A straightforward way to represent multivariate polynomial in software is to implement them recursively as univariate polynomials over a polynomial ring. This is especially common in an object oriented context. We present a short algorithm which maps polynomials from one polynomial ring to another polynomial ring where the order of variables is permuted. This algorithm uses the recursive repres...

We introduce a graph polynomial that distinguishes tree structures to represent dependency grammar and measure based on the representation quantify syntax similarity. The encodes accurate comprehensive information about structure relations of words in sentence, which enables in-depth analysis trees with data tools. apply polynomial-based methods analyze sentences ParallelUniversal Dependencies ...

Representation of a given nonnegative multivariate polynomial in terms of a sum of squares of polynomials has become an essential subject in recent developments of sums of squares optimization and SDP (semidefinite programming) relaxation of polynomial optimization problems. We disscuss effective methods to obtain a simpler representation of a “sparse” polynomial as a sum of squares of sparse p...

Private Set Intersection protocols (PSIs) allow parties to compute the intersection of their private sets, such that nothing about sets’ elements beyond is revealed. PSIs have a variety applications, primarily in efficiently supporting data sharing privacy-preserving manner. At Eurocrypt 2019, Ghosh and Nilges proposed three efficient based on polynomial representation sets proved security agai...

Risa/Asir consists of the Risa engine for performing operations on mathematical objects and an interpreter for programs written in the Asir user language. In Risa/Asir, polynomials are represented in two different internal forms: the recursive representation and the distributed representation. Polynomial factorization and GCD are based on the former representation, and computations related to t...

A representation of the eld GF (2 n) for various values of n is described, where the eld elements are palindromic polynomials, and the eld operations are polynomial addition and multiplication in the ring of polynomials modulo x 2n+1 ?1. This representation can be shown to be equivalent to a eld representation of Type-II optimal normal bases. As such, the suggested palindromic representation in...