fdej

12 ms·

61.
by fdej 8y ago
Wait, what? 50 milliseconds per line of code? How is that even possible?
62.
by fdej 8y ago
This trick does work. If the matrices are in row-major order, you transpose B in memory and then compute A * (B^T)^T. This multiplication reads both matrices in row order. However, while this does improve performance over the naive algorith
63.
by fdej 8y ago
I've never seen South America look that pointy.
64.
by fdej 8y ago
You have to work with multivariate polynomials (possibly over number fields). If you have symbolic expressions in another format, you would have to manually convert them to that representation first, possibly after introducing extra variabl
65.
by fdej 8y ago
In Julia, there is Nemo.jl for high performance exact and symbolic linear algebra. At least that is the goal; it doesn't have the best algorithms yet in all cases, but it has some of them (and more are being developed). You can see som
66.
by fdej 8y ago
> On the other hand, open source tools are catching up. SymPy is doing nicely, but it's decades behind Mathematica when it comes to symbolic computation. By the way, if you want to invert a symbolic matrix, chances are that generic
67.
by fdej 8y ago
Here is an article from a couple of years ago about how one group of mathematicians were misled by (and had to spend some time tracking down) a bug in Mathematica determinant evaluation: http://www.ams.org/notices/20141
68.
by fdej 9y ago
There are exceptions, notably among classical composers. Bach composed the Mass in B minor and The Art of Fugue in the last years of his life (the former completed the year before his death, the latter unfinished). They are among Bach'
69.
by fdej 9y ago
Could you elaborate on what you perceive as the problem with falsificationism? I'm familiar with the philosophical argument that Popper's demarcation of science is too narrow. What is less clear is that this argument over the defi
70.
by fdej 9y ago
Yes, this is just jargon specific to the HPC / numerical analysis field.
71.
by fdej 9y ago
It's a plain C library with an API very similar to GMP, so an option would be to wrap it from Rust, which should not be too difficult.
72.
by fdej 9y ago
I'm the main author of Arb. Note that it's an arbitrary-precision library. It's ~100x times slower than hardware floating-point because of using arbitrary-precision floating-point numbers implemented entirely in software. But
73.
by fdej 9y ago
It makes me sad that Knuth will no longer be at a prime age, but on the other hand, one more year and he will return to perfect power.
74.
by fdej 9y ago
It reminds me of Phoenix (to become Firefox), and how much of an improvement it was over the Mozilla browser. It makes me wonder where things went wrong, as I recall the Firefox of ~2005 being snappier than the one of ~2015. The only discre
75.
by fdej 9y ago
> 5-6 hours a day biking in -15C snow with wet feet (Mailman). As a Swede, aren't you familiar with the saying "There's no such thing as bad weather, only bad clothes"? :-) I did spend one summer planting trees in Swe
76.
by fdej 9y ago
There is plenty of cringey non-programmer humor.
77.
by fdej 9y ago
This is a good book. Note that it's mostly concerned with (software implementation of) arbitrary-precision arithmetic; which is just one branch of computer arithmetic.
78.
by fdej 9y ago
The idea is that computers spend much more energy moving data between the processor and memory than actually processing the data. Unums use a variable length encoding which makes processing more costly but reduces the amount of data transfe
79.
by fdej 9y ago
If only compiler developers had this attitude.
80.
by fdej 9y ago
Lots of related projects getting that long overdue major version number now. SymPy 1.0 was released last year and I released mpmath 1.0 less than a month ago, both projects 10 years old. SciPy's 16 years is a notch more impressive, tho
81.
by fdej 9y ago
We researchers don't get paid for our papers. We give the publishers our papers for free so that they can make money by putting them behind a paywall. We sometimes even need to pay the publishers to publish our papers. The paywall can
82.
by fdej 9y ago
My HP laptop has a single column with delete/home/pgup/pgdn/end, like this: https://h30434.www3.hp.com/t5/image/serverpage/image-id/3646... This works very nicely for me.
83.
by fdej 9y ago
This is not a new idea. If you have a variable-order, variable-precision implementation, it's the most obvious way to estimate the error of a numerical solution.
84.
by fdej 9y ago
In fact the more general N-body problem is perhaps one of the most classical uses of high order Taylor methods, in particular for studying the long term stability of the solar system. Here is a paper from 1993: http://adsabs.harv
85.
by fdej 9y ago
The "CNS" is as far as I can tell just the use of a high order Taylor series together with multiple precision arithmetic for solving ODEs. This is a well known method for long term simulation of dynamical systems that has been aro
86.
by fdej 9y ago
I do publish in paywalled journals but all my papers are freely available as preprints from arxiv. Also, all software is open source.
87.
by fdej 9y ago
As an academic who travels a fair amount, I try to pick the cheapest available flight (within reason), and I've certainly never even considered flying business class. I think flying business class is permitted under certain conditions
88.
by fdej 9y ago
I'm not so sure that we're missing anything basic. The top rated answer by Scott Aaronson seems spot on to me. The natural numbers are just too powerful. As the resolution of Hilbert's tenth problem shows, we can at best hope
89.
by fdej 9y ago
Yes, this was proved by F. Carlson in 1921 and it is known as the Pólya–Carlson theorem.
90.
by fdej 9y ago
Google was a huge improvement because if you searched for Foo Bar Baz it would only give you pages that had all the words Foo, Bar and Baz whereas AltaVista et al. would give you pages containing any of the words, if memory serves. But the

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