We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decompositions. We introduce a component-level parallelism for which ...
This paper deals with the computation of the rank and some integer Smith forms of a series of sparse matrices arising in algebraic K-theory. The number of non zero entries in the ...
Jean-Guillaume Dumas, Philippe Elbaz-Vincent, Pasc...
Supercomputing applications usually involve the repeated parallel application of discretized differential operators. Difficulties arise with higher-order discretizations of opera...
Thomas J. Ashby, Anthony D. Kennedy, Stephen M. Wa...
In this paper, it is shown that the Hilbert series of a Borel type ideal may be computed within a complexity which is polynomial in Dn where n + 1 is the number of unknowns and D ...
In this paper, we describe the design of a C library named PTPol implementing arithmetic operations for univariate polynomials and report on practical experiments showing the rele...
We describe some major recent progress in exact and symbolic linear algebra. These advances concern the improvement of complexity estimates for fundamental problems such as linear...