Viewing profile — fdej

If you don't want to allow division by 2 then there is Winograd's algorithm from 1967 which works over any commutative ring and uses 48 multiplications for 4 x 4.

> From the paper, "Notably, for multiplying two 4 × 4 matrices, applying the algorithm of Strassen recursively results in an algorithm with 49 multiplications, which works over any…

Just check for the existence of at least one odd digit mod 10^B for some well chosen B. Here is a C program that does the verification up to 2^(10^10) in 30 seconds: https://gist.g…

There's no a priori reason why the expected success rate of research projects should be 50% and not, say, 1% or 99%.

That is the way the FLINT fmpz type does it. The benefit is that you can check for pointers once and then use the operands like ordinary ints without the +1/-1 adjustments. For exa…

This is indeed the issue. Using provable bounds loses too many bits for complex FFTs to make sense for long multiplies.

This looks quite similar like the "Lagrange models" defined by Joris van der Hoeven in https://hal.science/hal-01188378/document , a version of Taylor models where the constant err…

There is an algorithm by Richardson to prove equality of real and complex numbers composed from exponentials and logarithms. (It doesn't have a complete proof of correctness, but i…

No, this is wrong. Richardson's theorem is about functions, not constants. Equality of constants constructed from exponentials and logarithms is decidable (assuming Schanuel's conj…

Author here. I'm only talking about using formalizable and mathematically consistent type definitions in a CAS, not requiring formal proofs in the implementations of types. For exa…

Correcting myself, the bound is worse than exponential (so read "at least exponential in N"), but the point I wanted to make is that it is explicit. Again, this follows from the ge…

Yes, the worst-case complexity is exponential in N, but the wording in the article could lead you to believe that no explicit exponential bound is known, which is false.

> But how long will we need to look through these sequences of digits before we find the disagreeing digit? It feels intuitively like we should be able to establish some kind of bo…

Yes, indeed, and Strassen is a bad default algorithm because of this. There are specialized situations where the numerical stability isn't an issue though.

What makes you say that? I've had good speedups with Strassen multiplication in variable precision (or with floating-point, in case you meant fixed-point arithmetic).

I'm the poster. I think you misunderstood the followup post -- the same library is definitely used in the Cloud (same as the standalone Mathematica).

Indeed. There's no way for users of Wolfram Cloud, for example, to see that information though.

My number one wish would be the ability to read definitions from .h files automatically. Other than that, I've had some issues with memory management with ctypes (objects being dea…

I'd like to see optimizations targeting ctypes, or a successor to ctypes. I wish I could write elegant, performant C wrappers in pure Python. Right now the best choices are Cython,…

This version of CM looks too thin. The version that comes with KaTeX ( https://github.com/KaTeX/katex-fonts ) looks great in the browser though. Would be nice if someone packaged t…

I don't know why people complain about the new design. It has been a very effective cure for my reddit addiction.

Chick Corea was my gateway drug to jazz as a teenager, after my guitar teacher gave me Spain to practice. A lot of musicians have the playing chops but few do truly interesting and…

That's a great question. Of course, you can express the computation as a function or a symbolic expression and evaluate it using a function that recomputes with greater precision a…

Should be fixed now. Thanks!

The library doesn't support this directly. What you can do for normed vector spaces over R (or C) is to use the number types of Arb for the coordinate vectors, implementing your ow…