wgorous search for probabdisuc algonthms In dlustratmn of this observaUon, vanous fast probabdlsttc algonthms, with probability of correctness guaranteed a prion, are presented for testing polynomial ldentmes and propemes of systems of polynomials. Ancdlary fast algorithms for calculating resultants

The secret lives of polynomial identities“An idea which can be used only once is a trick. If you can use it more than once it becomes a method. ” – George Pólya and Gábor

Polynomial identity testing (PIT) is the problem of checking whether a given arithmetic circuit is the zero circuit. PIT ranks as one of the most important open problems in the intersection of algebra and computational complexity. In the last few years, there has been an impressive progress

In this paper we consider PI-algebras A over the real and complex numbers and address the question of whether it is possible to find a normed PI-algebra B with the same polynomial identities as A, and moreover, whether there is some Banach PI-algebra with this property. Our main theorem provides

programs. Precision of the analysis can be measured by providing classes of programs for whichthe analysis is complete, i.e., decides the property in question. Here, we consider analyses of polynomial identities between integer variables such as x1 * x2- 2x3 = 0. We describe current approaches and clarify

This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras, and the corresponding dialgebras; the KP algorithm

. Precision of the analysis can be measured by providing classes of programs for which the analysis is complete, i.e., decides the property in question. Here, we consider analyses of polynomial identities between integer variables such as x1 · x2 − 2x3 = 0. We describe current approaches and clarify

We prove polynomial identities for the N = 1 superconformal model SM(2, 4ν) which generalize and extend the known Fermi/Bose character identities. Our proof uses the q-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing

Abstract. The talk is an introduction to the theory of alge-bras with polynomial identities. It stresses on matrix algebras and polynomial identities for them. The notion of Bergman polynomials is introduced. Such types of polynomials are in-vestigated being identities for algebras with symplectic

Presented are polynomial identities which imply generalizations of Euler and Rogers–Ramanujan identities. Both sides of the identities can be interpreted as generating functions of certain restricted partitions. We prove the identities by establishing a graphical one-to-one correspondence between