Polynomial systems and Kronecker invariants

Kronecker Matrices and Polynomial Gcds

Generating Polynomial Invariants for Hybrid Systems

We present a powerful computational method for automatically generating polynomial invariants of hybrid systems with linear continuous dynamics. When restricted to linear continuous dynamical systems, our method generates a set of polynomial equations (algebraic set) that is the best such over-approximation of the reach set. This shows that the set of algebraic invariants of a linear system is ...

Faster polynomial multiplication via multipoint Kronecker substitution

We give several new algorithms for dense polynomial multiplication based on the Kronecker substitution method. For moderately sized input polynomials, the new algorithms improve on the performance of the standard Kronecker substitution by a sizeable constant, both in theory and in empirical tests.

Computing polynomial program invariants

Invariants and intermediate assertions are the key to deductive verification of programs. Correspondingly, techniques for automatically checking and finding invariants and intermediate assertions have been studied (cf., e.g., [4, 3]). In this paper we present analyses that check and find valid polynomial relations in programs. A polynomial relation is a formula p(x1, . . . ,xk) = 0 where p(x1, ...

Polynomial Invariants of Graphs

We define two polynomials f(G) and /*(G) for a graph G by a recursive formula with respect to deformation of graphs. Analyzing their various properties, we shall discuss when two graphs have the same polynomials. Introduction. Our graphs are finite, undirected ones with or without self-loops and multiple edges. As elementary deformations of graphs, we have the deletion and the contraction of ed...