This paper presents two efficient implementations of fast and pipelined bit-parallel polynomial basis multipliers over GF (2m) by irreducible pentanomials and trinomials. The architecture of the first multiplier is based on a parallel and independent computation of powers of the polynomial variable. In the second structure only even powers of the polynomial variable are used. The par...

We present methods to compute verified square roots of a square matrix A. Given an approximation X to the square root, obtained by a classical floating point algorithm, we use interval arithmetic to find an interval matrix which is guaranteed to contain the error of X. Our approach is based on the Krawczyk method which we modify in two different ways in such a manner that the computational comp...

In this paper, we present the formal verification of a Common Lisp implementation of Buchberger’s algorithm for computing Gröbner bases of polynomial ideals. This work is carried out in the Acl2 system and shows how verified Computer Algebra can be achieved in an executable logic.

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There are many occasions where the base of a robotic manipulator is attached to a moving platform, such as on a moving ship, terrain or space shuttle. In this paper a dynamic model of a robotic manipulator mounted on a moving base is derived using both Newton-Euler and Lagrange-Euler methods. The presented models are simulated for a Mitsubishi PA10-6CE robotic manipulator characteristics mounte...