相关论文: The Fedosov *-product in Mathematica

We present a closed formula for a family of star-products by replacing the partial derivatives in the Moyal-Weyl formula with commuting vector fields. We show how to reproduce algebra relations on commutative spaces with these star-products…

We employ the generalized Remez algorithm, initially suggested by P. T. P. Tang, to perform an experimental study of Chebyshev polynomials in the complex plane. Our focus lies particularly on the examination of their norms and zeros. What…

We propose a new method to calculate coupling coefficients of E_7 tensor products. Our method is based on explicit use of E_7 characters in the definition of a tensor product. When applying Weyl character formula for E_7 Lie algebra, one…

In this paper the Benettin-Wolf algorithm to determine all Lyapunov exponents for a class of fractional-order systems modeled by Caputo's derivative and the corresponding Matlab code are presented. First it is proved that the considered…

We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of…

Mathematica offers, by way of the package Combinatorics, many useful functions to work on graphs and ordered structures, but none of these functions was specific enough to meet the needs of our research group. Moreover, the existing…

Algorithms of numeric (in exact arithmetic) deduction of analytical expressions, proposed and described by Shevchenko and Vasiliev (1993), are developed and implemented in a computer algebra code. This code is built as a superstructure for…

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…

We show that product Chebyshev polynomial meshes can be used, in a fully discrete way, to evaluate with rigorous error bounds the Lebesgue constant, i.e. the maximum of the Lebesgue function, for a class of polynomial projectors on cube,…

In this paper the local differential calculus over Fedosov algebra is constructed using the trivialization isomorphism. The explicit formulas for deformed derivations are given. The resulting calculus can be used as a "building block" for a…

We produce algorithms to detect whether a complex affine variety computed and presented numerically by the machinery of numerical algebraic geometry corresponds to an associated component of a polynomial ideal.

In this paper we explicitly construct local $\nu$-Euler derivations $\mathsf E_\alpha = \nu \partial_\nu + \Lie{\xi_\alpha} + \mathsf D_\alpha$, where the $\xi_\alpha$ are local, conformally symplectic vector fields and the $\mathsf…

There exist several methods for computing exact solutions of algebraic differential equations. Most of the methods, however, do not ensure existence and uniqueness of the solutions and might fail after several steps, or are restricted to…

A collection of algorithms in object-oriented MATLAB is described for numerically computing with smooth functions defined on the unit ball in the Chebfun software. Functions are numerically and adaptively resolved to essentially machine…

We present fast algorithms for computing rational first integrals with bounded degree of a planar polynomial vector field. Our approach is inspired by an idea of Ferragut and Giacomini. We improve upon their work by proving that rational…

In order to invariantly characterise spacetimes resulting from cosmological simulations in numerical relativity, we present two different methodologies to compute the electric and magnetic parts of the Weyl tensor, $E_{\alpha\beta}$ and…

It is shown how Seiberg-Witten equations can be obtained by means of Fedosov deformation quantization of endomorphism bundle and the corresponding theory of equivalences of star products. In such setting, Seiberg-Witten map can be…

We introduce a simple algorithm that efficiently computes tensor products of Pauli matrices. This is done by tailoring the calculations to this specific case, which allows to avoid unnecessary calculations. The strength of this strategy is…

This paper introduces an efficient tensor-vector product technique for the rapid and accurate approximation of integral operators within physics-informed deep learning frameworks. Our approach leverages neural network architectures to…

We describe an approach for finding upper bounds on an ODE dynamical system's maximal Lyapunov exponent among all trajectories in a specified set. A minimization problem is formulated whose infimum is equal to the maximal Lyapunov exponent,…