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Computer Algebra in Scientific Computing : 26th International Workshop, CASC 2024, Rennes, France, September 2–6, 2024, Proceedings / / edited by François Boulier, Chenqi Mou, Timur M. Sadykov, Evgenii V. Vorozhtsov
| Computer Algebra in Scientific Computing : 26th International Workshop, CASC 2024, Rennes, France, September 2–6, 2024, Proceedings / / edited by François Boulier, Chenqi Mou, Timur M. Sadykov, Evgenii V. Vorozhtsov |
| Autore | Boulier François |
| Edizione | [1st ed. 2024.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024 |
| Descrizione fisica | 1 online resource (407 pages) |
| Disciplina | 005.13 |
| Altri autori (Persone) |
MouChenqi
SadykovTimur M VorozhtsovEvgenii V |
| Collana | Lecture Notes in Computer Science |
| Soggetto topico |
Algorithms
Artificial intelligence Computer science - Mathematics Computer networks Design and Analysis of Algorithms Artificial Intelligence Mathematics of Computing Computer Communication Networks |
| ISBN |
9783031690709
9783031690693 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Organization -- Polynomial System Solving through Gröbner Bases in Scientific Computing (Invited Talk) -- Contents -- Recent Developments in Real Quantifier Elimination and Cylindrical Algebraic Decomposition (Extended Abstract of Invited Talk)*-12pt -- 1 Real Quantifier Elimination -- 2 Cylindrical Algebraic Decomposition -- 3 The Doubly Exponential Wall -- 4 CAD and Satisfiability Checking -- 4.1 SAT and SMT -- 4.2 CAD as Theory Solver -- 4.3 New CAD-Based Algorithms -- 4.4 SC2 -- 5 CAD and Machine Learning -- 5.1 CAD Variable Ordering Choice -- 5.2 Future Progress from Explainable AI? -- References -- Advances in Elimination Theory for Algebraic Differential and Difference Equations -- 1 Introduction -- 2 Basic Notions in Differential Algebra -- 3 Differential Chow Forms and Differential Chow Varieties -- 3.1 Differential Chow Forms -- 3.2 Differential Chow Varieties -- 3.3 Algorithms and Further Work -- 4 Differential Resultants, Sparse Differential Resultants and Sparse Difference Resultants -- 4.1 Differential Resultants -- 4.2 Sparse Differential Resultants -- 4.3 Sparse Difference Resultants -- 5 Effective Nullstellensatz and Elimination for Algebraic Differential-Difference Equations -- References -- A Modular Algorithm to Compute the Resultant of Multivariate Polynomials over Algebraic Number Fields Presented with Multiple Extensions -- 1 Introduction -- 1.1 Computing over Q(1,…,n) -- 1.2 Organization of the Paper -- 2 Preliminaries -- 2.1 Mapping Q(1,…,n) to a Single Extension Q() -- 2.2 Resultants -- 2.3 Computing Resultants of Univariate Polynomials -- 3 The Modular Resultant Algorithm -- 3.1 Algorithm PRES -- 3.2 Algorithm MRES -- 4 Implementation and Benchmarks -- 5 Complexity -- 6 Failure Probability -- 6.1 Lc-Bad Primes and Evaluation Points -- 6.2 Det-Bad Primes -- 7 Conclusion -- References.
