Re: Roadmap

I've been trolling my wife's cookbooks.
There I find basic ingredients (e.g. make batter, making
eggs), main dishes (steak), and 7-course means (how to
choose side dishes, wines, etc). The 'cake' section, for
example, has option "subroutines" such as toppings.

The idea would be to develop a cookbook-style of presentation
for computational mathematics. Pick an algorithm, write a page.
When something is used that is not explained, there is a reference
to other sections (ala cakes that suggest "see the frostings")

Each entry would be an algorithm or idea, explained in at most one
2-sided loose-leaf paper. The algorithms would be gathered into
sections, e.g. "basic ingredients" like resultant, "main dishes"
like polynomial factorization, and "7-course meals" like solving
the heat equation (target is the physics class). The 'cake'
subroutines would involve choice of polynomial representation,
sparse, dense, distributed, recursive, etc.

I want to be able to "write in the small" (1 page) with a focus on
a single subject but "organize in the large" so I can shuffle these
subjects into groups by purpose. The analogy is that my wife has
a cookbook that only deals with pickles. I'd like a cookbook that
only deals with rings, composed of loose-leaf selections from the
overall collection. This would be assembled for a computational
mathematics class. The same material could be re-arranged and
re-selected for a different class.

The key focus is on providing explanation and motivation. Most
books that mention the resultant spend pages on the proof and
not a word about why or where to use it.

The 1 page / 2 sides focus is much easier to write than a whole
chapter and, since you're staring at a single routine, it is easier
to provide motivation for why it exists and what the tradeoffs are.
"How" is interesting but "Why" is vital.

I've drafted a 0th cut at the idea. See
http://daly.axiom-developer.org/EUCDOMgcd.pdf
http://daly.axiom-developer.org/EUCDOM.tex

The explanation/motivation section will be written tomorrow,
actually later today (it's 5:20am).


On Thu, Jul 21, 2016 at 4:56 AM, Andrew Tonks <[email protected]> wrote:

> I have deadlines coming out of my ears, but I'll do what I can!  What's
> the best way to start?
> PS: did you read the slides from Stein last month?
> https://plus.google.com/+SagemathCloud/posts/SznVXWHQbyS
>
>
> On 21 July 2016 at 01:11, Tim Daly <[email protected]> wrote:
>
>> >I've been checking the progress of axiom over the years,
>> somewhat despondently, I probably even installed it 3 or 4
>> years ago but didn't spend enough time looking at it. Sagemath
>> has taken over maybe. But I'd be very interested if there is an
>> updated roadmap or research project in preparation somewhere.
>>
>> I'm trying hard to make Axiom live.
>>
>> You'll notice that of the many (I made a CD with over 100)
>> dozens of CAS started in the 1970-2000s, only Mathematica,
>> Maple, and Axiom (of the big systems) still seem to be maintained.
>>
>> Macsyma died when Symbolic died (although you can still run it on
>> DOS). Maxima, the FOSS version, has not been changed since
>> 2005.
>>
>> Symbolics Macsyma is what worries me the most. A LOT of
>> computational mathematicians depend on Mathematica and Maple.
>> But companies, like Symbolics, die (average less than 15 years).
>>
>> Maplesoft died (it was bought by a Japanese firm, fortunately).
>> Soft Warehouse (Derive) died. TI bought it and makes calculators.
>>
>> What happens when Wolfram goes out of business? Mathematica
>> can't be given away as software is now considered a "hard asset",
>> which means it would have to be sold to someone.
>>
>> If (when?) Maple and Mathematica get withdrawn from the market,
>> what will become of computational mathematics? What happens
>> when your code will no longer run?
>>
>> Open Source is not a solution. Maxima is open source but the only
>> changes seem to be in autoconf to keep it running. There is no
>> active development at all.
>>
>> FOSS projects die when their founders stop working on them.
>> One of the key reasons is that software is written in tiny files
>> (as if it had to run on a PDP-11), and stacked up into piles like
>> sand. This pile-of-sand (POS) approach makes it really hard to
>> get into an existing project, especially one the size of Axiom
>> (1.2 million lines of code).
>>
>> I'm trying to get Axiom to the point where it can be maintained,
>> modified, and extended by new people. To that end, I've spent
>> a lot of time converting the system, using Knuth's Literate
>> Programming idea. The hope is that people will be able to
>> read and understand the code.
>> https://en.wikipedia.org/wiki/Axiom_%28computer_algebra_system%29
>>
>> I want to add your code to the system but I also want to use
>> your paper (with attribution, of course) to explain the code so
>> others "have a clue". The raw code is completely opaque.
>>
>> So, in the near term, the "roadmap" is to try to relate the code
>> to the literature. I'm trolling the world for Axiom references,
>> building a bibliography, and connecting the ideas and papers
>> to the existing code.
>>
>> I'm asking people to write simple introductions
>> to their areas of expertise with a focus on Axiom (e.g. James
>> Davenport just wrote 2 chapters in Volume 2). Feel free to
>> explain simplical and cubical groups at a beginner level, e.g.
>> why and where you might find/use them and what are some
>> basic concepts needed as background.
>>
>> I find that computational mathematicians know WHY they
>> use resultants, chinese remainders, lifting and other ideas.
>> These don't seem to be common knowledge. I'm trying to
>> change that so the code doesn't look like magic.
>>
>> As for research, I'm doing my own (proving Axiom correct)
>> but nobody cares :-)
>>
>> Tim
>>
>>
>
>
> --
>
> Dr Andrew Tonks
>
> Department of Mathematics, University of Leicester,
> University Road, Leicester, LE1 7RH, UK
>
>
> www.le.ac.uk/people/andy-tonks
>
> 0116 252 3881 <+441162523881>
>
> [email protected]
>

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