On Mar 22, 2010, at 10:44 AM, Timo wrote:
Hello,
I would like the following commands to return 0 in sage:
sage: AA(1) - AA(1)
0
sage: AA(15/9) - AA(15/9)
0
sage: AA(sqrt(2)) - AA(sqrt(2))
0.?e-18
sage: AA(sqrt(3)) - AA(sqrt(3))
0.?e-18
sage: AA(3^(22/5)) - AA(3^(22/5))
0.?e-16
sage: AA(3^(222/5)) - AA(3^(222/5))
0.?e3
sage: AA(3^(222/54)) - AA(3^(222/54))
0.?e-16
All of these are == 0, it just doesn't do this by default because that
may be expensive to do on every operation.
Very strange behaviour occurs (division by zero is *sometimes*
possible!):
sage: AA(0) == 0
True
sage: 1/AA(0)
ValueError: algebraic number division by zero
sage: AA(sqrt(2)) - AA(sqrt(2)) == 0
True
sage: 1/(AA(sqrt(2)) - AA(sqrt(2)))
[-infinity .. +infinity]
Is this normal behaviour of the "Algebraic Real Field" object?
Yes. It is lazy in computing exact algebraic values in these cases. (I
might be in favor of exactifying division for possibly zero values.)
- Robert
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