Ricardo, Yes, I'm familar with Sage. Axiom was originally connected back around 2006 / 2007. William Stein showed me that it runs fine in the latest version.
Unfortunately it doesn't do all of the things Axiom supports. I will look at Elixer LiveView. Thanks. Tim On 9/24/20, Ricardo Corral C. <ricardocorr...@gmail.com> wrote: > Elixir LiveView offers a nice way to interact with the browser. I’ve been > playing rendering OpenAI Atari frames from their Python objects (using > erlport), so it seems like a plausible option for interacting with axiom > too. Note that sagemath.org already interacts with axiom, so maybe > connecting through it serves like a bridge. > > On Thu 24 Sep 2020 at 0:06 Tim Daly <axiom...@gmail.com> wrote: > >> The new Axiom version needs to have a better user interface. >> >> >> >> I'm experimenting with a browser front end that has an Axiom >> >> editor that runs Axiom in the background. This isn't really >> >> a new idea. Maxima has been doing it for years. >> >> >> >> Using the browser has the advantage of integrating the >> >> compiler, interpreter, graphics, and documentation in one >> >> interface. >> >> >> >> I managed to get the editor-in-browser working. >> >> >> >> Axiom already has a browser connection (book volume 11) >> >> designed to replace hyperdoc and working as an >> >> interpreter I/O so this editor would be an extension. >> >> >> >> Since almost all of Axiom is already in hyperlinked PDF >> >> files it will be possible to jump directly to related sections >> >> in the various books. >> >> >> >> Tim >> >> >> >> >> >> >> >> On 9/23/20, Tim Daly <axiom...@gmail.com> wrote: >> >> > Rich Hickey gave a keynote: >> >> > https://www.youtube.com/watch?v=oyLBGkS5ICk >> >> > which, like all of Hickey's talks, is worth watching. >> >> > >> >> > He talks about programs breaking due to things like >> >> > library changes. Around minute 30 he started to talk >> >> > about why "semantic versioning" (e.g. version 1.2.3) >> >> > is meaningless. >> >> > >> >> > I realized this years ago and changed Axiom to use >> >> > the date of the release. It provides the same sort of >> >> > "non-information" but it is easy to find in the changelog. >> >> > >> >> > Tim >> >> > >> >> > >> >> > On 9/5/20, Tim Daly <axiom...@gmail.com> wrote: >> >> >> Geometric algebra also affects another "in-process" goal. >> >> >> >> >> >> I have BLAS and LAPACK in the Axiom sources (volume 10.5). >> >> >> >> >> >> I've spent some time on the question of changing BLAS to use >> >> >> John Gustafson's UNUM representation, which eliminates a lot >> >> >> of code because various "standard errors" cannot occur. See >> >> >> his book "The End Of Error" >> >> >> >> https://www.amazon.com/End-Error-Computing-Chapman-Computational/dp/1482239868 >> >> >> >> >> >> But since Geometric algebra is coordinate free, many of the >> >> >> computations can be done symbolically and then evalulated >> >> >> in final form. >> >> >> >> >> >> BLAS re-caste in Geometric Algebra means that some of the >> >> >> errors, such as roundoff, cannot occur in the symbolic form. >> >> >> >> >> >> This has the potential to make Axiom's BLAS and LAPACK >> >> >> computations faster and more accurate. >> >> >> >> >> >> Tim >> >> >> >> >> >> >> >> >> On 9/5/20, Tim Daly <axiom...@gmail.com> wrote: >> >> >>> I'm in the process of re-architecting Axiom, of course. >> >> >>> >> >> >>> The primary research effort, as you know, is incorporating >> >> >>> proof technology. >> >> >>> >> >> >>> But in the process of re-architecting there are more things >> >> >>> to consider. Two of them are "front and center" at the moment. >> >> >>> >> >> >>> One concern is "Geometric Algebra". See >> >> >>> http://geometricalgebra.net/ >> >> >>> >> https://www.youtube.com/watch?v=0fF2xToQmgs&list=PLsSPBzvBkYjzcQ4eCVAntETNNVD2d5S79 >> >> >>> >> >> >>> Geometric algebra unifies a lot of mathematics. In particular, >> >> >>> it "cleans up" linear algebra, creating a "coordinate-free" >> >> >>> representation. This greatly simplifies and unifies a lot of >> >> >>> mathematics. >> >> >>> >> >> >>> So the question becomes, can this be used to "re-represent" >> >> >>> Axiom mathematics dependent on linear algebra? I don't >> >> >>> know but the idea