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In this paper we construct the optimal sets of dissimilar subalgebras up to dimension three for the Lie algebra of point symmetries of the system of three-dimensional stationary equations of perfect plasticity with the Huber–von Mises yield ...

This paper presents a quantum-inspired method for proving Ramsey’s theorem using symbolic computation on conventional computers, an improvement of the classical Ramsey’s theorem, and a mechanized proof of $R(3,4)=9$ implemented by symbolic ...

The usual univariate interpolation problem of finding a monic polynomial f of degree n that interpolates n given values is well understood. This paper studies a variant where f is required to be composite, say, a composition of two polynomials of ...

This paper deals with the stability of a differential model for quasi-periodic plasma perturbations. First, we derive the linear stability conditions on the parameters of the differential model by using symbolic computation of solving semi-...

Data have been playing a vital role in many successful applications of artificial intelligence. To embrace the power of modern artificial intelligence (AI) technology to accelerate symbolic algorithms, it is indispensable to have a large amount of ...

There has been a growing need to devise processes that can create comprehensive datasets in the world of Computer Algebra, both for accurate benchmarking and for new intersections with machine learning technology. We present here a method to ...

We are concerned with the arithmetic of solutions to ordinary or partial nonlinear differential equations which are algebraic in the indeterminates and their derivatives. We call these solutions D-algebraic functions, and their equations are ...

We present an algorithm for the index reduction of first-order differential–algebraic equations. The proposed approach can be applied to generic differential–algebraic equations and exploits neither a priori knowledge nor ad hoc techniques to ...

In a series of papers we develop symbolic computation algorithms to investigate finiteness of central configurations for the planar n-body problem. Our approach is based on Albouy-Kaloshin's work on finiteness of central configurations for the 5-...

A new Las Vegas algorithm is presented for the composition of two polynomials modulo a third one, over an arbitrary field. When the degrees of these polynomials are bounded by n, the algorithm uses O(n^1.43) field operations, breaking through the 3/2 ...

In this note, I present my personal view on the interaction of the three areas Automated Programming, Symbolic Computation, and Machine Learning. Programming is the activity of finding a (hopefully) correct program (algorithm) for a given problem. ...

This paper deals with the stability and zero-Hopf bifurcation of the Lorenz–Stenflo system by using methods of symbolic computation. Stability conditions on the parameters of the system are derived by using methods of solving semi-algebraic ...

The need to verify symbolic computation arises in diverse application areas. In this paper, based on earlier work on verifying computation of definite integrals in HolPy, we present a tool Iscalc for performing a variety of symbolic computations ...

We describe applications of symbolic computation towards automating the formal analysis of while-programs implementing polynomial arithmetic. We combine methods from static analysis, symbolic summation and computer algebra to derive polynomial ...

Consider a card guessing game with complete feedback in which a deck of n cards ordered 1 , … , n is riffle-shuffled once. With the goal to maximize the number of correct guesses, a player guesses cards from the top of the deck one at ...

In this paper, we present a symbolic computation method for constructing a small neighborhood U around a known local optimal maximal or minimal point $x_0$ of a given smooth function $f:{\mathbb{R}}^n\to \mathbb{R}$ that contains radical or rational expressions of several ...${}_{\mathrm{}}$${}_{\mathrm{}}$$$

In this article, a (2+1)-dimensional system of Broer–Kaup–Kupershmidt (BKK) equations, which describes the non-linear, and long gravity waves in a dispersive system, is investigated by applying the method of Lie group of invariance. ...

• The system of (2+1)-dimensional Broer–Kaup–Kupershmidt (BKK) equations is investigated using the Lie symmetry approach.

In this paper, a generalized (3+1)-dimensional Kadomtsev–Petviashvili Benjamin–Bona–Mahony equation which describes the fluid flow in the case of an offshore structure, is investigated. Here, making use of the bilinear form and ...

In this paper, two-to-one mappings and involutions without any fixed point on finite fields of even characteristic are investigated. First, we characterize a closed relationship between them by implicit functions and develop an AGW-...

We consider the problem of binomiality of the steady state ideals of biochemical reaction networks. We are interested in finding polynomial conditions on the parameters such that the steady state ideal of a chemical reaction network is binomial ...