> So, why exactly it is not going to happen ?
Axiom was a research platform for new ideas and new algorithms,
originally developed at IBM Research as "Scratchpad". The funding
dried up and we had to shut it down. The idea was proposed of
selling it but, for various reasons, IBM was not going to sell it as
an IBM product.
Axiom was removed from IBM Research and sold to the Numerical
Algorithms Group (NAG). NAG sold it for a few years and withdrew it
from the market. They generously gave me the source code.
It took a while to restructure Axiom for open source. As one of the
original IBM team I had a lot of knowledge about the program no one
else working on the open source had. It was clear that when I stopped
working on it the knowledge would be gone. This was already a problem
as some of the algebra authors were dead.
I thought about ways we could make it possible to capture, structure,
and pass on the knowledge. Eventually I settled on Knuth's Literate
Programming idea. Textbooks, such as Lisp In Small Pieces, were
what attracted me to the idea.
Like the Physically Based Rendering book, it should be possible to
find any algorithm. Each algorithm would have an explanation (note:
NOT documentation), literature references (since many algorithms are
PhD research results), proofs, cross references to supporting algorithms,
limitations, examples, tests, etc. I gave a talk on this at a conference:
When I introduced the Axiom project I also announced project goals.
One of those goals was to restructure Axiom into a literate program.
Apparently, like other project goals, this one was ignored.
So far I have done the primitive restructuring. See:
These books contain the actual source code which, during the
Axiom build process, is "tangled" and compiled. So most of the
system is "literate" but only in skeleton form. I've been concentrating
on collecting and entering historical documents that only I own as
well as getting permission from Scratchpad-related paper authors for
re-creating and re-publishing as part of the books. Along with other
project goals (e.g. the Computer Algebra Test Suite)
no-one seems to want to contribute.
At the moment, and for the last few years, I've been working on
another project goal. I'm trying to prove Axiom algorithms correct.
I spent 6 years attached to CMU as a visiting scholar working on
merging proof technology with computer algebra. Like other work
I have it partially implemented. The problems are hard and subtle.
I gave a talk on this effort at ICMS 2018
This is taking up all of my Axiom-related time and effort so although
I really want to expand and improve the literate programs I can't
seem to find the time to do it.
The potential for proven, explained, and tested computational
mathematics that anyone can "pick up, read, and contribute"
exists but won't happen. "Literate Axiom" is not going to win
a Fields Medal.
Tim