Problems in competitive programming, especially the ones involving enumeration some kind, are often solved by reducing the problem to computing something on polynomials and formal power series. This ...

The Abhyankar-Sathaye Problem asks whether any biregular embedding $\varphi \colon {\Bbb C}^{k}\hookrightarrow {\Bbb C}^{n}$ can be rectified, that is, whether there exists an automorphism α ∈ Aut Cn ...

Abstract: Polynomial methods are an effective method for the synthesis of control systems. The calculation of certain functions with polynomial matrices which are represented by coefficients of ...

MUCH use is made in combinatorial problems of generating functions in the form of polynomials and infinite power series, these being obtained by the manipulation of other algebraic expressions. In ...

Abstract: The paper expands the basic concepts of the coding theorists in the representation of data strings by algebraic polynomials, and develops the representation of both time and location of ...

PolyF2 is a tiny, educational project that shows how to implement algebra over the binary field F2 using native integer operations. On top of single polynomials over F2 (PolyF2), it builds PF2Int — a ...

This is a preview. Log in through your library . Abstract An analogue of Hubert's Syzygy Theorem is proved for the algebra 𝕊 n (A) of one-sided inverses of the polynomial algebra A[x₁,... , x n ] ...

An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of ...

Conjecture 1 (Anick Conjecture). There exists wild automorphisms in AutK〈x, y, z〉. In particular, the Anick automorphism is wild. Conjecture 2 (Strong Anick Conjecture). There exist wild coordinates ...

New research details an intriguing new way to solve "unsolvable" algebra problems that go beyond the fourth degree – something that has generally been deemed impossible using traditional methods for ...