Results 261 to 270 of about 4,716 (302)

ON POLYNOMIAL AUTOMORPHISM IDENTITY SETS AND IDENTITY POLYNOMIALS

Communications in Algebra, 2001
In this paper, we propose a new condition for hypersurfaces to be polynomial automorphism identity sets. This new condition can be used to give a new proof of Mckay-Wang's problem. Moreover, we also study the concepts of identity polynomials, and give a criterion for a polynomial to be identity polynomial.
Wang Mingsheng, Liu Zhuojun
openaire   +1 more source

Equivalence of Polynomial Identity Testing and Polynomial Factorization

computational complexity, 2015
In this research paper it is demonstrated that the problem of deterministically factoring multivariate polynomials reduces to the problem of deterministic polynomial identity testing. More specifically, it is explored that, given an arithmetic circuit (either explicitly or via black-box access) that computes a multivariate polynomial \(f\), the task of
Swastik Kopparty, Shubhangi Saraf, Amir Shpilka   +2 more
openaire   +1 more source

Polynomial identities on superalgebras and exponential growth

Journal of Algebra, 2003
Let A be a finitely generated superalgebra over a field F of characteristic 0. To the graded polynomial identities of A one associates a numerical sequence {cnsup(A)}n⩾1 called the sequence of graded codimensions of A.
Antonio Giambruno
exaly   +2 more sources

On the *-Polynomial Identities of a Class of *-Minimal Algebras

Communications in Algebra, 2010
The problem of classifying the finite dimensional *-minimal algebras up to *-PI equivalence has been recently faced by Di Vincenzo and Spinelli. Essentially, if A is a finite dimensional *-minimal algebra over the field F then there exists an n-tuple ...
Onofrio M Di Vincenzo, Vincenzo Nardozza   +1 more
exaly   +2 more sources

Derivations and Identities for Chebyshev Polynomials

Ukrainian Mathematical Journal, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bedratyuk, L. P., Lunio, N. B.
openaire   +1 more source

An Identity in Hermite Polynomials

Biometrika, 1971
SUMMARY An extension of the Runge (1914) identity in Hermite polynomials is derived, and a test of the assumption of bivariate normality is developed using the identity.
openaire   +1 more source

A q-Polynomial Identity

Proceedings of the American Mathematical Society, 1985
This q-polynomial identity involves the number of inversions between multisets \((a_ 1,...,a_ n)\) and \((m-a_ 1,...,m-a_ n)\), and generalizes the recurrence identity for q-binomial (Gaussian) coefficients [\textit{I. P. Goulden} and \textit{D. M. Jackson}, Combinatorial enumeration (1983; Zbl 0519.05001), p.
openaire   +2 more sources

Rings with Involution and Polynomial Identities

Canadian Journal of Mathematics, 1968
An involution * of a ring A is a one-one additive mapping of A onto itself such that (xy)* = y*x* and x** = x for all x, y ∊ A. If A is an algebra over a field Φ, one makes the additional requirement that (λx)* = λx* for all λ ∊ Φ, x ∊ A. S will generally denote the set of symmetric elements s* = s, K the set of skew elements , and Z the centre of A.
Baxter, W. E., Martindale, W. S. III
openaire   +1 more source

The Proof Complexity of Polynomial Identities

2009 24th Annual IEEE Conference on Computational Complexity, 2009
Devising an efficient deterministic -- or even a non-deterministic sub-exponential time -- algorithm for testing polynomial identities is a fundamental problem in algebraic complexity and complexity at large. Motivated by this problem, as well as by results from proof complexity, we investigate the complexity of _proving_ polynomial identities. To this
Pavel Hrubes, Iddo Tzameret
openaire   +1 more source

Polynomial Identities in Smash Products

Journal of Lie Theory, 2002
For a Lie algebra \(L\), \(U(L)\) (respectively \(u(L)\)) denotes the (restricted) universal enveloping algebra of \(L\). The main results of the article are the following two theorems. Theorem 2.3. Let \(G\) be a group, \(L\) be a Lie algebra over a field \(K\) of characteristic \(p>0\) and \(G\) act on \(L\) by automorphisms. Then the smash product \(
Bahturin, Yuri, Petrogradsky, Victor
openaire   +2 more sources