On the gradient of the coefficient of the characteristic polynomial

Authors: Ikenmeyer, Christian

Subject Terms: Computational Complexity, Commutative Algebra, Combinatorics, 68W30 Symbolic computation and algebraic computation

Access URL: http://arxiv.org/abs/2511.04954

A Finite Expression Method for Solving High-Dimensional Committor Problems: A finite expression method for solving high-dimensional committor problems

Authors: Zezheng Song, Maria K. Cameron, Haizhao Yang

Source: SIAM Journal on Scientific Computing. 47:C1-C21

Subject Terms: Computer Science - Symbolic Computation, FOS: Computer and information sciences, Computer Science - Machine Learning, Numerical methods for partial differential equations, boundary value problems, deep neural network, Computational learning theory, Numerical Analysis (math.NA), Symbolic Computation (cs.SC), Symbolic computation and algebraic computation, committor functions, rare events, Machine Learning (cs.LG), finite expression method, high dimensions, Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics, FOS: Mathematics, symbolic learning, PDEs with randomness, stochastic partial differential equations, Mathematics - Numerical Analysis, Brownian motion, Artificial neural networks and deep learning, PDEs in connection with statistical mechanics

File Description: application/xml

Access URL: http://arxiv.org/abs/2306.12268

A Two-Level Crank-Nicolson Difference Scheme and Its Richardson Extrapolation Methods for a Magneto-Thermo-Elasticity Model: A two-level Crank-Nicolson difference scheme and its Richardson extrapolation methods for a magneto-thermo-elasticity model

Authors: Deng, Dingwen, Zhang, Ruyu

Source: Advances in Applied Mathematics and Mechanics. 16:608-635

Subject Terms: Finite difference methods for boundary value problems involving PDEs, energy conservation, Iterative numerical methods for linear systems, Extrapolation to the limit, deferred corrections, convergence, Richardson extrapolation methods, priori estimation, Symbolic computation and algebraic computation, Finite difference methods applied to problems in solid mechanics, Thermal effects in solid mechanics, Electromagnetic effects in solid mechanics, Classical linear elasticity, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, finite difference method, solvability

File Description: application/xml

A library in CoCoA for implementing railway interlocking systems

Authors: Antonio Hernando, José Luis Galán–García, Yolanda Padilla–Domínguez, María Ángeles Galán–García, Gabriel Aguilera–Venegas

Source: RIUMA. Repositorio Institucional de la Universidad de Málaga
Universidad de Málaga

Subject Terms: Software, source code, etc. for problems pertaining to operations research and mathematical programming, Railway interlocking system, Symbolic computation and algebraic computation, railway interlocking system, decision making, Traffic problems in operations research, commutative algebra, Computer algebra, Transporte ferroviario - Modelos matemáticos, Commutative algebra, computer algebra, Decision making, Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Álgebra conmutativa

File Description: application/xml

Access URL: https://hdl.handle.net/10630/38153
https://zbmath.org/8031350
https://doi.org/10.1016/j.cam.2025.116594

Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables

Authors: Cano, Jose, Falkensteiner, Sebastian, Robertz, Daniel, Sendra, Rafael

Subject Terms: Mathematics - Algebraic Geometry, Computer Science - Symbolic Computation, 12H05 Differential algebra, 68W30 Symbolic computation and algebraic computation, 34A25 Analytical theory of ordinary differential equations

Access URL: http://arxiv.org/abs/2110.05558

Symbolic Treatment of Trigonometric Parametrizations: The General Unirational Case and Applications: Symbolic treatment of trigonometric parametrizations: the general unirational case and applications

Authors: Alberto Lastra, Juan Rafael Sendra, Juana Sendra

Source: Communications in Mathematics and Statistics. 13:481-505

Subject Terms: trigonometric parametrization, applications, Computational aspects of higher-dimensional varieties, implicitization algorithm, 0202 electrical engineering, electronic engineering, information engineering, 02 engineering and technology, 0101 mathematics, Symbolic computation and algebraic computation, hyperbolic parametrization, unirational algebraic variety, 01 natural sciences, symbolic computation

