Johannes Grabmeier wrote:
> 
> I am just adding and correcting feature to basic algebraic domains, e.g.
> SAE, LocalAlgebra and Fraction,

> To this end I came to change the output of SAE - and for that I invented
> a Category, which easily
> allows the user to change the coercion to OutputForm. I suggest to
> include that into the system
> to be able to use that on several places, e.g. different form of
> permutation representations as
> Lehmer code (e.g.).

This is rather unusual code.  AFAICS it uses default package
to esentially "inject" extra state into domains.  I do not
see why you think we need such extraordinay approach.
Namely, idea of OutputForm was to capture _structure_ of
the output so that different surface forms can be produced
on demand.  Things like greek letters, and similar could be
handled at OutputForm level.  If needed we can enrich
OutputForm to allow more features.

On more general level, FriCAS is divided into large number of
domians and categories.  That way a lot of things can be
changed in one part without affecting other parts.  But to
have usable complete system other things need coordination.
In particular, we need consistent way to control output.
Current system is somewhat rigid, but IMO resonably clear.
Designing more flexible system we need to make clear what
protocol is in use, what are responsibilities of domains,
what will be done by "central" code (like OutputForm and
formatters), at which point code should look at user preferences,
etc.  Without clear design next people extending system
will not know what to do and likely try different ways,
leading to incomprehensible mess.

IIUC you have an implementation.  So as first step in explaining
your design you could post all code needed to reproduce
the examples.

Best wishes

-- 
                              Waldek Hebisch

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