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


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?

Thanks in advance,
Timo

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