The Liouville Generator for Producing Integrable Expressions -- 1 Introduction -- 2 Existing Data Generation Methods -- 2.1 Deep Learning for Symbolic Mathematics -- 2.2 Generating Elementary Integrable Expressions -- 2.3 The Substitution Rule -- 3 Background Material for the New Method -- 3.1 Liouville's Theorem -- 3.2 Parallel Risch Algorithm -- 4 The LIOUVILLE Data Generation Method -- 4.1 The Main Idea -- 4.2 Design Choices -- 5 Discussion of the New Data Generation Method -- 5.1 Example -- 5.2 Benefits over FWD and BWD -- 5.3 Benefits over RISCH -- 5.4 The Effect of Normalisation -- 6 Conclusion and Future Work -- References -- Symbolic-Numeric Solving Boundary Value Problems: Collective Models of Atomic Nuclei -- 1 Introduction -- 2 Formulation of BVP and GTM and FEM Schemes -- 3 BVP for Five-Dimensional Quadrupole Hamiltonian -- 4 5D Harmonic Oscillator Model in Affine Coordinates -- 5 Benchmark Calculations of 154Gd in the RMF Model -- 6 Conclusions -- References -- On Formal Power Series Solutions of Regular Differential Chains -- 1 Introduction -- 2 Mathematical Background -- 3 The Prolongation Bounds -- 3.1 An Approximation Lemma -- 3.2 Examples -- 4 Basic Notions on Regular Chains -- 5 The Case of Series Depending on Parameters -- 6 Computation of the Nonnegative Integer Roots -- 7 Implementation -- References -- A Dataset for Suggesting Variable Orderings for Cylindrical Algebraic Decompositions -- 1 Introduction -- 2 Generation of the Dataset -- 2.1 The CAD Implementation to Use -- 2.2 The Initial Setting for Generating the Examples -- 2.3 Statistical Information of the Generated Datasets -- 2.4 Organization of the Datasets -- 3 Performance of the Heuristic Methods on the Datasets -- 4 Training and Testing on the Datasets -- 4.1 Feature Engineering -- 4.2 Training of the Models -- 4.3 Testing of the Models. 5 Conclusion and Future Work -- References -- Stability Analysis of a Differential Model for Quasi-Periodic Plasma Perturbations -- 1 Introduction -- 2 KCC Theory and Jacobi Stability of Dynamical Systems -- 3 Linear Stability Analysis of Model (1) -- 4 Jacobi Stability Analysis of Model (1) -- 4.1 The Nonlinear and Berwald Connections, and the KCC Invariants -- 4.2 Jacobi Stability of the Fixed Points -- 5 Dynamics of Deviation Vector in Model (1) -- 5.1 Dynamics of the Deviation Vector Near E0 -- 5.2 Dynamics of the Deviation Vector Near E+ and E- -- 5.3 The Curvature of the Deviation Vector -- 6 Conclusions -- References -- Counting the Integer Points of Parametric Polytopes: A Maple Implementation -- 1 Introduction -- 2 Generating Functions of Rational Cones and Polytopes -- 3 Quasi-polynomials -- 4 Generic Case Discussion -- 5 Counting the Integer Points -- 5.1 Counting the Integer Points of a Non-parametric Polytope -- 5.2 Counting the Integer Points of a Parametric Polytope -- 6 Experimentation -- References -- Algebraic Representations for Faster Predictions in Convolutional Neural Networks -- 1 Introduction -- 1.1 Machine Learning and Algebraic Geometry -- 1.2 Contributions and Structure -- 2 CNN Setup -- 3 Skip Connections in Linear Networks -- 3.1 Transformation Matrices for Resampling and Padding -- 3.2 Skip Connections -- 4 Removing Skip Connections with a Homotopy -- 5 Computational Experiments -- 5.1 Equipment, Software, and Data -- 5.2 Pre-computing CNNs -- 5.3 Practical Experiment for Removing Skip Connections -- 6 Future Directions -- 7 Conclusion -- References -- Computing a Basis of the Set of Isogenies Between Two Supersingular Elliptic Curves -- 1 Introduction -- 2 Mathematical Background -- 2.1 Elliptic Curves over Finite Fields -- 2.2 Properties of Supersingular Elliptic Curves. 3 Generators of Hom(E, E') for Supersingular Elliptic Curves E, E' -- 4 Computing a Basis of Hom(E, E') for Supersingular Elliptic Curves E, E' -- 4.1 Details and Implementation of Each Step -- 4.2 Numerical Examples -- 5 Conclusion -- References -- On the Radical of a Polynomial Ideal with Parameters -- 1 Introduction -- 2 Comprehensive Gröbner Systems -- 2.1 Preliminaries -- 2.2 Comprehensive Gröbner Systems -- 3 Tools for Parametric Ideals -- 3.1 Dimensions of a Parametric Ideal -- 3.2 Squarefree Part of a Univariate Polynomial with Parameters -- 3.3 Intersection of Parametric Ideals -- 3.4 Least Common Multiples of Parametric Polynomials -- 3.5 Saturation for a Parametric Ideal -- 4 Parametric Radical System -- 5 Zero Dimensional Case -- 6 Key Result -- 7 Non-zero