Ralf Hemmecke wrote:
>
> On 08/05/2014 06:38 PM, Waldek Hebisch wrote:
> > I am thinking about including (possibly improved)
> > version of this patch. Comments?
>
> This is probably only a side remark, but nevertheless, I would like to
> raise it here.
>
> I understand that a (technical) linear order is sometimes useful to get
> a "nice" result, but I must criticize the use or the definition of
> "smaller?".
>
> Looking at the definition at
> http://fricas.github.io/api/Comparable.html#index-1 doesn't tell me that
> smaller? has anything to do with a (possibly) partial order < on the domain.
>
> isign x ==
> zero? x => 0
> is?(x, opabs) => 1
> is?(x, opsign) => x
> smaller?(x, 0) => kernel(opsign, -x)
> kernel(opsign, x)
>
<snip>
> I would claim that the above is a clear bug, since it builds on an order
> that is specifiecd to be just some arbitrary technical linear order.
Note that 'sign' is an odd function. So the above is a bug
because it makes 'sign' symmetric. But once we add missing
minus using 'smaller?' just implements axiom of choice:
we do not care if we get x or -x, but want to get only
one of them, not both.
--
Waldek Hebisch
[email protected]
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