Polynomials, Basis Sets, and Deceptiveness in Genetic Algorithms

Boolean Gröbner Basis Reductions on Datapath Circuits Using the Unate Cube Set Algebra

Recent developments in formal datapath verification make efficient use of symbolic computer algebra algorithms for formal verification. The circuit is modeled as a set of polynomials over Boolean (or pseudo-Boolean) rings, and Gröbner basis (GB) reductions are performed over these polynomials to derive a canonical representation. GB reductions of Boolean polynomials tend to cause intermediate e...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Using an Imperialistic Competitive Algorithm in Global Polynomials Optimization (Case Study: 2D Geometric Correction of IKONOS and SPOT Imagery)

The number of high resolution space imageries in photogrammetry and remote sensing society is growing fast. Although these images provide rich data, the lack of sensor calibration information and ephemeris data does not allow the users to apply precise physical models to establish the functional relationship between image space and object space. As an alternative solution, some generalized mode...

A New Hybrid model of Multi-layer Perceptron Artificial Neural Network and Genetic Algorithms in Web Design Management Based on CMS

The size and complexity of websites have grown significantly during recent years. In line with this growth, the need to maintain most of the resources has been intensified. Content Management Systems (CMSs) are software that was presented in accordance with increased demands of users. With the advent of Content Management Systems, factors such as: domains, predesigned module’s development, grap...

Division algorithms for Bernstein polynomials

Three division algorithms are presented for univariate Bernstein polynomials: an algorithm for finding the quotient and remainder of two univariate polynomials, an algorithm for calculating the GCD of an arbitrary collection of univariate polynomials, and an algorithm for computing a μ-basis for the syzygy module of an arbitrary collection of univariate polynomials. Division algorithms for mult...