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Farnam Mansouri
With the advent of hardware accelerator technologies, multi-core processors and GPUs, much effort for taking advantage of those architectures by designing parallel algorithms has been made. To achieve this goal, one needs to consider both algebraic complexity and parallelism, plus making efficient use of memory traffic, cache, and reducing overheads in the implementations. Polynomial multiplication […]
Mickael Gastineau, Jacques Laskar
We present a highly scalable algorithm for multiplying sparse multivariate polynomials represented in a distributed format. This algo- rithm targets not only the shared memory multicore computers, but also computers clusters or specialized hardware attached to a host computer, such as graphics processing units or many-core coprocessors. The scal- ability on the large number of […]
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Pavel Emeliyanenko
In this article we report on our experience in computing resultants of bivariate polynomials on Graphics Processing Units (GPU). Following the outline of Collins’ modular approach [6], our algorithm starts by mapping the input polynomials to a finite field for sufficiently many primes m. Next, the GPU algorithm evaluates the polynomials at a number of […]
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Wei Pan
Regular chains, introduced about twenty years ago, have emerged as one of the major tools for solving polynomial systems symbolically. In this thesis, we focus on different algorithmic aspects of the theory of regular chains, from theoretical questions to high-performance implementation issues. The inclusion test for saturated ideals is a fundamental problem in this theory. […]
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Eric Berberich, Pavel Emeliyanenko, Alexander Kobel, Michael Sagraloff
We present a novel certified and complete algorithm to compute arrangements of real planar algebraic curves. It provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic curves in terms of a cylindrical algebraic decomposition. From a high-level perspective, the overall method splits into two main subroutines, namely […]
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Brian Guenter, John Rapp, Mark Finch
Derivatives arise frequently in graphics and scientific computation applications. As GPU’s become more widely used for scientific computation the need for derivatives can be expected to increase. To meet this need we have added symbolic differentiation as a built in language feature in the HLSL shading language. The symbolic derivative is computed at compile time […]
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Sandra Diaz-Pier, Salvador E. Venegas-Andraca, Jose Luis Gomez-Munoz
In this paper we present a simulation environment enhanced with parallel processing which can be used on personal computers, based on a high-level user interface developed on Mathematicacopyright which is connected to C++ code in order to make our platform capable of communicating with a Graphics Processing Unit. We introduce the reader to the behavior […]
Brice Boyer, Jean-Guillaume Dumas, Pascal Giorgi
We propose different implementations of the sparse matrix–dense vector multiplication (spmv{}) for finite fields and rings $Zb/mZb$. We take advantage of graphic card processors (GPU) and multi-core architectures. Our aim is to improve the speed of spmv{} in the linbox library, and henceforth the speed of its black box algorithms. Besides, we use this and […]

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