Timescales of Chaos in the Inner Solar System: Lyapunov Spectrum and Quasi-integrals of Motion by Federico Mogavero, Nam H. Hoang, Jacques Laskar

“…A systematic analysis of the Fourier harmonics of the Hamiltonian, based on computer algebra, reveals three symmetries that characterize the strongest resonances responsible for the orbital chaos. …”
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Exact Bayesian inference on discrete models via probability generating functions: a probabilistic programming approach by Zaiser, F, Murawski, AS, Ong, C-HL

“…<p>We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors.To express such models, we introduce a probabilistic programming language that supports discrete and continuous sampling, discrete observations, affine functions, (stochastic) branching, and conditioning on discrete events.Our key tool is <em>probability generating functions</em>:they provide a compact closed-form representation of distributions that are definable by programs, thus enabling the exact computation of posterior probabilities, expectation, variance, and higher moments.Our inference method is provably correct and fully automated in a tool called <em>Genfer</em>, which uses automatic differentiation (specifically, Taylor polynomials), but does not require computer algebra.Our experiments show that Genfer is often faster than the existing exact inference tools PSI, Dice, and Prodigy.On a range of real-world inference problems that none of these exact tools can solve, Genfer's performance is competitive with approximate Monte Carlo methods, while avoiding approximation errors.…”

Risk Management of Innovation Projects in the Context of Globalization by Liudmila V. Nikolova, Juriy Ju. Kuporov, Dmitriy G. Rodionov

“…As a result, the authors have built a model of innovation project sustainability region in the context of globalization, using MATHCAT software (computer algebra system from a class of computer-aided design, focused on preparation of interactive documents with computations and visual tracking).…”
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Evolution over Two Decades of CAS-Active Senior Secondary Mathematics Curriculum and Assessment by David Leigh-Lancaster, Kaye Stacey

“…The Victorian Curriculum and Assessment Authority (VCAA) introduced the use of Computer Algebra System (CAS) technology (calculator and software) into the senior secondary mathematics curriculum and examination assessment in three phases, starting with a research-based pilot from 2000, followed by parallel implementation of CAS and non-CAS subjects from 2006 and culminating in transition to CAS-assumed subjects in 2010. …”
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Dynamic and Interactive Tools to Support Teaching and Learning by Ana C. Conceição

“…Current digital technology allows students to work interactively with a large number and variety of graphics, complementing the theoretical results and often used paper and pencil calculations. The computer algebra system <i>Mathematica</i> is a very powerful software that allows the implementation of many interactive visual applications. …”
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Lower Bounds on the Redundancy of Huffman Codes With Known and Unknown Probabilities by Ian Blanes, Miguel Hernandez-Cabronero, Joan Serra-Sagrista, Michael W. Marcellin

“…The method operates on a computer algebra system, yielding closed-form numbers for all results. …”
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Risk Management of Innovation Projects in the Context of Globalization by Liudmila V. Nikolova, Juriy Ju. Kuporov, Dmitriy G. Rodionov

“…As a result, the authors have built a model of innovation project sustainability region in the context of globalization, using MATHCAT software (computer algebra system from a class of computer-aided design, focused on preparation of interactive documents with computations and visual tracking). …”
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Supercomputers against strong coupling in gravity with curvature and torsion by W. E. V. Barker

“…Abstract Many theories of gravity are spoiled by strongly coupled modes: the high computational cost of Hamiltonian analysis can obstruct the identification of these modes. A computer algebra implementation of the Hamiltonian constraint algorithm for curvature and torsion theories is presented. …”
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Risk Management of Innovation Projects in the Context of Globalization by Liudmila V. Nikolova, Juriy Ju. Kuporov, Dmitriy G. Rodionov

“…As a result, the authors have built a model of innovation project sustainability region in the context of globalization, using MATHCAT software (computer algebra system from a class of computer-aided design, focused on preparation of interactive documents with computations and visual tracking). …”
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An algorithm for analysis of the structure of finitely presented Lie algebras by Vladimir P. Gerdt, Vladimir V. Kornyak

“…For this reason, in practice one needs to use a computer algebra tool. We describe here an algorithm for constructing the basis of a finitely presented Lie algebra and its commutator table, and its implementation in the C language. …”
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A Symbolic Method for Solving a Class of Convolution-Type Volterra–Fredholm–Hammerstein Integro-Differential Equations under Nonlocal Boundary Conditions by Efthimios Providas, Ioannis Nestorios Parasidis

“…The proposed methods are suitable for integration into any computer algebra system. Several linear and nonlinear examples are solved to demonstrate the effectiveness of the method.…”
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Privacy-Preserving Blockchain Technologies by Dalton Cézane Gomes Valadares, Angelo Perkusich, Aldenor Falcão Martins, Mohammed B. M. Kamel, Chris Seline

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Models for Tree Taper Form: The Gompertz and Vasicek Diffusion Processes Framework by Martynas Narmontas, Petras Rupšys, Edmundas Petrauskas

“…All results are obtained in the Maple computer algebra system.…”
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Computations in finite-dimensional Lie algebras by A. M. Cohen, W. A. Graaf, L. Rónyai

“…This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System), within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. …”
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Two-dimensional unsteady waves in an electromagnetoelastic sphere by V.A. Vestyak, D.V. Tarlakovskii

“…For the mechanical field, the explicit form of Green's bulk functions found using computer algebra and complex analysis methods has been used.…”
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Calculation of special functions arising in the problem of diffraction by a dielectric ball by Ksaverii Yu. Malyshev

“…These equations belong to the class of linear ordinary differential equations with Fuchsian singularities and, in the case of the Lneburg lens, are integrated in special functions of mathematical physics, namely, the Whittaker and Heun functions. The Maple computer algebra system has tools for working with Whittaker and Heun functions, but in some cases this system gives very large values for these functions, and their plots contain various kinds of artifacts. …”
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Determining the covariance matrix for a nonlinear implicit multivariate measurement equation uncertainty analysis by Ramnath Vishal

“…In this paper, a general purpose deterministic approach is developed using a computer algebra system (CAS) approach that avoids the need for Monte Carlo simulations in order to analytically construct the covariance matrix for arbitrary nonlinear implicit multivariate measurement models. …”
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Analysis of Longitudinal Forest Data on Individual-Tree and Whole-Stand Attributes Using a Stochastic Differential Equation Model by Petras Rupšys, Edmundas Petrauskas

“…All the results were implemented in the Maple computer algebra system.…”
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Exploiting the Abstract Calculus Pattern for the Integration of Ordinary Differential Equations for Dynamics Systems: An Object-Oriented Programming Approach in Modern Fortran by Stefano Zaghi, Cristiano Andolfi

“…The results presented prove manifold findings, in particular that our ACP approach enables ease of code development, clearness and robustness, maximization of code re-usability, and conciseness comparable with computer algebra system (CAS) programming (interpreted) but with the computational performance of compiled programming. …”
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Symbolic Computation Applied to Cauchy Type Singular Integrals by Ana C. Conceição, Jéssica C. Pires

“…In our work, we use the computer algebra system <i>Mathematica</i> to implement, for the first time on a computer, analytical algorithms developed by us and others within operator theory. …”
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