catacomb/__init__.py: Prepare rational classes for upcoming changes.

In the near future, we won't be able to guarantee that all rings allow
implicit conversions of (integer) 0 and 1 to the additive and
multiplicative ring identities, so:

  * define `ZERO' and `ONE' class attributes on the concrete classes to
    hold the respective ring identities;

  * make the `_split_rat' function into a private method of the
    `BaseRat' class and adjust callers to match;

  * compare against `ZERO' to detect an exact element of the base ring;
    and

  * return `ONE' as the implicit denominator for a base-ring element or
    foreign object to be converted.

No functional change.

diff --git a/catacomb/__init__.py b/catacomb/__init__.py
index d59d3f3..dc5ecbb 100644 (file)
--- a/catacomb/__init__.py
+++ b/catacomb/__init__.py
@@ -272,15 +272,12 @@ def secret_unbox(k, n, c):
 ###--------------------------------------------------------------------------
 ### Multiprecision integers and binary polynomials.
 
-def _split_rat(x):
-  if isinstance(x, BaseRat): return x._n, x._d
-  else: return x, 1
 class BaseRat (object):
   """Base class implementing fields of fractions over Euclidean domains."""
   def __new__(cls, a, b):
     a, b = cls.RING(a), cls.RING(b)
     q, r = divmod(a, b)
-    if r == 0: return q
+    if r == cls.ZERO: return q
     g = b.gcd(r)
     me = super(BaseRat, cls).__new__(cls)
     me._n = a//g
@@ -294,31 +291,34 @@ class BaseRat (object):
   def __repr__(me): return '%s(%s, %s)' % (_clsname(me), me._n, me._d)
   _repr_pretty_ = _pp_str
 
+  def _split_rat(me, x):
+    if isinstance(x, me.__class__): return x._n, x._d
+    else: return x, me.ONE
   def __add__(me, you):
-    n, d = _split_rat(you)
+    n, d = me._split_rat(you)
     return type(me)(me._n*d + n*me._d, d*me._d)
   __radd__ = __add__
   def __sub__(me, you):
-    n, d = _split_rat(you)
+    n, d = me._split_rat(you)
     return type(me)(me._n*d - n*me._d, d*me._d)
   def __rsub__(me, you):
-    n, d = _split_rat(you)
+    n, d = me._split_rat(you)
     return type(me)(n*me._d - me._n*d, d*me._d)
   def __mul__(me, you):
-    n, d = _split_rat(you)
+    n, d = me._split_rat(you)
     return type(me)(me._n*n, me._d*d)
   __rmul__ = __mul__
   def __truediv__(me, you):
-    n, d = _split_rat(you)
+    n, d = me._split_rat(you)
     return type(me)(me._n*d, me._d*n)
   def __rtruediv__(me, you):
-    n, d = _split_rat(you)
+    n, d = me._split_rat(you)
     return type(me)(me._d*n, me._n*d)
   if _sys.version_info < (3,):
     __div__ = __truediv__
     __rdiv__ = __rtruediv__
   def _order(me, you, op):
-    n, d = _split_rat(you)
+    n, d = me._split_rat(you)
     return op(me._n*d, n*me._d)
   def __eq__(me, you): return me._order(you, lambda x, y: x == y)
   def __ne__(me, you): return me._order(you, lambda x, y: x != y)
@@ -329,6 +329,7 @@ class BaseRat (object):
 
 class IntRat (BaseRat):
   RING = MP
+  ZERO, ONE = MP(0), MP(1)
   def __new__(cls, a, b):
     if isinstance(a, float) or isinstance(b, float): return a/b
     return super(IntRat, cls).__new__(cls, a, b)
@@ -336,6 +337,7 @@ class IntRat (BaseRat):
 
 class GFRat (BaseRat):
   RING = GF
+  ZERO, ONE = GF(0), GF(1)
 
 class _tmp:
   def negp(x): return x < 0