Polynomial identities of nonassociative rings Part III: Applications

Efficient Identity Testing and Polynomial Factorization in Nonassociative Free Rings

In this paper we study arithmetic computations over non-associative, and non-commutative free polynomials ring F{x1, x2, . . . , xn}. Prior to this work, the non-associative arithmetic model of computation was considered by Hrubes, Wigderson, and Yehudayoff [HWY10]. They were interested in completeness and explicit lower bound results. We focus on two main problems in algebraic complexity theor...

Differential Polynomial Rings of Triangular Matrix Rings

Part III: Polynomial-Based Interpolation for DSP Applications

Part III: Polynomial-Based Interpolation for DSP Applications • This pile of lecture notes is mainly based on the research work done by Jussi Vesma and the lecturer during the last three years. • Many thanks to Jussi Vesma for his help in preparing this pile of lecture notes. • If there is some interest to get the pile of lecture notes of the overall course, please contact Tapio Saramäki using ...

Some Polynomial Identities that Imply Commutativity of Rings

In this paper, we establish some commutativity theorems for certain rings with polynomial constraints as follows: Let R be an associative ring, and for all x, y ∈ R, and fixed non-negative integers m > 1, n ≥ 0, r > 0, s ≥ 0, t ≥ 0, p ≥ 0, q ≥ 0 such that P (x, y) = ±Q(x, y), where P (x, y) = ys[x, y]yt and Q(x, y) = xp[xm, yn]ryq. First,it is shown that a semiprime ring R is commutative if and...

Polynomial extension operators. Part III

In this concluding part of a series of papers on tetrahedral polynomial extension operators, the existence of a polynomial extension operator in the Sobolev space H(div) is proven constructively. Specifically, on any tetrahedron K, given a function w on the boundary ∂K that is a polynomial on each face, the extension operator applied to w gives a vector function whose components are polynomials...