Titlebook: Computer Algebra in Scientific Computing; 24th International W Fran?ois Boulier,Matthew England,Evgenii V. Vorozh Conference proceedings 20

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,Computer Science for?Continuous Data, envisions the future of Computer Science for continuous data: natively, beyond brute-force discretization, based on and guided by and extending classical discrete Computer Science, as bridge between Pure and Applied Mathematics.

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,On Boundary Conditions Parametrized by?Analytic Functions,in this context, we extend these models to analytic boundary conditions. Additionally, we describe the necessary algorithms for Gr?bner and Janet bases of Weyl algebras with certain analytic coefficients. Using these algorithms, we provide examples of divergence-free flow in domains bounded by analytic functions and adapted to observations.

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,New Heuristic to?Choose a?Cylindrical Algebraic Decomposition Variable Ordering Motivated by?Comple. The best of these new heuristics chooses orderings that lead to timings on average 17% slower than the virtual-best: an improvement compared to the prior state-of-the-art which achieved timings 25% slower.

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,Locating the?Closest Singularity in?a?Polynomial Homotopy,series expansions of the solution paths defined by the homotopy. For numerical stability, we recondition the homotopy. To compute the coefficients of the series we propose the quaternion Fourier transform. We locate the closest singularity computing at a regular solution, avoiding numerical difficulties near a singularity.

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