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Arithmetic of Finite Fields: 5th International Workshop, by Çetin Kaya Koç, Sihem Mesnager, Erkay Savaş

By Çetin Kaya Koç, Sihem Mesnager, Erkay Savaş

This publication constitutes the refereed lawsuits of the fifth overseas Workshop at the mathematics of Finite box, WAIFI 2014, held in Gebze, Turkey, in September 2014. The nine revised complete papers and forty three invited talks awarded have been rigorously reviewed and chosen from 27 submissions. This workshop is a discussion board of mathematicians, laptop scientists, engineers and physicists appearing learn on finite box mathematics, drawn to speaking the advances within the thought, functions, and implementations of finite fields. The workshop might help to bridge the space among the mathematical conception of finite fields and their hardware/software implementations and technical applications.

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Extra info for Arithmetic of Finite Fields: 5th International Workshop, WAIFI 2014, Gebze, Turkey, September 27-28, 2014. Revised Selected Papers

Example text

More particularly, given P a closed point of X of degree n, D a divisor and l a positive integer, we will need the following map: the evaluation of a global section of the line bundle O(D) at the thickened point P [l] , which takes values F n [y] v (D) in qyl . Let tP be a local parameter at P : multiplication by tPP provides a local trivialization of O(D) at P , and thus an evaluation map: evQ : L(D) −→OX,P /(tlP ) v (D) f −→tPP fP mod (tlP ) (4) Fn [y] The target space maps isomorphically3 to the Fq -algebra qyl .

Sum ← 0; // 1 machine word initialized to 0 // position of beginning for each thread j ← ptri + tid / n ; While j < ptri+1 do sum ← addmul word(sum,dataj ,uidj ×n+tid mod n ); // process 1 word j ← j + nGPS ; reduction csr v par(sum,tid); If tid< n then // first group of the warp writes in global memory vi×n+tid ← sum; 36 H. Jeljeli For the other kernels, both schemes are applicable and the parallel scheme always performs significantly better than the sequential scheme. 6 Comparative Analysis of SpMV Kernels In this section, we compare the performances of the kernels that we presented.

For this candidate value of deg G, find a combination (ui , Pi )i of points and multiplicities that, numerically, minimises the upper bound of 8 under the constraint deg G i ui . deg Pi . 4 For this fixed candidate value deg G, given such a numerically optimal G = i ui Pi , check the existence of an interpolation system (G, D, Q). 1 is the motivation for the next paragraph. 2 is the motivation for the last section. 3 is an integer programme and will be illustrated in Sect. 2. 4 will be discussed in the next section.

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