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Rigorous modelling of natural and industrial systems still conveys various challenges related to abstractions, methods to proceed with and easy-to-use tools to build, compose and reason on models. Operads are mathematical structures that…
Despite the relevance of the binomial distribution for probability theory and applied statistical inference, its higher-order moments are poorly understood. The existing formulas are either not general enough, or not structured and…
We present the $\textit{NumericalImplicitization}$ package for $\textit{Macaulay2}$, which allows for user-friendly computation of the invariants of the image of a polynomial map, such as dimension, degree, and Hilbert function values. This…
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…
Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…
In this paper we present a Mathematica notebook for computing nonsymmetric and interpolation Macdonald polynomials. We present the new recursive generation algorithm employed within the notebook and the theory required for its development.…
Superposition -- when a neural network represents more ``features'' than it has dimensions -- seems to pose a serious challenge to mechanistically interpreting current AI systems. Existing theory work studies \emph{representational}…
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…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
The paper deals with the process of mathematical modeling representations of exponential and logarithmic functions hypercomplex number system of generalized quaternions via determining a linear differential equation with hypercomplex…
This paper presents a new Matlab toolbox, aimed at facilitating the use of polynomial optimization for stability analysis of nonlinear systems. In the past decade several decisive contributions made it possible to recast this type of…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
Interactive computing notebooks, such as Jupyter notebooks, have become a popular tool for developing and improving data-driven models. Such notebooks tend to be executed either in the user's own machine or in a cloud environment, having…
SOSOPT is a Matlab toolbox for formulating and solving Sum-of-Squares (SOS) polynomial optimizations. This document briefly describes the use and functionality of this toolbox. Section 1 introduces the problem formulations for SOS tests,…
We introduce $\texttt{mosca}$, a $\texttt{Mathematica}$ package designed to facilitate on-shell calculations in effective field theories (EFTs). This initial release focuses on the reduction of Green's bases to physical bases, as well as…
Algebraic effects & handlers have become a standard approach for side-effects in functional programming. Their modular composition with other effects and clean separation of syntax and semantics make them attractive to a wide audience.…
Mathematical expressions can be represented as a tree consisting of terminal symbols, such as identifiers or numbers (leaf nodes), and functions or operators (non-leaf nodes). Expression trees are an important mechanism for storing and…
MathLink is Wolfram Research's protocol for communicating with the Mathematica Kernel and is used extensively in their own Notebook Frontends. The Mathematica Book insinuates that linking C programs with MathLink is straightforward but in…
We describe the qFunctions Mathematica package for $q$-series and partition theory applications. This package includes both experimental and symbolic tools. The experimental set of elements includes guessers for $q$-shift equations and…
The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behavior of an experiment? How many of the…