Results 11 to 20 of about 9,360 (297)
EVALUATION PROPERTIES OF SYMMETRIC POLYNOMIALS [PDF]
International Journal of Algebra and Computation, 2006 By the fundamental theorem of symmetric polynomials, if P ∈ ℚ[X1,…,Xn] is symmetric, then it can be written P = Q(σ1,…,σn), where σ1,…,σn are the elementary symmetric polynomials in n variables, and Q is in ℚ[S1,…,Sn]. We investigate the complexity properties of this construction in the straight-line program model, showing that the complexity of ...
Pierrick Gaudry +2 more
openaire +4 more sources
AN IDENTITY ON SYMMETRIC POLYNOMIALS
Tạp chí Khoa học Đại học Đà Lạt, 2020 In this paper, we propose and prove an identity on symmetric polynomials. In order to obtain this identity, we use the interpolation theory, in particular, the Lagrange interpolation formula. In the proof of the identity, we propose two different proofs.
Đặng Tuấn Hiệp, Lê Văn Vĩnh
doaj +3 more sources
Symmetric $*$-polynomials on $\mathbb C^n$
Karpatsʹkì Matematičnì Publìkacìï, 2018 $*$-Polynomials are natural generalizations of usual polynomials between complex vector spaces. A $*$-polynomial is a function between complex vector spaces $X$ and $Y,$ which is a sum of so-called $(p,q)$-polynomials.
T.V. Vasylyshyn
doaj +2 more sources
PySymmPol - Symmetric Polynomials
Journal of Open Source Software<p>A Python package designed for efficient manipulation of symmetric polynomials. It provides functionalities for working with various types of symmetric polynomials, including elementary, homogeneous, monomial symmetric, (skew-) Schur, and Hall ...
Rocha Araujo, Thiago
core +5 more sources
Symmetric polynomials and Hall's theorem
Discrete Mathematics, 1988 Let A[X,Y] be the polynomial ring in 2n variables \(X=(X_ 1,..,X_ n)\), \(Y=(Y_ 1,...,Y_ n)\) over a commutative unitary ring A and let \({\mathcal P}\) and \({\mathcal D}\) be the following ideals of A[X,Y]: \({\mathcal P}=\); \({\mathcal D}=\), where the \(\sigma_ k\) are the k-th elementary symmetric polynomials in n variables.
Klaus G. Fischer, Fischer, Klaus G.
openaire +2 more sources
Symmetric functions on spaces $\ell_p(\mathbb{{R}}^n)$ and $\ell_p(\mathbb{{C}}^n)$
Karpatsʹkì Matematičnì Publìkacìï, 2020 This work is devoted to the study of algebras of continuous symmetric polynomials, that is, invariant with respect to permutations of coordinates of its argument, and of $*$-polynomials on Banach spaces $\ell_p(\mathbb{R}^n)$ and $\ell_p(\mathbb{C}^n ...
T.V. Vasylyshyn
doaj +1 more source
Algebraic basis of the algebra of block-symmetric polynomials on $\ell_1 \oplus \ell_{\infty}$
Karpatsʹkì Matematičnì Publìkacìï, 2019 We consider so called block-symmetric polynomials on sequence spaces $\ell_1\oplus \ell_{\infty}, \ell_1\oplus c, \ell_1\oplus c_0,$ that is, polynomials which are symmetric with respect to permutations of elements of the sequences.
V.V. Kravtsiv
doaj +1 more source
Vanishing Results for Hall-Littlewood Polynomials [PDF]
, 2012 It is well-known that if one integrates a Schur function indexed by a partition λ over the symplectic (resp. orthogonal) group, the integral vanishes unless all parts of λ have even multiplicity (resp. all parts of λ are even).
Venkateswaran, Vidya
core +1 more source
On the Complexity of Symmetric Polynomials.
ITCS, 2018 Peer ...
Markus Bläser, Gorav Jindal
openaire +6 more sources
Singular polynomials from orbit spaces [PDF]
, 2012 We consider the polynomial representation S(V*) of the rational Cherednik algebra H_c(W) associated to a finite Coxeter group W at constant parameter c.
Feigin, M., Silantyev, A.
core +1 more source