Efficient algorithms are derived for computing the entries of the Bezout resultant matrix for two univariate polynomials of degree n and for calculating the entries of the Dixon–Cayley resultant matrix for three bivariate polynomials of bidegree (m, n). Standard methods based on explicit formulas require O(n3) additions and multiplications to compute all the entries of the Bezout resultant matr...

The resultant of a square system of homogeneous polynomials is a polynomial in their coefficients which vanishes whenever the system has a solution. Canny gave an algorithm running in polynomial space to compute it but no lower bound was known. We investigate the complexity of the associated decision problem and give a hardness result: Testing the resultant for zero lies in the class Arthur −Me...

Given two curves in P 3 , either implicitly or by a param-eterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant techniques. Our aim is to provide a closed formula in the inputs which vanishes if and only if the two curves intersect. This could be useful in Computer Aided Design, for computing the intersection of algebraic surfaces.

This case report describes the anomalous development of maxillary permanent lateral incisors in a seven-year-old white male. The maxillary right permanent lateral incisor radiographically demonstrated anomalous development characteristic of dens invaginatus. A coincidental finding of a microdontic maxillary left permanent lateral incisor also was observed at this time. This patient presented wi...

OBJECTIVE To illustrate a case of an iatrogenic mucosal tear in the trachea which caused a one-way valve effect, obstructing the airway and manifesting as post-extubation stridor. CASE REPORT We report a case of iatrogenic tracheal mucosal tear secondary to violent movement during intubation. The patient presented with post-extubation stridor that worsened over three days. Initial evidence su...

Throughout history, a proportion of men appear to correlate penis size and dimensions directly with physical fitness and sexual prowess. Foreign materials, such as paraffin oil, paraffin balm, mineral oils, and silicone, have been used to promise an improvement in penile shaft contour and dimensions. These materials are injected directly into the penis; inducing granuloma formation to achieve i...

Hidden-variable resultant methods are a class of algorithms for solving multidimensional polynomial rootfinding problems. In two dimensions, when significant care is taken, they are competitive practical rootfinders. However, in higher dimensions they are known to miss zeros, calculate roots to low precision, and introduce spurious solutions. We show that the hidden-variable resultant method ba...

A new method for constructing Sylvester-type resultant matrices for multivariate elimination is proposed. Unlike sparse resultant constructions discussed recently in the literature or the Macaulay resultant construction, the proposed method does not explicitly use the support of a polynomial system in the construction. Instead, a multiplier set for each polynomial is obtained from the Dixon for...

The main question of this paper is: What is the dense (Macaulay) resultant of composed polynomials? By a composed polynomial f ◦ (g1, . . . , gn), we mean the polynomial obtained from a polynomial f in the variables y1, . . . , yn by replacing yj by by some polynomial gj . Cheng, McKay and Wang and Jouanolou have provided answers for two particular subcases. The main contribution of this paper ...

We propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix F (s): The proposed method exploits the structure of the left null space of generalized Wolovich or Sylvester resultants to compute row polynomial vectors that form a minimal polynomial basis of left kernel of the given polynomial matrix. The entire procedure can be imple...