I am trying to use the Real Interval Field (RIF), which in principle
does exactly what I want. But I cannot understand this:
sage: a=RIF(-1,1)
sage: a.diameter()
2.00000000000000
sage: [b.diameter() for b in a.bisection()]
[1.00000000000000, 1.00000000000000]
sage: [[c.diameter() for c in b.bisection()] for b in a.bisection()]
[[0.666666666666667, 0.500000000000000],
[0.500000000000000, 0.666666666666667]]
I bisect an interval of length ("diameter") 2 twice, but 2 of the 4
pieces have diameter 2/3! I assumed that the diameters of the output
of bisection() added to the original diameter, but this appears not to
be happening. If this is not a bug then I don't understand something.
Perhaps this makes it clearer:
sage: a=RIF(-1,1)
sage: b=a.bisection()[0]
sage: c=b.bisection()[0]
sage: c.lower()
-1.00000000000000
sage: c.upper()
-0.500000000000000
sage: c.diameter()
0.666666666666667
I think that what I need is
sage: c.absolute_diameter()
0.500000000000000
but did not understand "diameter". OK, so I have answered my own
question, but I think I might as well post it anyway!
John Cremona
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