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)

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