[Changed thread subject from: Sources of funding - perhaps computer
manufacturers? ]

What I find hard to swallow is the peculiar mix of "parent",
"category", and Python data types (class system and inheritance). In
spite of the available documentation in the category system in Sage, I
really don't know what to use when and how to map it properly to
abstract mathematics in such a way as to gain as much as possible from
the existing Sage libraries.  The situation is very different in
Axiom/Aldor.

It is good that you mention Aldor because it was designed specifically
as the "next generation" of Axiom library compiler but for entirely
non-technical reasons never achieved this status. On the other hand
the Aldor documentation is still the best available documentation of
the Axiom type system.

http://www.aldor.org/docs/aldorug.pdf

Aldor is currently supported only by the FriCAS fork of Axiom. Aldor
development itself is not dead, merely sleeping, and apparently a low
priority for the several people involved.

https://github.com/pippijn/aldor

To the best of my knowledge the Sage-combinat development of the
category system in Sage was motivated largely by the experience of
some of the developers with the Axiom-like category system that was
implemented in MuPad. MuPad was originally modeled after an early
version of Maple and so far as I know has a syntactic/symbolic
orientation at it's core (like Maple, Mathematica and Maxima) rather
than a more "algebraic" one. The MuPad developers borrowed from Axiom
in developing a more static type-oriented architecture for the
library.  Maple itself as you might know has taken a rather different
approach. But in any case, compared to Axiom, the MuPad category
systems seems to me to be more or less grafted-on.  And the Sage
category system seems much more so.

The little that I know about the Julia type system, mostly from
discussions about Axiom and Aldor on that mailing list about a year
ago, is that it has a more malleable design that one might expect to
enable a more integrated implementation of the central ideas of the
Axiom category system.  So far as I know however no one is working on
this specifically.

---

I am happy to continue the discussion of Axiom, Aldor and FriCAS but I
am not sure if this discussion is entirely appropriate the the
sage-devel list.  Is there a Julia/Nemo list where this should be
continued?

Regards,
Bill Page.


On 1 October 2015 at 10:56, Bill Hart <goodwillh...@googlemail.com> wrote:
>
> On Thursday, 1 October 2015 16:35:20 UTC+2, Bill Page wrote:
> <SNIP>
>>
>> Unfortunately while I am very much in favor of the category/domain
>> approach of Axiom and related systems, I find the Sage implementation
>> of this idea almost entirely indigestible.  Perhaps this is not the
>> case for a sufficiently large number of potential Sage developers.
>
>  Bill, I would be very interested if you could elaborate on this point in
> more detail (assume I don't know anything about Aldor/Spad because it is so
> long ago that I read the manual for Aldor that I really have forgotten how
> this works over there).
>
> I'm currently implementing a system in Julia which really follows the design
> of Sage's parent/element setup quite closely (we tried another approach, but
> it failed). Since the project I'm working on is yet very young, I'd like to
> understand what is unpalatable about the Sage approach, since I'm
> essentially using it.
>

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