Franz Lehner wrote:
>
> for some unknown reason OrderedCompletion R required
> R to have OrderedRing rather than OrderedSet to provide
> "x < y". Strangely enough, OrderedSet was not even exported.
> In order to make FriCAS fit for tropical algebra the attached patch tries
> to repair this issue and also adds AbelianMonoid.
> I don't know if it makes sense to add other structures at this point.
Hmm, OrderedSet is fine. However, OrderedRing, AbelianMonoid etc
is a lie: operations are only partial. Do you need extra
structures or is OrderedSet enough? I would prefer to
limit amount of lying in algebra, so it would be better to
avoid adding extra structures, unless it is hard to do things
without them.
BTW: OnePointCompletion claims that it is a ring when argument
is a ring. AFAICS nothing in algebra depends on this.
Some finctions depends on 0 in OnePointCompletion, but
this should be easy to fix.
--
Waldek Hebisch
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