you are absolutely right, this argument was to quick and unprecise, I
have to confess - after all, it was R. Wisbauer and myself who designed
non-associative structures ages ago in 1991 and added recip to
MagmaWithUnit (which was called MonadWithUnit at that time)
So my remark shoud better read:
All general functions as leftRecip and rightRecip and associator are
soon as we have an associative structure, also it should not disappear
I hope, however, you agree with the intensions of my comment.
Am 02.02.18 um 19:54 schrieb Bill Page:
> On Fri, Feb 2, 2018 at 3:53 AM, Prof. Dr. Johannes Grabmeier privat
> <johan...@grabmeier.net> wrote:
>> All general functions as leftRecip and rightRecip are superfluous as
>> soon we have a recip, ...
> I don't think so. For example 'MagmaWithUnit' is inherited by a very
> large number of domains. It exports 'leftRecip' and 'rightRecip' as
> well as 'recip'. The intended semantics is that, for all x, if
> 'recip(x)' is not "failed" then 'leftRecip(x) = rightRecip(x) =
> recip(x)'. However if 'recip(x)' is "failed" then separate left and/or
> right inverses of x might independently still exist. To make
> 'leftRecip' and 'rightRecip' superfluous requires an additional
> assumption but this could be the default assumption implemented in
> diff --git a/src/algebra/naalgc.spad b/src/algebra/naalgc.spad
> index a9209da..9ae411f 100644
> --- a/src/algebra/naalgc.spad
> +++ b/src/algebra/naalgc.spad
> @@ -112,6 +112,8 @@ MagmaWithUnit() : Category == Magma with
> recip x ==
> (x = 1) => x
> + leftRecip(x) == recip(x)
> + rightRecip(x) == recip(x)
Mit freundlichen Grüßen
Prof. Dr. Johannes Grabmeier
Köckstraße 1, D-94469 Deggendorf
Tel. +49-(0)-991-2979584, Tel. +49-(0)-151-681-70756
Tel. +49-(0)-991-3615-141 (d), Fax: +49-(0)-32224-192688
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