File Description: application/xml

Report on an extended three-coupled Korteweg-de Vries system

Authors: Gao, Xin-Yi, Guo, Yong-Jiang, Shan, Wen-Rui, Zhou, Tian-Yu

Source: Ricerche di Matematica. 74:575-584

Subject Terms: Computing methodologies and applications, extended three-coupled Korteweg-de Vries system, KdV equations (Korteweg-de Vries equations), \(N\)-soliton solutions, Fluid mechanics, Hirota method, Symbolic computation and algebraic computation, bilinear forms, symbolic computation

File Description: application/xml

Access URL: https://zbmath.org/8023262
https://doi.org/10.1007/s11587-023-00769-x

Higher Order Geometric Algebras and Their Implementations Using Bott Periodicity: Higher order geometric algebras and their implementations using Bott periodicity

Authors: Marek Stodola, Jaroslav Hrdina

Source: Advances in Applied Clifford Algebras. 34

Subject Terms: GAC, Witt pairs, PGA, Symbolic computation and algebraic computation, geometric algebra, 01 natural sciences, CGA, Clifford algebras, spinors, Geometric algebra, conics, 0103 physical sciences, Conics, 0101 mathematics, Python

File Description: application/xml; text; application/pdf

Access URL: http://hdl.handle.net/11012/250095

For the Shallow Water Waves: Bilinear-Form and Similarity-Reduction Studies on a Boussinesq-Burgers System: For the shallow water waves: bilinear-form and similarity-reduction studies on a Boussinesq-Burgers system

Authors: Gao, Xiao-Tian, Tian, Bo, Zhou, Tian-Yu, Shen, Yuan, Feng, Chun-Hui

Source: International Journal of Theoretical Physics. 63

Subject Terms: Water waves, gravity waves, dispersion and scattering, nonlinear interaction, Boussinesq-Burgers system, Soliton solutions, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), shallow water waves, similarity reductions, bilinear forms through the Hirota method, PDEs in connection with fluid mechanics, Symbolic computation and algebraic computation, Methods of ordinary differential equations applied to PDEs

File Description: application/xml

Access URL: https://zbmath.org/7898343
https://doi.org/10.1007/s10773-024-05715-7

A note on minimal resolutions of vector–spread Borel ideals: A note on minimal resolutions of vector-spread Borel ideals

Authors: Crupi M., Ficarra A.

Source: Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, Vol 31, Iss 2, Pp 71-84 (2023)

Subject Terms: monomial ideals, vector–spread borel ideals, Cohen-Macaulay ideals, extremal betti numbers, Combinatorial aspects of matroids and geometric lattices, Symbolic computation and algebraic computation, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Syzygies, resolutions, complexes and commutative rings, extremal Betti numbers, 01 natural sciences, Polynomials over commutative rings, QA1-939, FOS: Mathematics, cohen–macaulay ideals, vector-spread Borel ideals, primary 05b35, 05e40, 13b25, 13d02, 68w30, Combinatorial aspects of commutative algebra, 0101 mathematics, Mathematics

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2208.02181
https://zbmath.org/8036481
https://doi.org/10.2478/auom-2023-0020
https://doaj.org/article/c79f9b40de7d47c3a5129061a69332cb
https://hdl.handle.net/11570/3257246
https://doi.org/10.2478/auom-2023-0020

Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables

Authors: Cano, José, Falkensteiner, Sebastian, Robertz, Daniel, Sendra Pons, Juan Rafael

Contributors: Universidad de Alcalá. Departamento de Física y Matemáticas: Unidad docente Matemáticas

Source: e_Buah Biblioteca Digital Universidad de Alcalá
instname
Journal of symbolic computation 114, 1-17 (2023). doi:10.1016/j.jsc.2022.04.012

