How to represent the infinite ?

[Cliff Wells]

On Thu, 20 Jun 2002 17:02:33 +0200
erreur wrote:

> Will somebody have an idea, to represent the infinite one?
> 
> I have variables to initialize with is +inf (or - inf).  To be sure that
> later, all will be smaller (or larger) than my variables.
> I tried to redefine the operators on an object.  It goes for Inf>10 but I do
> not arrive for 10>Inf (because that takes > of Int).
> 
> --------------------
> 
> def __gt__(self, val):
> 
>     return 1
> 
> --------------------

Hm, for some reason, my last two posts on this thread didn't seem to go
through...  one more try (with a couple of little enhancements):

from __future__ import generators

class Infinity(int):
    def __init__(self):
        int.__init__(self)
        self.sign = 1

    def __str__(self):
        return "%sInfinity" % {-1: "-", 1: ""}[self.sign]

    def __repr__(self):
        return "<%s>" % self

    def __cmp__(self, n):
        if isinstance(n, Infinity):
            return cmp(self.sign, n.sign)
        return self.sign
    
    def __neg__(self):
        retval = Infinity()
        retval.sign = self.sign * -1
        return retval

    def __mul__(self, n):
        retval = Infinity()
        retval.sign = self.sign * cmp(n, 0)
        return retval

    def __div__(self, n):
        if isinstance(n, Infinity):
            # or should this raise an exception?
            return self.sign / n.sign
        return self * n

    def __add__(self, n):
        if isinstance(n, Infinity):
            if n.sign != self.sign:
                return 0
        return self

    def __sub__(self, n):
        return self + -n

    def __iter__(self):
        return self.next()

    def next(self):
        n = 0
        while 1:
            yield n
            n += self.sign            

    
if __name__ == '__main__':
    import sys
    
    m = -Infinity()
    n = Infinity()

    print m
    print n
    print m * n
    print n * n
    print m * m

    assert(m < n)
    assert(n > m)
    assert(m == m)
    assert(n == n)
    assert(m != n)
    assert(m < 0)
    assert(n > 0)
    assert(m != 0)
    assert(m < -sys.maxint)
    assert(n > sys.maxint)
    assert(m < -m)
    assert(n == -m)

    assert(n * 1 == n == -m)
    assert(n * 1000 == n)
    assert(n * -1 == m)
    assert(n * -1000 == m)
    assert(n * 0 == 0)
    assert(m * 1 == m)
    assert(m * 1000 == m)
    assert(m * -1 == n)
    assert(m * -1000 == -m == n)
    assert(m * 0 == 0)
    
    assert(n / 1 == n)
    assert(n / -1 == m)
    assert(n / -1000 == m)
    assert(m / 1 == m)
    assert(m / 1000 == m)
    assert(m / -1 == n)
    assert(m / -1000 == n)

    assert(m + 1 == m)
    assert(m - 1 == m)
    assert(n + 1 == n)
    assert(n - 1 == n)
    
    assert(n + m == 0)
    assert(n - m == n)
    assert(n - n == 0)
    assert(m + m == m)
    assert(m - m == 0)
    assert(m - n == m)

    print m / m
    print n / n
    print m / n
    print n / m
    
    try:
        print 1 / m
    except ZeroDivisionError:
        print "Can't divide by %s" % m

    try:
        print 1 / n
    except ZeroDivisionError:
        print "Can't divide by %s" % n

    for i in Infinity():
        if i > 10:
            break
        print i,

-- 
Cliff Wells, Software Engineer
Logiplex Corporation (www.logiplex.net)
(503) 978-6726 x308  (800) 735-0555 x308