The idea reminds me of FORM, popular in Particle physics community: https://github.com/vermaseren/form http://www.nikhef.nl/~form/ https://en.wikipedia.org/wiki/FORM_(symbolic_manipulation_sy...
I was about to say that.
Symbolica Computer Algebra System
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Re: Symbolica Computer Algebra System
#72The idea reminds me of FORM, popular in Particle physics community: https://github.com/vermaseren/form http://www.nikhef.nl/~form/ https://en.wikipedia.org/wiki/FORM_(symbolic_manipulation_sy...
I've actually been a developer of FORM since my PhD (which I did with the author of FORM, Jos Vermaseren)! In Symbolica, I am taking the best features of FORM, while making it easier to use.
I've never got to solve a simple equation under Form. Everything else looks easy,
as most of the answers are either tautological or factor arrangements without stating
explicit units or magnitudes; but I didn't know how to get numerical answers.
Even by defining functions equally to 0.
Re: Symbolica Computer Algebra System
#73Earlier quoted context omitted.
This is fascinating. What is the real-world application of these polynomials? I mean, what technical-scientific problems can only be solved with such large objects? I love the thought of "if I don't solve this enormous polynomial, this solar panel won't have very good efficiency" or something like that.
I used polynomials and specifically special symmetric polynomials extensively during my Phd research (mathematical physics). For instance symmetric polynomials (x_1^2 + x_2^2 + ...) can describe the state of a system of particles where exchanging any 2 particles does not change the system at all (exchange x_1 and x_2 in the previous expression, same polynomial = same system & state). If you have a system of equation…
That an exercise on SICP, a Scheme learning book. And there are similar ones for Common Lisp.
Re: Symbolica Computer Algebra System
#74Earlier quoted context omitted.
Compare it to a free CAS like Maxima for example, Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, sets, lists, vectors, matrices and tensors.
Most of these features are included in Symbolica in some capacity (ODE solving is missing) and there are CAS features Symbolica has and that Maxima has not (like advanced pattern matching), even though it is only a year old. It is not just a matter of whether a feature is there, it needs to be usable in practice. You cannot use Maxima to do computation with large rational polynomials as this paper shows: https://arxi…
Use a different Common Lisp implementation. There's a huge difference between Clisp, ECL and SBCL.
Sith SBCL, open maxima and run:
load("maximalocal.mac");
:lisp (sb-ext:save-lisp-and-die "maxima-optimised" :toplevel #'run :executable t)
Re: Symbolica Computer Algebra System
#75I feel like this is missing some comparisons to Sympy and Mathematica. Probably it's more polished than Sympy, but if I'm going to closed-software software why would I pick this over MMA?
Despite Symbolica being licensed, its source code is still available which clearly shows the author's intent. It may be important in various contexts, e.g. security or satisfying certain grant requirements in academia, or whenever custom minor modifications are necessary.
What intent do you infer from the fact that it's source-available instead of being FOSS?
Re: Symbolica Computer Algebra System
#76Earlier quoted context omitted.
Wow. Could you share the equation/code you worked on? I can't imagine a mathematical object being 84KB long, that's insanely huge
Indeed, it's hard to me to imagine such an expression without any of the following qualities: - immediately converges to zero - immediately heads to infinity - is dominated by only a few terms (thus obviating the needs for the other X million terms)
It sounds like the problem is that it’s dominated by a few terms, but finding them is tricky. If you have 1.0 x + 2.0 x - 3.0 x - 5/4 x + x - x + x - x … (etc for a few GB) and then quadratic terms, it’ll take work to figure out whether the dominant term is linear or quadratic. Cancelling out the potentially important intermediate terms (especially in higher dimensions) sounds like a mess.
Re: Symbolica Computer Algebra System
#77Cool stuff! One comment on the landing page: the slideshow view thingy of examples is fast, and when I click one to read it, it moves to the next one so fast again, so I can’t really look at the demos.
I also can’t quickly find any details about what field/algebra/whatever these cover. If I make a Expression.var, what structure is it assumed to have?
Great job on this project :)
Re: Symbolica Computer Algebra System
#78> Sometimes a Symbolica license key is needed on a machine that is not connected to the internet. For this purpose, an offline key that is valid for 24 hours can be generated from a valid license key on a machine that is connected to the internet. Even Mathematica doesn't pull shit like that.
Author of Symbolica here: this may change in the future. Note that it is easy to do this, you just call the function from symbolica import \* set_license_key('YOUR_KEY') print(get_offline_license_key())
Isn't this one of those cases where those who do it right get punished and others don't?
Re: Symbolica Computer Algebra System
#79How does source-available work together with license keys? Can I not just compile it myself and be done with the license key?
Re: Symbolica Computer Algebra System
#80Earlier quoted context omitted.
Compare it to a free CAS like Maxima for example, Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, sets, lists, vectors, matrices and tensors.
Most of these features are included in Symbolica in some capacity (ODE solving is missing) and there are CAS features Symbolica has and that Maxima has not (like advanced pattern matching), even though it is only a year old. It is not just a matter of whether a feature is there, it needs to be usable in practice. You cannot use Maxima to do computation with large rational polynomials as this paper shows: https://arxi…
> Symbolica is 10 times faster and uses 60 times less memory than Maxima on a medium-sized problem. The larger sized problem does not run with Maxima
Hah...change "Maxima" to "Macsyma" and "Symbolica" to "SMP" and that is close to a slide I remember seeing around 1980 in a presentation by Wolfram and Cole explaining why they had developed a new computer algebra system, SMP, instead of using one of the already available systems.
I don't remember the exact numbers on their slide, but same situation. Existing systems could handle the medium problems that came up in their physics research but were slow and used a lot of memory, and could not do the large problems.