Re: [Axiom-developer] branches/daly/axiom

[Martin Rubey]

Dear Tim,

address@hidden writes:

> Second, I think we need to concentrate on having a comprehensive
> test mechanism for the algebra that will alert us to things we
> break. I'm concerned that "obvious" fixes in one domain end up
> introducing "non-obvious" breakage in another. It is not obvious
> how to do this. 

Yes it is: make Christian Aistleitners AldorUnit available.  Please, do not try
to invent the wheel yet another time.  I'm not going to do it on my own, but I
can help, if someone starts it.  I'm sure Christian will help, too.

> Future plans are to look at updating the algebra, do a review of
> the outstanding bugs, and a review of the complaints and comments
> posted to the mailing list archives. It would be useful if other
> people did the same and, hopefully, create a diff-Naur patch.

Those bugs on issue tracker I know how to fix are fixed.  The others are
difficult, i.e., need better organization of the categories, or need a better
compiler, i.e., Aldor.

Apart from that, don't believe that the algebra code of Axiom would be
especially good.  I'm not saying it's bad, but it is *far* behind MuPAD's, for
example.

The way to fix this is

* reorganize old categories (for example, implement the missing bits of PFE)

* implement new, "good" domains.  I believe, for many many mathematicians,
  domains for algebraic differential equations and a related class of
  recurrence relations would be very helpful.

  Implementing provisos for the EXPR domain would also be very good, but
  perhaps not as easy.

* implement algorithms which are known to be very effective, like Gruntz's for
  limits, work of Bernhard Gittenberger et al. for asymptotic expansions, work
  of Carsten Schneider for summation, etc.

I think the first two items are easier, and will assist in work on the third
item.

Martin