Subject Terms: Computer Science - Symbolic Computation, FOS: Computer and information sciences, Thomas decomposition, Matemáticas, Artin approximation, 0102 computer and information sciences, Symbolic Computation (cs.SC), 12H05 Differential algebra, 68W30 Symbolic computation and algebraic computation, 34A25 Analytical theory of ordinary differential equations, 01 natural sciences, Algebraic solution, Convergent solution, Mathematics - Algebraic Geometry, FOS: Mathematics, 0101 mathematics, Algebraic autonomous ordinary differential equation, Puiseux series solution, Algebraic Geometry (math.AG), Mathematics

File Description: application/pdf

Access URL: http://arxiv.org/abs/2110.05558
http://hdl.handle.net/10017/51628
https://publications.rwth-aachen.de/record/848250

Extended abstract for: solving rupert's problem algorithmically

Authors: Steininger, Jakob, Yurkevich, Sergey

Contributors: Yurkevich, Sergey

Source: ACM Communications in Computer Algebra. 56:32-35

Subject Terms: Three-dimensional polytopes, [MATH] Mathematics [math], 0102 computer and information sciences, Rupert property, 0101 mathematics, Symbolic computation and algebraic computation, 01 natural sciences

File Description: application/xml; application/pdf

Access URL: https://zbmath.org/7721512
https://doi.org/10.1145/3572867.3572870
https://inria.hal.science/hal-03874324v1/document
https://inria.hal.science/hal-03874324v1
https://doi.org/10.1145/3572867.3572870

Symbolic computation for the qualitative theory of differential equations

Authors: Huang, Bo, Niu, Wei, Wang, Dongming

Source: Acta Mathematica Scientia. 42:2478-2504

Subject Terms: center-focus, Bifurcation theory for ordinary differential equations, limit cycles, 0103 physical sciences, biological systems, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, qualitative analysis, Stability of solutions to ordinary differential equations, 0101 mathematics, Symbolic computation and algebraic computation, 01 natural sciences, symbolic computation

File Description: application/xml

A novel Lax–Wendroff type procedure of two-derivative time-stepping schemes for Euler and Navier–Stokes equations: A novel Lax-Wendroff type procedure of two-derivative time-stepping schemes for Euler and Navier-Stokes equations

Authors: Xueyu Qin, Xin Zhang, Jian Yu, Chao Yan

Source: Communications in Nonlinear Science and Numerical Simulation. 140:108436

Subject Terms: Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Finite difference methods for boundary value problems involving PDEs, two-derivative Runge-Kutta schemes, strong stability preserving, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, multistep temporal schemes, Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs, Navier-Stokes equations, Symbolic computation and algebraic computation, Euler equations, Lax-Wendroff procedure, Finite difference methods applied to problems in fluid mechanics

File Description: application/xml

Access URL: https://zbmath.org/8010071
https://doi.org/10.1016/j.cnsns.2024.108436

On the commutator in Leibniz algebras

Authors: Ismailov, N. A., Sartayev, B. K., Dzhumadil'daev, A. S.

Source: International Journal of Algebra and Computation. 32:785-805

Subject Terms: polynomial identities, Nonassociative algebras satisfying other identities, anti-commutator, Rings with involution, Lie, Jordan and other nonassociative structures, commutator, 0101 mathematics, Symbolic computation and algebraic computation, computer algebra, Free nonassociative algebras, 01 natural sciences, Leibniz algebras

File Description: application/xml

Access URL: https://zbmath.org/7538388
https://doi.org/10.1142/s0218196722500333
http://acikerisim.sdu.edu.tr/xmlui/handle/123456789/98148

On the Oceanic/Laky Shallow-Water Dynamics through a Boussinesq-Burgers System: On the oceanic/laky shallow-water dynamics through a Boussinesq-Burgers system

Authors: Gao, Xin-Yi, Guo, Yong-Jiang, Shan, Wen-Rui

Source: Qualitative Theory of Dynamical Systems. 23

Subject Terms: Hydrology, hydrography, oceanography, hetero-Bäcklund transformation, similarity reduction, Water waves, gravity waves, dispersion and scattering, nonlinear interaction, shallow-water waves, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), PDEs in connection with fluid mechanics, Symbolic computation and algebraic computation, PDEs in connection with geophysics, Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems, Boussinesq-Burgers system, computerized symbolic computation, Soliton solutions, lakes, ocean beaches

