fdej

10 ms·

31.
by fdej 6y ago
Author here. The table-maker's dilemma is a problem if you insist on correct rounding. However, interval arithmetic does not require correct rounding. It merely requires rigorous error bounds. It turns out that a lot of the time when p
32.
by fdej 6y ago
Thanks, it was a temporary mental lapse to forget mentioning Fortran. I have added a sentence.
33.
by fdej 6y ago
Nemo ( http://nemocas.org/ ) and Oscar ( https://oscar.computeralgebra.de/ ) are such projects. However, they are focused on algebra and have no support for expression manipulation, symbolic integration and the
34.
by fdej 6y ago
I think SymPy already flourishes in its space: it's a great tool for users who need some computer algebra functionality with the ability to glue that together with other code (thanks to Python). It's fine as long as you don't
35.
by fdej 6y ago
And then why not: the designer originated through evolution. Which in turn...
36.
by fdej 6y ago
Ah, too bad that the sequencer mode is being delayed. For about 20 years now, I'm still holding my breath for a MIDI sequencer that runs on Linux and has all the functionality and user-friendliness of Cakewalk 3 ( http://www.
37.
by fdej 6y ago
Do you have a link?
38.
by fdej 6y ago
The API itself is perhaps less interesting than the implementation strategy. I'm presently developing a C library for exact real and complex numbers ( http://fredrikj.net/calcium/ ) that goes much further to make eq
39.
by fdej 6y ago
Sure, go ahead and set something up!
40.
by fdej 6y ago
There is nothing in depth yet. I'm happy to discuss (here or by email).
41.
by fdej 6y ago
Indeed. I decided not to use MathML for various reasons: 1. The syntax is horrible (for writing by hand). 2. I'm more interested in computation than presentation, so something closer to S-expressions along the lines of Mathematica feel
42.
by fdej 6y ago
Nice project! I'm working on something similar with http://fungrim.org/grim/ and http://fungrim.org/
43.
by fdej 7y ago
Has anyone tested this with Glenn Gould recordings?
44.
by fdej 7y ago
That complexity bound applies to polynomials over more general coefficient rings which may not have roots of unity. Over the usual complex numbers the complexity is O(n log n).
45.
by fdej 7y ago
Huh, weird that this is making such big headlines. A fast (O(n log n)) inverse chirp z-transform was described 16 years ago in Alin Bostan's PhD thesis https://specfun.inria.fr/bostan/these/These.pdf Also in
46.
by fdej 7y ago
Here's GMP's current tuning (for Skylake CPUs, from https://gmplib.org/devel/thres/ ) Basecase: up to 520 digits (27 limbs x 19.26 digits per 64-bit limb = 520) Karatsuba: 520 - 1425 digits Toom3: 1425 -
47.
by fdej 7y ago
All good remarks. > The "rewrite engine" ambitions for Fungrim seem potentially misplaced. It would probably be better to contribute to an existing open source state-of-the-art CAS like Fricas For the record, I have contributed
48.
by fdej 7y ago
Cheers :)
49.
by fdej 7y ago
Arbitrarily precise is not the same as exact. There are many possible examples to illustrate why this matters. Here's one: let's say that you compute floor(f(x)) where f(x) falls right on an integer n. If you evaluate f(x) in floa
50.
by fdej 7y ago
That's a good question. The S-expressions are actually a trivial part of the project right now, because there is no symbolic computation going on, just composing S-expressions without any form of rewriting and then generating the websi
51.
by fdej 7y ago
Also (shameless self-promotion) python-flint! http://fredrikj.net/python-flint/
52.
by fdej 8y ago
Note that number of digits is actually 10^(85 billion), not 85 billion.
53.
by fdej 8y ago
I really wish browsers would just render formulas directly from TeX. Let me write <tex>\sqrt{1+x}</tex> or whatever. TeX is the de facto standard for writing mathematical formulas. That browsers don't render it nativel
54.
by fdej 8y ago
Here's hoping that he follows up Linux and git by going and making a better social network!
55.
by fdej 8y ago
The propulsive efficiency as defined in the Wikipedia article is the product of the cycle efficiency (the efficiency turning heat into mechanical power) and the mechanical efficiency (the efficiency turning the mechanical power generated by
56.
by fdej 8y ago
The underlying weakness of the Miller-Rabin test has been known for a long time, and yet "just do N rounds of Miller-Rabin" keeps being perpetuated as the folklore solution to probabilistic primality testing. The BPSW test is basi
57.
by fdej 8y ago
There are more specific cases where open source tooling outperforms Mathematica than where the opposite holds. This especially true when you move away from basic calculus and towards research math. For example, many number theorists don&#x2
58.
by fdej 8y ago
Agreed. I still boot up my Windows computer just to use PSP 6 occasionally when I need to do some raster graphics editing!
59.
by fdej 8y ago
It's possible that evolution inherently drives life towards intelligence (as a likely outcome, not in the teleological sense). Three counter-points: * Sure, an extreme minority of organisms are intelligent right now, but considering th
60.
by fdej 8y ago
"around 20. Not K, just lines/sec"

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