On Tue, Jun 12, 2012 at 4:11 PM, William Stein <wst...@gmail.com> wrote:
> On Tue, Jun 12, 2012 at 3:54 PM, rych <rych...@gmail.com> wrote:
>> Interval arithmetics also gives False,
>>
>> sage: from mpmath import iv
>> sage: # iv.prec = 24
>> sage: # iv.prec = 53 # for double precision
>> sage: x = 0.1
>> sage: iv.prec = x.prec() # precision of Sage Real numbers, 53
>> sage: iv.pretty = True
>> sage: iv.mpf('10.44')
>> [10.439999999999999503, 10.440000000000001279]
>> sage: iv.mpf('10.44')-iv.mpf('10.30')
>> [0.13999999999999879208, 0.14000000000000234479]
>> sage: iv.mpf('0.14')
>> [0.13999999999999998557, 0.14000000000000001332]
>> sage: iv.mpf('10.44')-iv.mpf('10.30') == iv.mpf('0.14')
>> False
>> sage: iv.mpf('10.44')==iv.mpf('10.44')
>> True
>
> Another approach to interval arithmetic:
>
> sage: RIF
> Real Interval Field with 53 bits of precision
> sage: RIF('10.44') - RIF('10.30')
> 0.14000000000000?
> sage: RIF('10.44') - RIF('10.30') == RIF('0.14')
> False
> sage: a = RIF('10.44') - RIF('10.30'); b = RIF('0.14')
> sage: a in b
> False
> sage: b in a
> True
sage: a.intersection(b)
0.1400000000000000?
sage: 0 in (a-b)
True
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