oldk1331 wrote:
>
> The problem is about branch cuting:
>
> For Integers and Fractions, (-1/8)^(1/3) gives AlgebraicNumber
> containing (-1)^(1/3), avoids branch cuting.
>
> For numeric computing, for example Float, I think it's better
> to have signature:
> ^ : (%, Fraction Integer) -> %
> aka keep current definition of '^'.
>
> People can use "((-0.125)^(1/3))$Complex Float" to get principle
> complex value.
Signature is clear. But the question is if current behaviour
is useful? I suppose that if a teacher defines x^(1/3) as
returning negative values for negative x, then the definition
is useful for him. But otherwise it is not clear: there
is discrepancy with symbolic behaviour. I other posts
I argued that we can not always have agreement between
symbolic and numeric values. But here we introduce
large discrepancy (for "half" of allowed x-ses) with
unclear gain. Do people depend on numeric x^(1/3) beeing
defined for negative arguments? When going from
positive to negative values we hop from one brnach to
the other -- it seems unlikely that such thing can
happen in realistic useful formula.
--
Waldek Hebisch
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