A Symbolic-Numeric Software Package for the Computation of the GCD of Several Polynomials

This survey is intended to present a package of algorithms for the computation of exact or approximate GCDs of sets of several polynomials and the evaluation of the quality of the produced solutions. These algorithms are designed to operate in symbolic-numeric computational environments. The key of their effectiveness is the appropriate selection of the right type of operations (symbolic or numeric) for the individual parts of the algorithms. Symbolic processing is used to improve on the conditioning of the input data and handle an ill-conditioned sub-problem and numeric tools are used in accelerating certain parts of an algorithm. A sort description of the basic algorithms of the package is presented by using the symbolic-numeric programming code of Maple

The Euclidean Division as an Iterative ERES-based Process

Considering the Euclidean division of two real polynomials, we present an iterative process based on the ERES method to compute the remainder of the division and we represent it using a simple matrix form

Determination of the magnetic anisotropy axes of single-molecule magnets

Simple methods are presented allowing the determination of the magnetic anisotropy axes of a crystal of a single-molecule magnet (SMM). These methods are used to determine an upper bound of the easy axis tilts in a standard Mn12-Ac crystal. The values obtained in the present study are significately smaller than those reported in recent high frequency electron paramagnetic resonance (HF-EPR) studies which suggest distributions of hard-axes tilts.Comment: 10 pages, 6 figure

Construction of Simulation Wavefunctions for Aqueous Species: D3O+

This paper investigates Monte Carlo techniques for construction of compact wavefunctions for the internal atomic motion of the D3O+ ion. The polarization force field models of Stillinger, et al and of Ojamae, et al. were used. Initial pair product wavefunctions were obtained from the asymptotic high temperature many-body density matrix after contraction to atom pairs using Metropolis Monte Carlo. Subsequent characterization shows these pair product wavefunctions to be well optimized for atom pair correlations despite that fact that the predicted zero point energies are too high. The pair product wavefunctions are suitable to use within variational Monte Carlo, including excited states, and density matrix Monte Carlo calculations. Together with the pair product wavefunctions, the traditional variational theorem permits identification of wavefunction features with significant potential for further optimization. The most important explicit correlation variable found for the D3O+ ion was the vector triple product {\bf r}$_{OD1}\cdot$({\bf r}$_{OD2}\times${\bf r}$_{OD3}$). Variational Monte Carlo with 9 of such explicitly correlated functions yielded a ground state wavefunction with an error of 5-6% in the zero point energy.Comment: 17 pages including 6 figures, typos correcte