We report on a £rst parallel implementation of a recent algorithm to factor positive dimensional solution sets of polynomial systems. As the algorithm uses homotopy continuation,...
We reduce the problem of computing the rank and a nullspace basis of a univariate polynomial matrix to polynomial matrix multiplication. For an input n×n matrix of degree d over ...
The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the inp...
We study ways to expedite Yates's algorithm for computing the zeta and Moebius transforms of a function defined on the subset lattice. We develop a trimmed variant of Moebius ...
This paper is concerned with the complexity of proofs and of searching for proofs in two propositional proof systems: Resolution and Polynomial Calculus (PC). For the former syste...