###--------------------------------------------------------------------------
### 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)
+ a, b = cls.RING._implicit(a), cls.RING._implicit(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
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)
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)
class GFRat (BaseRat):
RING = GF
+ ZERO, ONE = GF(0), GF(1)
class _tmp:
def negp(x): return x < 0