has a lot of potential for simplification. >> >> >>> >> >> >>> >> >> >>> The second concern is "Category Theory". This theory >> >> >>> provides a simplification and a generalization of various >> >> >>> ideas in Axiom. It also puts constraints on things like an >> >> >>> Axiom "category" to Axiom "category" functors so that the >> >> >>> conversion preserves the mathematical "Category" >> >> >>> structure and properties. >> >> >>> >> >> >>> MIT has a "course" on "Programming with Categories" >> >> >>> >> https://www.youtube.com/playlist?list=PLhgq-BqyZ7i7MTGhUROZy3BOICnVixETS >> >> >>> which makes things rather more understandable. >> >> >>> >> >> >>> So one question is how to re-represent Axiom's type >> >> >>> structure so that it has a correct mathematical "Category" >> >> >>> structure. This, of course, raises the question of Group >> >> >>> Theory with Type Theory with Proof Theory with Category >> >> >>> Theory. >> >> >>> >> >> >>> Getting all of this "aligned" (and hopefully reasonably >> >> >>> correct) will give Axiom a solid mathematical foundation. >> >> >>> >> >> >>> Mathematics has changed a lot since Axiom was created >> >> >>> and many of those changes have shown that we need a >> >> >>> much stronger basis for ad-hoc things like coercion, etc. >> >> >>> >> >> >>> >> >> >>> Tim >> >> >>> >> >> >>> >> >> >>> On 8/21/20, Tim Daly <axiom...@gmail.com> wrote: >> >> >>>> A briliant essay: >> >> >>>> >> >> >>>> In exactly the same way a small change in axioms >> >> >>>> (of which we cannot be completely sure) is capable, >> >> >>>> generally speaking, of leading to completely different >> >> >>>> conclusions than those that are obtained from theorems >> >> >>>> which have been deduced from the accepted axioms. >> >> >>>> The longer and fancier is the chain of deductions >> >> >>>> ("proofs"), the less reliable is the final result. >> >> >>>> >> >> >>>> https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html >> >> >>>> >> >> >>>> >> >> >>>> On 8/8/20, Tim Daly <axiom...@gmail.com> wrote: >> >> >>>>> Mark, >> >> >>>>> >> >> >>>>> You're right, of course. The problem is too large. >> >> >>>>> So what. is the plan to achieve a research result? >> >> >>>>> >> >> >>>>> There are 3 major restrictions on the effort (so far). >> >> >>>>> >> >> >>>>> First, the focus is on the GCD in NonNegativeInteger. >> >> >>>>> Volume 13 is basically a collection of published thoughts >> >> >>>>> by various authors on the GCD, a background literature >> >> >>>>> search. Build a limited system with essentially one user >> >> >>>>> visible function (the NNI GCD) and implement all of the >> >> >>>>> ideas there. This demonstrates inheritance of axioms, >> >> >>>>> specification of functions, pre- and post-conditions, >> >> >>>>> proof integration, provisos, the new compiler, etc. >> >> >>>>> >> >> >>>>> Second, make the SANE GCD work in the current Axiom >> >> >>>>> system by generating compatible code. This gives a >> >> >>>>> stepping-stone approach where things can be grounded. >> >> >>>>> Obviously none of the new proof ideas will be expected >> >> >>>>> to work in the current system but it "gives a place to stand". >> >> >>>>> >> >> >>>>> Third, develop a lattice of functions. The idea is to attack the >> >> >>>>> functions that depend on almost nothing, prove them correct, >> >> >>>>> and use them to prove functions that only depend on the >> >> >>>>> prior layer. I did this with the category structure when I first >> >> >>>>> got the system since it was necessary to bootstrap Axiom >> >> >>>>> without a running system (something that was not possible >> >> >>>>> with the IBM/NAG version). That effort took several months >> >> >>>>> so I expect that function-lattice to take about the same time. >> >> >>>>> >> >> >>>>> This makes the research "incremental" so that a result can >> >> >>>>> be achieved in one lifetime. Like a PhD thesis, it is initially >> >> >>>>> intended as a small step forward but still be a valid instance >> >> >>>>> of "computational mathematics", deeply combining proof and >> >> >>>>> computer algebra. >> >> >>>>> >> >> >>>>> Tim >> >> >>>>> >> >> >>>> >> >> >>> >> >> >> >> >> > >> >> >> >> -- > Ricardo Corral C. > -------------------------------------------- >