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 and implemented 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 superfluous as 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 > 'MagmaWithUnit'. > > 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 > "failed" > + leftRecip(x) == recip(x) > + rightRecip(x) == recip(x) > -- Mit freundlichen Grüßen Johannes Grabmeier 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 -- 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 fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to firstname.lastname@example.org. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.