Dimensional Case -- References -- Contribution to Integral Elimination -- 1 Introduction -- 2 Background -- 2.1 Integral Algebra -- 2.2 Ordering the Integral Monomials -- 2.3 Basic Rewriting Rules -- 3 Extended Rewriting Rules and Reduction -- 3.1 Reduced-Product Rule -- 3.2 Reduced-Power Rule -- 3.3 Reduction -- 4 Critical Pairs -- 5 Exponentials -- 5.1 Algorithms find_A_A0_G_Fand update_exp -- 6 Integral Elimination Prototype -- 7 Examples -- 7.1 Intra-Host Model of Malaria (taken from ch13malaria) -- 7.2 SIWR Model Cholera (taken from ch13dong2022differential) -- References -- Sparse Tensors and Subdivision Methods for Finding the Zero Set of Polynomial Equations -- 1 Introduction -- 1.1 Amortized Evaluation on a Grid of Boxes -- 1.2 Amortized Evaluation on a Sparse Subset of a Grid -- 1.3 Notations -- 1.4 Main Result -- 2 Evaluating Polynomials with Compressed Sparse Fibers -- 2.1 Sparse Tensor Data Structure -- 2.2 Evaluation Algorithm -- 3 Applications -- 3.1 The Fast Fourier Transform Revisited -- 3.2 Subdivision Algorithm -- 4 Experiments -- 4.1 Random Polynomials. 4.2 Polynomials Coming from Applications -- References -- Merging Adjacent Cells During Single Cell Construction -- 1 Introduction -- 2 Preliminaries -- 2.1 Cylindrical Algebraic Decomposition, McCallum's Projection, and Levelwise Single Cell Construction -- 3 Detecting ``Irrelevant'' Roots -- 4 Local Delineability and Modified Projection -- 5 Weak Orderings and (Half-)closed Intervals -- 6 Experimental Results -- 7 Conclusion -- References -- Computing Clipped Products -- 1 Introduction -- 2 Preliminaries -- 3 Straightforward Methods -- 4 Clipped Polynomial Products -- 5 Clipped Integer Multiplication -- 6 Combining Methods -- 7 Further Thoughts and Conclusions -- References -- Fast Integral Bases Computation -- 1 Introduction -- 2 OM Algorithm and Local Integral Basis -- 2.1 Local Integral Basis and OM Factorisation -- 2.2 Precision of the OM Algorithm -- 3 Triangular p-Integral Bases -- 3.1 Reduced Triangular p-integral Bases -- 3.2 The MaxMin Algorithm -- 3.3 Global Integral Bases -- 4 Bases of Fractional Ideals -- 4.1 Fractional Ideals -- 4.2 p-Bases of Fractional Ideals -- 4.3 Improvements via S-basis -- 4.4 Global Triangular Bases of Fractional Ideals -- 5 Complexity and Proofs of the Main Results -- 6 An Illustrative Example -- References -- On Rational Recursion for Holonomic Sequences -- 1 Introduction -- 2 Problem Statement in Difference Algebra -- 3 Lower-Degree Holonomic Difference Polynomials -- 4 Proof and Algorithms -- 5 Concluding Remarks -- References -- GPU Accelerated Newton for Taylor Series Solutions of Polynomial Homotopies in Multiple Double Precision -- 1 Introduction -- 1.1 Problem Statement -- 1.2 Multiprecision Arithmetic -- 1.3 Numerical Condition of Taylor Series -- 2 Linearized Series and Newton's Method -- 3 Columns of Monomials -- 4 Staggered Computations -- 5 Accelerating Newton's Method. 5.1 Arithmetic Intensity of Convolutions. |
| Record Nr. | UNINA-9910882888103321 |
Boulier François
|
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| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computer Algebra in Scientific Computing [[electronic resource] ] : 25th International Workshop, CASC 2023, Havana, Cuba, August 28 – September 1, 2023, Proceedings / / edited by François Boulier, Matthew England, Ilias Kotsireas, Timur M. Sadykov, Evgenii V. Vorozhtsov
| Computer Algebra in Scientific Computing [[electronic resource] ] : 25th International Workshop, CASC 2023, Havana, Cuba, August 28 – September 1, 2023, Proceedings / / edited by François Boulier, Matthew England, Ilias Kotsireas, Timur M. Sadykov, Evgenii V. Vorozhtsov |
| Autore | Boulier François |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (441 pages) |
| Disciplina | 005.13 |
| Altri autori (Persone) |
EnglandMatthew
KotsireasIlias SadykovTimur M VorozhtsovEvgenii V |
| Collana | Lecture Notes in Computer Science |
| Soggetto topico |
Algorithms
Artificial intelligence Computer science - Mathematics Computer networks Design and Analysis of Algorithms Artificial Intelligence Mathematics of Computing Computer Communication Networks |
