No, the name 'Axiom" is used by many different companies. Trademarks only cover infringement "in the same area" (although the Lexus car company sued a diner named Lexus and "won" because the diner couldn't compete against big corporate lawyer money).
One company in New Jersey named their language "Axiom" and I keep getting calls from recruiters because that company will pay big bucks to hire an "Axiom Developer". Sigh. I just thought the space one was "over the top". I'd sign up to go to space in a heartbeat. I applied to be an astronaut in the 1990s. NASA wanted someone with at least a Master's degree, a background in Robotics, and less than 5'9" tall. I fit the criteria but never heard back. Tim On 9/25/20, William Sit <w...@ccny.cuny.edu> wrote: > Axiom Space, a Houston-based company, is not related to Axiom the scientific > computation system. Or is it? > > William > > William Sit > Professor Emeritus > Department of Mathematics > The City College of The City University of New York > New York, NY 10031 > homepage: wsit.ccny.cuny.edu > > ________________________________________ > From: Axiom-developer > <axiom-developer-bounces+wyscc=sci.ccny.cuny....@nongnu.org> on behalf of > Tim Daly <axiom...@gmail.com> > Sent: Thursday, September 24, 2020 4:26 AM > To: Ricardo Corral C. > Cc: axiom-developer@nongnu.org > Subject: [EXTERNAL] Re: Axiom musings... > > Today's Headline: > > Axiom finalizing agreements for private astronaut mission to space station > > https://urldefense.proofpoint.com/v2/url?u=https-3A__spaceflightnow.com_2020_09_23_axiom-2Dfinalizing-2Dagreements-2Dfor-2Dprivate-2Dastronaut-2Dmission-2Dto-2Dspace-2Dstation_&d=DwIFaQ&c=4NmamNZG3KTnUCoC6InoLJ6KV1tbVKrkZXHRwtIMGmo&r=qW9SUYRDo6sWEVPpx7wwWYZ79PdSWMRxNZvTih0Bkxc&m=HjfsC447T7m29H3fRO5mjUS7vORbNarNjIlj8UKFSH8&s=AvUAZpZ9vnJiQ37yQyMSdNeJQH8qv3HLt5_V1qQ3q2g&e= > > Wow. I HAVE been busy :-) > > Tim > > > On 9/24/20, Tim Daly <axiom...@gmail.com> wrote: >> 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://urldefense.proofpoint.com/v2/url?u=https-3A__www.youtube.com_watch-3Fv-3DoyLBGkS5ICk&d=DwIFaQ&c=4NmamNZG3KTnUCoC6InoLJ6KV1tbVKrkZXHRwtIMGmo&r=qW9SUYRDo6sWEVPpx7wwWYZ79PdSWMRxNZvTih0Bkxc&m=HjfsC447T7m29H3fRO5mjUS7vORbNarNjIlj8UKFSH8&s=oF9rfp-E-CqJ8LCcpq87aURaYtjVP8DwSljlOvjZUFw&e= >>>> >>>> > 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://urldefense.proofpoint.com/v2/url?u=https-3A__www.amazon.com_End-2DError-2DComputing-2DChapman-2DComputational_dp_1482239868&d=DwIFaQ&c=4NmamNZG3KTnUCoC6InoLJ6KV1tbVKrkZXHRwtIMGmo&r=qW9SUYRDo6sWEVPpx7wwWYZ79PdSWMRxNZvTih0Bkxc&m=HjfsC447T7m29H3fRO5mjUS7vORbNarNjIlj8UKFSH8&s=yWXuK9IV2lgeUVht6IFybABGGvhsgr0zuqsb6jwFr-4&e= >>>> >>>> >> >>>> >>>> >> 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 >>>> >>>> >>> https://urldefense.proofpoint.com/v2/url?u=http-3A__geometricalgebra.net_&d=DwIFaQ&c=4NmamNZG3KTnUCoC6InoLJ6KV1tbVKrkZXHRwtIMGmo&r=qW9SUYRDo6sWEVPpx7wwWYZ79PdSWMRxNZvTih0Bkxc&m=HjfsC447T7m29H3fRO5mjUS7vORbNarNjIlj8UKFSH8&s=ZSIE2k7gRluHIWuMRbAKuxvuEhNW5fsAY_7JkHIt_6Y&e= >>>> >>>> >>> >>>> https://urldefense.proofpoint.com/v2/url?u=https-3A__www.youtube.com_watch-3Fv-3D0fF2xToQmgs-26list-3DPLsSPBzvBkYjzcQ4eCVAntETNNVD2d5S79&d=DwIFaQ&c=4NmamNZG3KTnUCoC6InoLJ6KV1tbVKrkZXHRwtIMGmo&r=qW9SUYRDo6sWEVPpx7wwWYZ79PdSWMRxNZvTih0Bkxc&m=HjfsC447T7m29H3fRO5mjUS7vORbNarNjIlj8UKFSH8&s=ajUPImTLlq7Lp3ZyQySQVbWMzGahjwqMv3VbbDADxyc&e= >>>> >>>> >>> >>>> >>>> >>> 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://urldefense.proofpoint.com/v2/url?u=https-3A__www.youtube.com_playlist-3Flist-3DPLhgq-2DBqyZ7i7MTGhUROZy3BOICnVixETS&d=DwIFaQ&c=4NmamNZG3KTnUCoC6InoLJ6KV1tbVKrkZXHRwtIMGmo&r=qW9SUYRDo6sWEVPpx7wwWYZ79PdSWMRxNZvTih0Bkxc&m=HjfsC447T7m29H3fRO5mjUS7vORbNarNjIlj8UKFSH8&s=wAlbj134BiwAcAdG60K3dYfrkb5lDwA7M0swRlmjAU8&e= >>>> >>>> >>> 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://urldefense.proofpoint.com/v2/url?u=https-3A__www.uni-2Dmuenster.de_Physik.TP_-7Emunsteg_arnold.html&d=DwIFaQ&c=4NmamNZG3KTnUCoC6InoLJ6KV1tbVKrkZXHRwtIMGmo&r=qW9SUYRDo6sWEVPpx7wwWYZ79PdSWMRxNZvTih0Bkxc&m=HjfsC447T7m29H3fRO5mjUS7vORbNarNjIlj8UKFSH8&s=b11uIoYmlhACkj0JDy8Bbl3aTCMbW6OC_caxDDDN2YU&e= >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> 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. >>> -------------------------------------------- >>> >> > >