Related papers: Deducing factoring methods through concrete materi…

Using Newton polygons, a key factorization result for polynomials over discrete valuation domains is proved, which in particular yields new irreducibility criteria including a generalization of the classical irreducibility criterion of…

A generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in Quantum Mechanics. The method is applied in the study of radial oscillator, Morse…

Let $R=K[x_{1},x_{2},\cdots, x_{m}]$ and $S=$ $K[y_{1},y_{2},\cdots, y_{m}]$ where $K$ is a field. %commutative ring with unity. In this paper, we propose a method showing how to obtain $3$-matrix factors for a given polynomial using either…

We provide some statistics about an irreducibility/reducibility test for multivariate polynomials over finite fields based on counting points. The test works best for polynomials in a large number of variables and can also be applied to…

This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…

The following result, a consequence of Dumas criterion for irreducibility of polynomials over integers, is generally proved using the notion of Newton diagram: Let $f(x)$ be a polynomial with integer coefficients and $k$ be a positive…

We classify the discriminantly separable polynomials of degree two in each of three variables, defined by a property that all the discriminants as polynomials of two variables are factorized as products of two polynomials of one variable…

In this paper, we prove several theorems on systems of polynomials with at least one positive real zero based on the theory of conceive polynomials. These theorems provide sufficient conditions for systems of multivariate polynomials…

This article provides a gentle introduction for a general mathematical audience to the factorization theory of motion polynomials and its application in mechanism science. This theory connects in a rather unexpected way a seemingly abstract…

We lay the combinatorial foundations for [ShSt:340] by setting up and proving the essential properties of the coding apparatus for singular cardinals. We also prove another result concerning the coding apparatus for inaccessible cardinals.

We give a short direct proof of Agler's factorization theorem that uses the abstract characterization of operator algebras. the key ingredient of this proof is an operator algebra factorization theorem. Our proof provides some additional…

We generalize the classical lifting and recombination scheme for rational and absolute factorization of bivariate polynomials to the case of a critical fiber. We explore different strategies for recombinations of the analytic factors,…

We obtain various irreducibility criteria for pairs of polynomials $(f(X),g(X))$ with integer coefficients whose resultant $Res(f,g)$ is a prime number, or is divisible by a sufficiently large prime number, and also for some of their linear…

The decomposition of a matrix, as a product of factors with particular properties, is a much used tool in numerical analysis. Here we develop methods for decomposing a matrix $C$ into a product $X Y$, where the factors $X$ and $Y$ are…

To cater to the needs of (Zero Knowledge) proofs for (mathematical) proofs, we describe a method to transform formal sentences in 2x2-matrices over multivariate polynomials with integer coefficients, such that usual proof-steps like…

For an arbitrary finite set S of natural numbers greater 1, we construct an integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of lengths of f is the set of all natural numbers n, such that f has a factorization as a…

In this paper we investigate factorizations of polynomials over the ring of dual quaternions into linear factors. While earlier results assume that the norm polynomial is real ("motion polynomials"), we only require the absence of real…

We consider bivariate polynomials over the skew field of quaternions, where the indeterminates commute with all coefficients and with each other. We analyze existence of univariate factorizations, that is, factorizations with univariate…

We study the probability that a random polynomial with integer coefficients is reducible when factored over the rational numbers. Using computer-generated data, we investigate a number of different models, including both monic and non-monic…

The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…