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To interpolate a supersparse polynomial with integer coefficients, two alternative approaches are the Prony-based big prime technique, which acts over a single large finite field, or the more recently-proposed small primes technique, which reduces the unknown sparse polynomial to many low-degree dense polynomials. While the latter technique has not yet reached the same theoretical efficiency as Prony-based methods, it has an obvious potential for parallelization. We present a heuristic small primes interpolation algorithm and report on a low-level C implementation using FLINT and MPI.
Given a straight-line program whose output is a polynomial function of the inputs, we present a new algorithm to compute a concise representation of that unknown function. Our algorithm can handle any case where the unknown function is a multivariate
We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to linear algeb
We present sparse interpolation algorithms for recovering a polynomial with $le B$ terms from $N$ evaluations at distinct values for the variable when $le E$ of the evaluations can be erroneous. Our algorithms perform exact arithmetic in the field of
After an introduction to the sequential version of FORM and the mechanisms behind, we report on the status of our project of parallelization. We have now a parallel version of FORM running on Cluster- and SMP-architectures. This version can be used to run arbitrary FORM programs in parallel.
This work is a comprehensive extension of Abu-Salem et al. (2015) that investigates the prowess of the Funnel Heap for implementing sums of products in the polytope method for factoring polynomials, when the polynomials are in sparse distributed repr