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#404 axiom gold does not build on openSUSE 10.3 x86_64 ←	↑	→ #406 test specification of axiom version in issues

#405 ContinuedFraction and Polynomial Domains

Edit detail for #405 ContinuedFraction and Polynomial Domains revision 2 of 7

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Editor: kratt6 Time: 2007/12/05 06:44:02 GMT-8
Note:

changed:
- d := continuedFraction(0,[1 for i in 1..], [1 for i in 0..])$CONTFRAC INT
- 2*d
d := continuedFraction(0,[1 for i in 1..], [1 for i in 0..])$CONTFRAC INT
2*d

Consider

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

(1)

Type: ContinuedFraction? Integer

axiom
2*d

(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