>
> There seem to be problems with the various orderings.
>
> As a partial order is reflexive the basic operation in PartialOrder is "<="
> and hence there are categorial implementations for >, >= and < there.
>
> for the category OrderedSet for the total (linear) orderings in FriCAS we
> have "<" as the basic operation. This gives confusion what to implement in
> a domain of OrderedSet.
>
> E.g. I defined a FiniteSet using as first parameter Symbol and a second
> parameter a List of Symbols using as the linear ordering the one from
> the occurence in the List - and implemented <= using smaller? - of
> course a mistake, as smaller? is really < which strange results for
> min and max. But the setting confused.
Well, 'smaller?' should be only used when "I need linear order but
I do not care which one", which should be exceptional. Also
from the name it should be clear that 'smaller?' corresponds to
'<'.
>
> I suggest the following:
>
> stay on "<=" as basic operations also for OrderedSet.
For PartialOrder we do not assume existence of equality and in
cases where we have equality we do not assume that 'x <= y' and
'y <= x' imply 'x = y' (so our is most general definition of
partial order appearing in litarature). In this case using
'<=' is essentially a necessity: we have easy definition of
strict inequality from weak one, but no way to define
weak inequality from strict one.
For OrderedSet we have a choice and using '<' has some
advantages. So I do not see strong reasons to change.
AFAICS existence of 'smaller?' is argument against
change: due to name 'smaller?' should be a strict order
and it good to be able to implement 'smaller? by basic
operation from OrderedSet.
--
Waldek Hebisch
[email protected]
--
You received this message because you are subscribed to the Google Groups
"FriCAS - computer algebra system" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/fricas-devel.
For more options, visit https://groups.google.com/d/optout.
