Related papers: An Alternative Approach to Polynomial Mappings

In the recent years, several polynomial algorithms of a dynamical nature have been proposed to address the graph isomorphism problem. In this paper we propose a generalization of an approach exposed in cond-mat/0209112 and find that this…

The number of linear independent algebraic relations among elementary symmetric polynomial functions over finite fields is computed. An algorithm able to find all such relations is described. It is proved that the basis of the ideal of…

We produce algorithms to detect whether a complex affine variety computed and presented numerically by the machinery of numerical algebraic geometry corresponds to an associated component of a polynomial ideal.

Equivalence between algebraic equations of motion may be detected by using a $p$-adic method, methods using factorization and linear algebra, or by systematic computer search of suitable Tschirnhausen transformations. Here, we show standard…

We provide a novel tool which may be used to construct new examples of positive maps in matrix algebras (or, equivalently, entanglement witnesses). It turns out that this can be used to prove positivity of several well known maps (such as…

Many hard combinatorial problems can be modeled by a system of polynomial equations. N. Alon coined the term polynomial method to describe the use of nonlinear polynomials when solving combinatorial problems. We continue the exploration of…

Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…

The article presents an algebra to represent two dimensional patterns using reciprocals of polynomials. Such a representation will be useful in neural network training and it provides a method of training patterns that is much more…

A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…

In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…

Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…

We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.

In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…

We introduce three simple polynomial maps with integer coefficients that have interesting dynamical properties modulo primes.

Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…

In this paper polynomial maps are represented by the use of matrices whose entries are numbered by pair of multiindices and a new product of such matrices is introduced. A matrix representation of composition of polynomial maps is given. In…

Using the diagrammatic approach to integrals over Gaussian random matrices, we find a representation for polynomial Lie group integrals as infinite sums over certain maps on surfaces. The maps involved satisfy a specific condition: they…

In this paper we introduce a new approach to the concept of multipolynomials and generalize several results of the homogeneous polynomials and symmetric multilinear applications. We also present an abstract approach to the concept of…

In this paper it is shown that it is possible to associate several polynomial ideals to a directed graph $D$ in order to find properties of it. In fact by using algebraic tools it is possible to give appropriate procedures for automatic…

Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…