If this is not a bug then I don't know what a Set is in Sage! I
define two objects which are equal as tested by == but when I put them
into a Set I get two elements, not one:
sage: K.<z> = CyclotomicField(3)
sage: Ku.<u> = FractionField(PolynomialRing(K,'u'))
sage: a = 27*u^2+81*u+243
sage: b = 27*u-81
sage: c = u^2 + 3*u + 9
sage: d = u-3
sage: s = a/b
sage: t = c/d
sage: s==t
True
sage: Set([s,t])
{(27*u^2 + 81*u + 243)/(27*u - 81), (u^2 + 3*u + 9)/(u - 3)}
In my application I have 12 such expressions (and some of them do
involve the algebraic number z, but not all, as this example shows)
and I wanted a quick way to see how many distinct ones there are. For
simpler objects, Set() has done this. Obviously I can also manually
test them for equality pairwise, but I would prefer not to.
John
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