In this paper, a multiplicity preserving triangular set decomposition algorithm is proposed for a system of two polynomials. The algorithm decomposes the variety defined by the polynomial system into unmixed components represented by triangular sets, which may have negative multiplicities. In the bivariate case, we give a complete algorithm to decompose the system into multiplicity preserving t...

A Steinhaus matrix is a binary square matrix of size n which is symmetric, with diagonal of zeros, and whose upper-triangular coefficients satisfy ai,j = ai−1,j−1+ai−1,j for all 2 6 i < j 6 n. Steinhaus matrices are determined by their first row. A Steinhaus graph is a simple graph whose adjacency matrix is a Steinhaus matrix. We give a short new proof of a theorem, due to Dymacek, which states...

Where to find decomposition matrices? Try www.math.rwth-aachen.de/∼MOC In hard copy, [6] has several (at the end) for small primes. For p = 2, a paper by Juergen Mueller(Aachen) [7], for an electronic version try his homepage. General background can be found in [6]. Column removal: Due to G.D. James, sometime after '76. Just now I cannot find the precise reference. However, a generalization of ...

In symmetric tensor decomposition one expresses a given symmetric tensor T a sum of tensor powers of a number of vectors: T = v⊗d 1 + · · · + v ⊗d k . Orthogonal decomposition is a special type of symmetric tensor decomposition in which in addition the vectors v1, ..., vk are required to be pairwise orthogonal. We study the properties of orthogonally decomposable tensors. In particular, we give...

We present a method to handle cubic trimmed triangular Bézier patches. This scheme makes use of levels of detail and surface subdivision to achieve a fast and flexible hierarchical data structure that is specially useful to compute surface intersections in a robust and efficient way. The accuracy of the results can be adjusted by adding or subtracting elements to the levels of detail hierarchy,...

Statistical process control ($SPC$), an internationally recognized technique for improving product quality and productivity, has been widely employed in various industries. $SPC$ relies on the use of control charts to monitor a manufacturing process for identifying causes of process variation and signaling the necessity of corrective action for the process. Fuzzy data exist ubiquitously in the ...

We describe a new extension to ScaLAPACK [2] for computing with symmetric (Hermi-tian) matrices stored in a packed form. The new code is built upon the ScaLAPACK routines for full dense storage for a high degree of software reuse. The original ScaLAPACK stores a symmetric matrix as a full matrix but accesses only the lower or upper triangular part. The new code enables more efficient use of mem...

We describe a new extension to ScaLAPACK [2] for computing with symmetric (Hermi-tian) matrices stored in a packed form. The new code is built upon the ScaLAPACK routines for full dense storage for a high degree of software reuse. The original ScaLAPACK stores a symmetric matrix as a full matrix but accesses only the lower or upper triangular part. The new code enables more efficient use of mem...

The combination of six Cu(II) centres with four cyclotricatechylene (ctc(6-)) ligands generates large (Cu(6)ctc(4))(12-) cages with the topology of the tetrahedron. The anionic tetrahedral cages are cemented together, triangular face to triangular face, by Na(+) cations together with water molecules to generate a highly symmetric diamond-like assembly (space group Fd-3m, the same as that of dia...