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Submitted by : kratt6 at: 2007-12-05T06:41:43-08:00 (14 years ago)
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Consider

fricas
(1) -> d := continuedFraction(0,[1 for i in 1..], [1 for i in 0..])$CONTFRAC INT

\label{eq1}\zag{1}{1}+ \zag{1}{1}+ \zag{1}{1}+ \zag{1}{1}+ \zag{1}{1}+ \zag{1}{1}+ \zag{1}{1}+ \zag{1}{1}+ \zag{1}{1}+ \zag{1}{1}+ \ldots(1)
Type: ContinuedFraction?(Integer)
fricas
2*d

\label{eq2}1 + \zag{1}{4}+ \zag{1}{4}+ \zag{1}{4}+ \zag{1}{4}+ \zag{1}{4}+ \zag{1}{4}+ \zag{1}{4}+ \zag{1}{4}+ \zag{1}{4}+ \zag{1}{4}+ \ldots(2)
Type: ContinuedFraction?(Integer)

so far, so good. But changing the domain to CONTFRAC UP(x, FRAC INT) makes axiom crash.

The problem appears to be, that INT is ordered, while UP(x, FRAC INT) is not. In contfrac.spad we find:

    eucWhole(a: Q): R == numer a quo denom a

    eucWhole0(a: Q): R ==
        isOrdered =>
            n := numer a
            d := denom a
            q := n quo d
            r := n - q*d
            if r < 0 then q := q - 1
            q
        eucWhole a

If R is INT, eucWhole0(4/3) yields 1, in the other case it returns 4/3. I haven't been able to investigate further yet, though.

Martin




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