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] >
_______________________________________________ Axiom-developer mailing list [email protected] https://lists.nongnu.org/mailman/listinfo/axiom-developer
