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)

Furthermore, unless there is a clear specification (i.e. axioms) of how

   smaller?: (F, F) -> Boolean
   0: F
   -: F -> F

and perhaps even <: (F, F) -> Boolean are related

  -- Note that we have
  --   CombinatorialFunction(R, F) : Exports == Implementation where
  --     R : Join(Comparable, IntegralDomain)
  --     F : FunctionSpace R
  -- in this context and x: F.)

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.

Ralf

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