Yes, #(0 0 0) is the additive identity in *that* case.
But in #((1 2) (3 4) (5 6)) sum it is #(0 0).
And in #(((1 2 3) (4 5 6)) ((9 8 7) (6 5 4))) sum
==> #(#(10 10 10) #(10 10 10)) it is #((0 0 0) (0 0 0)).
I suppose you could have
SequenceableCollection>>zero
^self collect: [:each | each zero]
The point is that it cannot in general be based on the *class* of some
element of the receiver but depends on the *value*.
But then we run into the amusing cases like
{ 1 hour. DateAndTime now} sum
where an additive identity for Durations makes sense but an
additive identity for DateAndTimes does not, and similarly
{Date today. 1} sum
In my case, an additional problem is that I have
Object
Enumerable (#sum and #product go here)
Collection
where Enumerable holds everything that can be defined just using #do:
without assuming that you can do it more than once, so it was necessary
to come up with a streaming definition for #sum that examines each
element once and only once. When you do that, you discover that you
don't *need* a zero except when the collection is empty, and in that case
you can't *tell* what sort of zero would be appropriate.
On Thu, 26 Mar 2020 at 01:00, Sven Van Caekenberghe <s...@stfx.eu> wrote:
>
> #(0 0 0) is the additive identity in that case
>
> > On 25 Mar 2020, at 12:38, Richard O'Keefe <rao...@gmail.com> wrote:
> >
> > There are situations where #+ and #sum make sense but there is no additive
> > identity. Here is an example:
> > #((1 2 3) (4 5 6) (7 8 9)) sum
> >
> > On Tue, 24 Mar 2020 at 02:46, James Foster <smallt...@jgfoster.net> wrote:
> >>
> >>
> >>> On Mar 23, 2020, at 6:06 AM, Sven Van Caekenberghe <s...@stfx.eu> wrote:
> >>>
> >>> What you found out now is that the clever trick used to avoid picking an
> >>> additive identity (picking an element, counting it twice and then
> >>> subtracting it) leads to a loss of precision when floating point numbers
> >>> are involved. This is an important issue.
> >>
> >> If this approach is to be preserved, then each class should have an
> >> additive identity so instead of adding and subtracting an object, we let
> >> the object tell us its zero.
> >>
> >> James
> >
>
>
