = re.compile(r'%s\d+' % SAGE_REF)
+
 INTRINSIC_CACHE = '%s/magma_intrinsic_cache.sobj' % DOT_SAGE
 EXTCODE_DIR = None
 
 
-def extcode_dir(iface=None):
+def extcode_dir(iface=None) -> str:
     """
-    Return directory that contains all the Magma extcode.  This is put
-    in a writable directory owned by the user, since when attached,
-    Magma has to write sig and lck files.
+    Return directory that contains all the Magma extcode.
+
+    This is put in a writable directory owned by the user, since when
+    attached, Magma has to write sig and lck files.
 
     EXAMPLES::
 
@@ -413,7 +414,7 @@ def __reduce__(self):
         """
         return reduce_load_Magma, tuple([])
 
-    def _read_in_file_command(self, filename):
+    def _read_in_file_command(self, filename) -> str:
         """
         Return the command in Magma that reads in the contents of the given
         file.
@@ -433,7 +434,7 @@ def _read_in_file_command(self, filename):
         """
         return 'load "%s";' % filename
 
-    def _post_process_from_file(self, s):
+    def _post_process_from_file(self, s) -> str:
         r"""
         Used internally in the Magma interface to post-process the result
         of evaluating a string using a file. For Magma what this does is
@@ -462,7 +463,7 @@ def _post_process_from_file(self, s):
             return ''
         return s[i + 1:]
 
-    def __getattr__(self, attrname):
+    def __getattr__(self, attrname) -> MagmaFunction:
         """
         Return a formal wrapper around a Magma function, or raise an
         :exc:`AttributeError` if attrname starts with an underscore.
@@ -494,7 +495,7 @@ def __getattr__(self, attrname):
             raise AttributeError
         return MagmaFunction(self, attrname)
 
-    def eval(self, x, strip=True, **kwds):
+    def eval(self, x, strip=True, **kwds) -> str:
         """
         Evaluate the given block x of code in Magma and return the output
         as a string.
@@ -553,7 +554,7 @@ def eval(self, x, strip=True, **kwds):
             raise RuntimeError("Error evaluating Magma code.\nIN:%s\nOUT:%s" % (x, ans))
         return ans
 
-    def _preparse(self, s):
+    def _preparse(self, s) -> str:
         """
         All input gets preparsed by calling this function before it gets evaluated.
 
@@ -578,7 +579,7 @@ def _preparse(self, s):
             pass
         return s
 
-    def _start(self):
+    def _start(self) -> None:
         """
         Initialize a Magma interface instance. This involves (1) setting up
         an obfuscated prompt, and (2) attaching the MAGMA_SPEC file (see
@@ -619,7 +620,7 @@ def set(self, var, value):
         if out.lower().find("error") != -1:
             raise TypeError("Error executing Magma code:\n%s" % out)
 
-    def get(self, var):
+    def get(self, var) -> str:
         """
         Get the value of the variable var.
 
@@ -1880,10 +1881,11 @@ def __getattr__(self, attrname):
 
     def _sage_(self):
         """
-        Return Sage version of this object. Use self.sage() to get the Sage
-        version.
+        Return Sage version of this object.
+
+        Use self.sage() to get the Sage version.
 
-        Edit src/ext/magma/sage/basic.m to add functionality.
+        Edit ``src/sage/ext_data/magma/sage/basic.m`` to add functionality.
 
         EXAMPLES: Enumerated Sets::