ISSAC

Linear algebra expressions appear in fields as diverse as computational biology, signal processing, communication technology, finite element methods, and control theory. Libraries such as BLAS and LAPACK provide highly optimized building blocks for just ...

The goal of this abstract is to report on some parallel and high performance computations in combinatorics, each involving large datasets generated recursively: we start by presenting a small framework implemented in Sagemath [12] allowing performance ...

We present a parallel algorithm to evaluate a sparse polynomial in Zp[x0, ..., xn] into many bivariate images, based on the fast multi-point evaluation technique described by van der Hoeven and Lecerf [11]. We have implemented the fast parallel ...

One of the most important cryptographic characteristics of the Boolean and vector Boolean functions is the algebraic degree which is connected with the Algebraic Normal Form. In this paper, we present an algorithm for computing the Algebraic Normal Form ...

Combinatorial search problems in mathematics, e.g. in finite geometry, are notoriously hard; a state-of-the-art backtracking search algorithm can easily take months to solve a single problem. There is clearly demand for parallel combinatorial search ...

Modern CPUs have vector instruction sets such as SSE2 and AVX2 which support the bit level operations (and, or, xor, etc. ) as well as floating point and integer arithmetic. Furthermore compilers, such as g++ and Clang, have auto-vectorization features ...

In this paper, we present the results of our experiments to compute the rank of several large sparse matrices from Dumas's Sparse Integer Matrix Collection, by computing sparse PLUQ factorizations.

Our approach consists in identifying as many pivots as ...

The computation of the tropical prevariety is the first step in the application of polyhedral methods to compute positive dimensional solution sets of polynomial systems. In particular, pretropisms are candidate leading exponents for the power series ...

We present multithreaded adaptations of the Euclidean plain division and the Euclidean GCD algorithms to the many-core GPU architectures We report on implementation with NVIDIA CUDA and complexity analysis with an enhanced version of the PRAM model.

We present algorithms for splitting polynomial systems using Gröbner bases. For zero dimensional systems, we use FGLM to compute univariate polynomials and factor them, placing the ideal into general position if necessary. For positive dimensional ...

We present a cache-oblivious adaptation of matrix multiplication to be incorporated in the parallel TU decomposition for rectangular matrices over finite fields, based on the Morton-hybrid space-filling curve representation. To realise this, we ...