File Description: application/xml

Access URL: https://zbmath.org/7790240
https://doi.org/10.1007/s12346-023-00905-w

Bilinear Form, Bilinear Bäcklund Transformations, Breather and Periodic-Wave Solutions for a (2+1)-Dimensional Shallow Water Equation with the Time-Dependent Coefficients: Bilinear form, bilinear Bäcklund transformations, breather and periodic-wave solutions for a \((2+1)\)-dimensional shallow water equation with the time-dependent coefficients

Authors: Feng, Chun-Hui, Tian, Bo, Yang, Dan-Yu, Gao, Xiao-Tian

Source: Qualitative Theory of Dynamical Systems. 22

Subject Terms: breather and periodic-wave solutions, Hydrology, hydrography, oceanography, Water waves, gravity waves, dispersion and scattering, nonlinear interaction, Geophysical flows, Asymptotic behavior of solutions to PDEs, Hirota method, PDEs in connection with fluid mechanics, Symbolic computation and algebraic computation, PDEs in connection with geophysics, symbolic computation, Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems, \((2+1)\)-dimensional shallow water equation with time-dependent coefficients, Soliton solutions, bilinear Bäcklund transformations, shallow water waves, bilinear form, Periodic solutions to PDEs

File Description: application/xml

Access URL: https://zbmath.org/7736300
https://doi.org/10.1007/s12346-023-00813-z

Efficient Relative Pose Estimation for Cameras and Generalized Cameras in Case of Known Relative Rotation Angle: Efficient relative pose estimation for cameras and generalized cameras in case of known relative rotation angle

Authors: Evgeniy Martyushev, Bo Li

Source: Journal of Mathematical Imaging and Vision. 62:1076-1086

Subject Terms: FOS: Computer and information sciences, 0209 industrial biotechnology, generalized cameras, Computer Vision and Pattern Recognition (cs.CV), relative pose estimation, Computer Science - Computer Vision and Pattern Recognition, 02 engineering and technology, Gröbner bases, other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, relative rotation angle, Machine vision and scene understanding, Computer graphics, computational geometry (digital and algorithmic aspects), epipolar constraints, 0202 electrical engineering, electronic engineering, information engineering, multi-view geometry, Gröbner basis, Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)

File Description: application/xml

Access URL: http://arxiv.org/pdf/1901.11357
http://arxiv.org/abs/1901.11357
https://zbmath.org/7289202
https://doi.org/10.1007/s10851-020-00958-5
https://link.springer.com/article/10.1007/s10851-020-00958-5
https://dblp.uni-trier.de/db/journals/corr/corr1901.html#abs-1901-11357
http://dblp.uni-trier.de/db/journals/corr/corr1901.html#abs-1901-11357

(Pseudo)digraphs and Leibniz algebra isomorphisms

Authors: Manuel Ceballos, Juan Núñez, Ángel F. Tenorio

Source: Brújula
Universidad Loyola Andalucía

Subject Terms: algorithm, Isomorphism class, Directed graphs (digraphs), tournaments, isomorphic digraphs, Symbolic computation and algebraic computation, 01 natural sciences, Algorithm, Combinatorial structure, Leibniz algebra, Computational methods for problems pertaining to nonassociative rings and algebras, (Pseudo)digraph, isomorphic Leibniz algebras, 0101 mathematics, Leibniz algebras, (pseudo)digraph

File Description: application/xml

Access URL: http://hdl.handle.net/20.500.12412/937
http://ui.adsabs.harvard.edu/abs/2018MMAS...41.7481C/abstract

A General Solver Based on Sparse Resultants

Authors: Emiris, Ioannis Z.

Subject Terms: Computer Science - Symbolic Computation, Computer Science - Numerical Analysis, Mathematics - Commutative Algebra, 13P15 Solving polynomial systems, resultants (Primary), 68W30 Symbolic computation and algebraic computation (secondary), I.1, F.2.1, G.4

Access URL: http://arxiv.org/abs/1201.5810