sage: 3%(-1)
0
sage: Rational(3)%Rational(-1)
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call
last)
....
/usr/local/src/sage-4.1.1/local/lib/python2.6/site-packages/sage/rings/
rational.so in sage.rings.rational.Rational.__mod__ (sage/rings/
rational.c:17130)()
....
ZeroDivisionError: Inverse does not exist.
---------------------------------------------------------------------------
Line 17130 comes from rational.pyx:
2277 def __mod__(Rational self, other):
....
2295 other = integer.Integer(other)
2296 if not other:
2297 raise ZeroDivisionError, "Rational modulo by zero"
2298 n = self.numer() % other
2299 d = self.denom() % other
2300 _sig_on
2301 d = d.inverse_mod(other)
2302 _sig_off
2303 return (n*d)%other
When self.denom() is divisible by other, d is 0 and that causes the
error.
So why does the following work?
sage: Rational(3)%Rational(1)
0
Let's look at integer.pyx:
4705 if mpz_cmp_ui(m.value, 1) == 0:
4706 return zero
Thus d.inverse_mod(1) will return 0. However, this contradicts the
docstring, which states:
- ``x`` - Integer such that x*self = 1 (mod m), or
raises ZeroDivisionError.
It is not true that 0*d = 1 (mod 1).
Lines 4705 and 4706 of integer.pyx look like a kludge that in some
situations, such as calculating Rational(3)%Rational(1), makes a wrong
algorithm appear to be correct.
Why not replace lines range(2298,2304) of rational.pyx by the natural
n = floor(self)
return n%d + (self-n)
In fact, this code is applicable to anything that has the attribute
floor() (except SR) and could appear at a higher level.
Dirk
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