| ISBN | 3-031-41724-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Computing GCDs of Multivariate Polynomials over Algebraic Number Fields Presented with Multiple Extensions -- Generating Elementary Integrable Expressions -- How to Automatise Proofs of Operator Statements: Moore–Penrose Inverse a Case Study -- A Modular Algorithm for Computing the Intersection of a One-Dimensional Quasi-Component and a Hypersurface -- Certified Study of Internal Solitary Waves -- Root-Squaring for Root-Finding -- Symbolic-Numerical Algorithm for Solving the Problem of Heavy Ion Collisions in an Optical Model with a Complex Potential -- On the Complexity of Linear Algebra Operations over Algebraic Extension Fields -- Range Functions of Any Convergence Order and their Amortized Complexity Analysis -- Stability and Zero-Hopf Bifurcation Analysis of the Lorenz–Stenflo System Using Symbolic Methods -- Non-Principal Branches of Lambert W. A Tale of 2 circles -- On the Qualitative Analysis of the Equations of Motion of a Nonholonomic Mechanical System -- Solving Parametric Linear Systems Using Sparse Rational Function Interpolation -- On the Distance to the Nearest Defective Matrix -- Effective Algorithm for Computing Noetherian Operators of Positive Dimensional Ideals -- On the Structure and Generators of Differential Invariant Algebras -- An Algorithm for the Intersection Problem of Planar Parametric Curves -- A Symbolic-numeric Method for Solving the Poisson Equation in Polar Coordinates -- Two Variants of B´ezout Subresultants for Several Univariate Polynomials -- Efficient Quotients of Non-Commutative Polynomials -- Inverse Kinematics and Path Planning of Manipulator Using Real Quantifier Elimination Based on Comprehensive Gröbner Systems. |
| Record Nr. | UNISA-996546850803316 |
|
Boulier François
|
||
| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Computer Algebra in Scientific Computing : 25th International Workshop, CASC 2023, Havana, Cuba, August 28 – September 1, 2023, Proceedings / / edited by François Boulier, Matthew England, Ilias Kotsireas, Timur M. Sadykov, Evgenii V. Vorozhtsov
| Computer Algebra in Scientific Computing : 25th International Workshop, CASC 2023, Havana, Cuba, August 28 – September 1, 2023, Proceedings / / edited by François Boulier, Matthew England, Ilias Kotsireas, Timur M. Sadykov, Evgenii V. Vorozhtsov |
| Autore | Boulier François |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (441 pages) |
| Disciplina | 005.13 |
| Altri autori (Persone) |
EnglandMatthew
KotsireasIlias SadykovTimur M VorozhtsovEvgenii V |
| Collana | Lecture Notes in Computer Science |
| Soggetto topico |
Algorithms
Artificial intelligence Computer science - Mathematics Computer networks Design and Analysis of Algorithms Artificial Intelligence Mathematics of Computing Computer Communication Networks |
| ISBN | 3-031-41724-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Computing GCDs of Multivariate Polynomials over Algebraic Number Fields Presented with Multiple Extensions -- Generating Elementary Integrable Expressions -- How to Automatise Proofs of Operator Statements: Moore–Penrose Inverse a Case Study -- A Modular Algorithm for Computing the Intersection of a One-Dimensional Quasi-Component and a Hypersurface -- Certified Study of Internal Solitary Waves -- Root-Squaring for Root-Finding -- Symbolic-Numerical Algorithm for Solving the Problem of Heavy Ion Collisions in an Optical Model with a Complex Potential -- On the Complexity of Linear Algebra Operations over Algebraic Extension Fields -- Range Functions of Any Convergence Order and their Amortized Complexity Analysis -- Stability and Zero-Hopf Bifurcation Analysis of the Lorenz–Stenflo System Using Symbolic Methods -- Non-Principal Branches of Lambert W. A Tale of 2 circles -- On the Qualitative Analysis of the Equations of Motion of a Nonholonomic Mechanical System -- Solving Parametric Linear Systems Using Sparse Rational Function Interpolation -- On the Distance to the Nearest Defective Matrix -- Effective Algorithm for Computing Noetherian Operators of Positive Dimensional Ideals -- On the Structure and Generators of Differential Invariant Algebras -- An Algorithm for the Intersection Problem of Planar Parametric Curves -- A Symbolic-numeric Method for Solving the Poisson Equation in Polar Coordinates -- Two Variants of B´ezout Subresultants for Several Univariate Polynomials -- Efficient Quotients of Non-Commutative Polynomials -- Inverse Kinematics and Path Planning of Manipulator Using Real Quantifier Elimination Based on Comprehensive Gröbner Systems. |
| Record Nr. | UNINA-9910742490403321 |
|
Boulier François
|
||
| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||