I have to say that I am quite pleased with how the workshop played out. We planned the whole thing to be hands on: people were strongly encouraged to work on projects, i.e., to write code preferably together, in addition to attending talks. Those who attended a Sage Days workshop in the past, will know what workshop format I am referring to. Continue reading “Report: Workshop on Efficient Linear Algebra for Gröbner Basis Computations”
I am writing this while waiting for my taxi to leave Sage Days 35. Although, I didn’t get much actual coding done, it was great fun and very useful. I met a lot of old friend, new faces and managed to put faces to e-mail addresses.
In terms of coding projects, first, I tried to speed up linear algebra mod p where p is a 32 or 64 bit prime. But it turns out that any trick I could think of could not improve on Frederik’s code. So that didn’t lead anywhere but I allowed me to read some code of FLINT2 (very readable) and admire how carefully it is written.
My other two projects both involved evaluate–pointwise-multiply–interpolate algorithms for fast matrix-matrix products over finite extension fields or for matrices with polynomial coefficients (over prime fields). After my talk on M4RI(E) David Harvey worked out how to improve multiplication over from 17 multiplications over to 15, which then lead to a general approach for with composite . Much of it remains to be implemented (efficiently), but the example indeed shows a 10% speed-up as expected. The code is not clean yet, uses way too much memory and doesn’t deal with the more advanced finite field stuff appropriately. It should end up in M4RIE eventually though.
I also contributed a bit to #12177 which is about a “prime slice” implementation of matrices over . The idea is essentially to represent these matrices as polynomials with matrix coefficients and to use fast polynomial multiplication algorithms for these polynomials. It turns out, this works very well even for small finite fields. Burcin Eröcal did all the coding, I only helped with some discussions. We need to polish the code a lot to be usable, so if you like matrices over head over to #12177 and help out.
“A Sage Days workshop around the theme of Algorithms in Number Theory and FLINT.”
See http://wiki.sagemath.org/SageFlintDays for more information and registration.
PS: I’ll be talking about M4RI(E) … big surprise.
During last weeks Sage Days 32 I worked on finishing a patch by Clément Pernet and Burcin Eröcal which switches Sage’s native matrices mod n (for ) to FFLAS/FFPACK. The purpose of this exercise was to make operations with dense matrices mod n both faster and more memory efficient (currently, Sage does a lot of copying around when calling any LinBox function). Well, we almost succeeded. Continue reading “Dense matrices mod n via FFLAS/FFPACK”
I’m en route to Kaiserslautern where Sage Days 23.5 will start tomorrow morning. If you have any suggestions what you want to see improved in the Sage <-> Singular interface, let me know. Afterwards I’m moving on to Sage Days 24 at RISC. Not that I know a lot about “Symbolic Computation in Differential Algebra and Special Functions”.