We introduce new polynomial invariants of a finite-dimensional semisimple and cosemisimple Hopf algebra A over a field k by using the braiding structures of A. We investigate basic properties of the polynomial invariants including stability under extension of the base field. Furthermore, we show that our polynomial invariants are indeed tensor invariants of the representation category of A, and...

A lot of libraries for neural networks are written Turing-complete programming languages such as Python, C++, PHP, and Java. However, at the moment, there no suitable implemented a p-complete logical language L. This paper investigates issues polynomial-computable representation this language, where basic elements hereditarily finite list elements, programs defined using special terms formulas ...

finite field representation, optimal normal basis, palindromic representation A representation of the field GF(2n) for various values of n is described, where the field elements are palindromic polynomials, and the field operations are polynomial addition and multiplication in the ring of polynomials modulo x2n+1–1. This representation can be shown to be equivalent to a field representation of ...

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 a sum of squares optimization and SDP (semidefinite programming) relaxation of polynomial optimization problems. We disscuss effective methods to get a simpler representation of a “sparse” polynomial as a sum of squares of sparse pol...