... [snip] ...

SANE version of Axiom is my attack on a fundamental p=
roblem.

--00000000000032148705dda2b5e3--
I guess that's where we differ. Axiom is a piece of research software=
.

Axiom was never intended to be a product. IBM gave us two cho=
ices. Either

find someone to marke=
t it (NAG) or throw it away. FOSS software did

not exist at that time and we were not allowed to work on it i=
n any

capacity once it was so=
ld. That stopped the research but not the desire.

On the "little problem" front I ha=
ve many things I would like to do with

Axiom. For example, I have a hierarchical graph of about 50 different<=
/font>

kinds of matrices arranged so Axio=
m's inheritence would fit perfectly.

Within that set are things like unitary matrices which would have ju=
st

the algorithms you need to do q=
uantum computers. The DHMATRIX

dom=
ain would be usefully extended to drive the several robots I have

He used to ask his Bell Labs colleagues "Wh=
at are the fundamental

in my office. Fourier and Laplace transform=
algorithms would be very

useful f=
or robot dynamics. Graphics algorithms should be extended

=
to show Bode plots. The graphics world could be ext=
ended to do 3D solid

models to use=
with my 3D printer. Quantum-safe encryption uses

lattices which would fit well with skew matrix algorithms. =
There are

a lot of "litt=
le problems" I wish I had time to work on.

Richard Ham=
ming (of Hamming distance fame) has a youtube video [0].

problems in=
your area and why aren't you working on them?"

<=
font color=3D"#888888">

So wha=
t are the "fundamental problems" of combining computers and math?=

Why aren't you working on=
them?

<=
font color=3D"#888888">I see two streams of computer mathematics. The compu=
ter algebra

stream started in the =
60s/70s and uses the "It works for me" approach.

The proof stream started in the 90s and uses the &=
quot;Lets prove my

current theorem=
". The two streams have only James Davenport

in common.

"Computational Mathematics"=
; would be a combination of both of these

streams. Proofs would make Axiom less ad-hoc. Proven computer

algebra algorithms would vastly expand =
proof assistants with trusted

resu=
lts.

I view "Computational Mathematics", combining co=
mputer algebra

and proofs as one o=
f the "fundamental problems" of this era. The

=
Axiom is the best research platform available to sh=
ow both camps

what is possible in =
future mathematics. Axiom showed the power that

comes from using mathematics as a scaffold architecture guidi=
ng

the organization. Grounding the=
group theory scaffold with proofs

will make Axiom a much more solid structure for future mathematics.=

That said, my real motivation is that this research is fun.

I am pretty sure nobody but me will ev=
er care.

I'm a "rese=
arch rat" by nature.

Tim

[0] You and =
Your Research