Related papers: Multivariate Power Series in Maple
Hensel's lemma, combined with repeated applications of Weierstrass preparation theorem, allows for the factorization of polynomials with multivariate power series coefficients. We present a complexity analysis for this method and leverage…
A blend of two Taylor series for the same smooth real- or complex-valued function of a single variable can be useful for approximation. We use an explicit formula for a two-point Hermite interpolational polynomial to construct such blends.…
We offer a Maple package {\tt Poincare\_Series} for calculating the Poincar\'e series for the algebras of invariants/covariants of binary forms, for the algebras of joint invariants/covariants of several binary forms, for the kernel of…
In this paper we present a Maple library (MOPs) for computing Jack, Hermite, Laguerre, and Jacobi multivariate polynomials, as well as eigenvalue statistics for the Hermite, Laguerre, and Jacobi ensembles of Random Matrix theory. We also…
The library \emph{fast\_polynomial} for Sage compiles multivariate polynomials for subsequent fast evaluation. Several evaluation schemes are handled, such as H\"orner, divide and conquer and new ones can be added easily. Notably, a new…
In this paper, we extend our previous work on the power series method for computing backstepping kernels. Our first contribution is the development of initial steps towards a MATLAB toolbox dedicated to backstepping kernel computation. This…
Multi-Agent Reinforcement Learning (MARL) encompasses a powerful class of methodologies that have been applied in a wide range of fields. An effective way to further empower these methodologies is to develop libraries and tools that could…
Machine learning potentials (MLPs) are becoming powerful tools for performing accurate atomistic simulations and crystal structure optimizations. An approach to developing MLPs employs a systematic set of polynomial invariants including…
A novel method, the Pareto Envelope Augmented with Reinforcement Learning (PEARL), has been developed to address the challenges posed by multi-objective problems, particularly in the field of engineering where the evaluation of candidate…
This study explores the integration of the hyper-power sequence, a method commonly employed for approximating the Moore-Penrose inverse, to enhance the effectiveness of an existing preconditioner. The approach is closely related to…
This is a user guide for the first version of our developed Maple library, named Singularity. The first version here is designed for the qualitative study of local real zeros of scalar smooth maps. This library will be extended for symbolic…
In this paper, we present a new Python library called mPyPl, which is intended to simplify complex data processing tasks using functional approach. This library defines operations on lazy data streams of named dictionaries represented as…
In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. We extend its application to the case of formal power series over a field of arbitrary characteristic and illustrate the proposed approach…
This paper focuses on multirate time-domain simulations of power system models. It proposes a matrix pencil-based approach to evaluate the spurious numerical deformation introduced into power system dynamics by a given multirate integration…
The Cayley-Hamilton theorem is used to implement an iterative process for the efficient numerical computation of matrix power series and their differentials. In addition to straight-forward applications in lattice gauge theory simulations…
We present the Matlab toolbox MacaulayLab, which implements numerical linear algebra algorithms for solving multivariate polynomial systems and rectangular multiparameter eigenvalue problems. Its structure and functionality are the result…
There have been some effective tools for solving (constant/parametric) semi-algebraic systems in Maple's library RegularChains since Maple 13. By using the functions of the library, e.g., RealRootClassfication, one can prove and discover…
The advent of large language models (LLMs) has sparked significant interest in using natural language for preference learning. However, existing methods often suffer from high computational burdens, taxing human supervision, and lack of…
We introduce SeeMPS, a Python library dedicated to implementing tensor network algorithms based on the well-known Matrix Product States (MPS) and Quantized Tensor Train (QTT) formalisms. SeeMPS is implemented as a complete finite precision…
In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which…