Computer Algebra in Scientific Computing

Tropical Geometry of Biological Systems (Invited Talk).- Algebraic and Geometric Analysis of Singularities of Implicit Differential Equations (Invited Talk).- On the Complexity of Computing Integral Bases of Function Fields.- Truncated and Infinite Power Series in the Role of Coefficients of Linear Ordinary Differential Equations.- On Periodic Approximate Solutions of the Three-Body Problem Found by Conservative Difference Schemes.- Univariate Polynomials With Long Unbalanced Coefficients as Bivariate Balanced Ones: a Toom-Cook Multiplication Approach.- Power Series Arithmetic with the BPAS Library.- Enhancements to Lazard's Method for Cylindrical Algebraic Decomposition.- The Complexity and Parallel Implementation of two Sparse Multivariate Hensel Lifting Algorithms for Polynomial Factorization.- The GPGCD Algorithm with the Bézout Matrix.- On Parametric Linear System Solving.- Symbolic-Numeric Algorithm for Computing Orthonormal Basis of O(5) SU(1,1) Group.- Symbolic-Numeric Study of Geometric Properties of Adiabatic Waveguide Modes.- Intrinsic Complexity for Constructing Zero-Dimensional Gröbner Bases.- On the Study of the Motion of a System of Two Connected Rigid Bodies by Computer Algebra Methods.- Complexity Estimates for Fourier-Motzkin Elimination.- Progress Report on the Scala Algebra System.- Routh - Hurwitz Stability of a Polynomial Matrix Family. Real Perturbations.- Hermite Rational Function Interpolation with Error Correction.- Good Pivots for Small Sparse Matrices.- Nullstellensatz-Proofs for Multiplier Verification.- "Mathemachines" via LEGO, GeoGebra and CindyJS.- Balanced NUCOMP.- Contact Linearizability of Scalar Ordinary Differential Equations of Arbitrary Order.- Faster Numerical Univariate Polynomial Root-Finding by Means of Subdivision Iterations.- Computing Parametric Standard bases for Semi-weighted Homogeneous Isolated Hypersurface Singularities.- Acceleration of Subdivision Root-Finding for Sparse Polynomials.- Analytical Computationsin Studying Translational-Rotational Motion of a Non-Stationary Triaxial Body in the Central Gravitational Field.- A Linear Algebra Approach for Detecting Binomiality of Steady State Ideals of Reversible Chemical Reaction Networks.- First-Order Tests for Toricity.- Looking for Compatible Routes in the Railway Interlocking System of an Overtaking Station Using a Computer Algebra System.- Computing Logarithmic Vector Fields along an ICIS Germ via Matlis Duality.- Robust Numerical Tracking of One Path of a Polynomial Homotopy on Parallel Shared Memory Computers.- Symbolic-Numeric Computation of the Bernstein Coefficients of a Polynomial from Those of One of Its Partial Derivatives and of the Product of Two Polynomials.- Comparative Study of the Accuracy of Higher-order Difference Schemes for Molecular Dynamics Problems Using the Computer Algebra Means.- Characterizing Triviality of the Exponent Lattice of a Polynomial through Galois and Galois-Like Groups.