Ideals, Varieties, and Algorithms

From MaRDI portal
Publication:5245268

DOI10.1007/978-3-319-16721-3zbMath1335.13001OpenAlexW4240837394MaRDI QIDQ5245268

David A. Cox, Donal O'Shea, John B. Little

Publication date: 7 April 2015

Published in: Undergraduate Texts in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-16721-3



Related Items

A study of a family of monomial ideals, Towards van der Waerden’s conjecture, Classification of 7-dimensional solvable Lie algebras having 5-dimensional nilradicals, A polynomial ideal associated to any $t$-$(v,k,\lambda)$ design, Ideal Membership Problem over 3-Element CSPs with Dual Discriminator Polymorphism, Algorithms for fundamental invariants and equivariants of finite groups, Algebraic compressed sensing, Automorphisms of affine Veronese surfaces, Computing level lines of a polynomial on the plane, Beam functions for \(N\)-jettiness at \(\mathrm{N^3LO}\) in perturbative QCD, \( \mathcal{N} = 4\) SYM, (super)-polynomial rings and emergent quantum mechanical symmetries, Polar germs, Jacobian ideal and analytic classification of irreducible plane curve singularities, Distinguishing secant from cactus varieties, Sarkisov links for index 1 Fano 3‐folds in codimension 4, The 3-wave resonant interaction model: spectra and instabilities of plane waves, A solution to the global identification problem in DSGE models, Fast Algorithms for Discrete Differential Equations, A Direttissimo Algorithm for Equidimensional Decomposition, Algorithm for Connectivity Queries on Real Algebraic Curves, Universal Analytic Gröbner Bases and Tropical Geometry, Revisiting algebraic attacks on MinRank and on the rank decoding problem, Boolean cumulants and subordination in free probability, Time-Reversibility and Ivariants of Some 3-dim Systems, An algorithm for solving over-determined multivariate quadratic systems over finite fields, Conormal spaces and Whitney stratifications, Refined F5 Algorithms for Ideals of Minors of Square Matrices, From Polynomial Invariants to Linear Loops, Symbol alphabets from the Landau singular locus, Varieties of Borel subalgebras for the Jacobson-Witt Lie algebras, Geometric vertex decomposition and liaison for toric ideals of graphs, Gröbner bases plugged into graphical skills to solve a set of multiple bifurcation equations in structural compound stability problems, An efficient method of finding new symplectic schemes for Hamiltonian mechanics problems with the aid of parametric Gröbner bases, An atlas for the pinhole camera, Conformally Einstein Lorentzian Lie groups: extensions of the Euclidean and Poincaré groups, Some extremal problems for polygons in the Euclidean plane, INEQUALITIES BETWEEN MIXED VOLUMES OF CONVEX BODIES: VOLUME BOUNDS FOR THE MINKOWSKI SUM, Some properties of affine \({\mathcal{C}}\)-semigroups, Families of polytopes with rational linear precision in higher dimensions, Sufficient conditions for the surjectivity of radical curve parametrizations, Adaptation of the closest tree method for a two state quartet to Jukes-Cantor tripod trees, A constructive picture of Noetherian conditions and well quasi-orders, Axioms for a theory of signature bases, MultivariateApart: generalized partial fractions, Efficient NIZKs for algebraic sets, Fixed points and steady solitons for the two-loop renormalization group flow, Noncommutative nullstellensätze and perfect games, Computing Circuit Polynomials in the Algebraic Rigidity Matroid, Methodologies of Symbolic Computation, Sum-of-squares certificates for Vizing's conjecture via determining Gröbner bases, What else is undecidable about loops?, On forced periodicity of perfect colorings, Identifiability of hidden Markov models for learning trajectories in cognitive diagnosis, Low-Rank Univariate Sum of Squares Has No Spurious Local Minima, Distance to the loss of structural properties for linear systems under parametric uncertainties, Minimal degree rational open up mappings and related questions, High dimensional Bernoulli distributions: algebraic representation and applications, Exact convergence rates of alternating projections for nontransversal intersections, Partition and analytic rank are equivalent over large fields, Entanglement-assisted quantum error-correcting codes from subfield subcodes of projective Reed-Solomon codes, Subfield subcodes of projective Reed-Muller codes, Results on the algebraic matroid of the determinantal variety, Zero testing and equation solving for sparse polynomials on rectangular domains, Generalized splines on graphs with two labels and polynomial splines on cycles, Gröbner geometry for regular nilpotent Hessenberg Schubert cells, Hadamard products and binomial ideals, On a relationship between the characteristic and matching polynomials of a uniform hypertree, Harmonic differential forms for pseudo-reflection groups II. Bi-degree bounds, Unnamed Item, Tropical Geometry, Gröbner Bases of Convex Neural Code Ideals (Research), Unnamed Item, The computation of factorization invariants for affine semigroups, Resolvability of Hamming Graphs, On the distribution of the Rudin-Shapiro function for finite fields, Exotic Bifurcations in Three Connected Populations with Allee Effect, A Factorization Theory for some Free Fields, Unnamed Item, The syzygy theorem for Bézout rings, The Geometry of Ambiguity in One-Dimensional Phase Retrieval, Moment Ideals of Local Dirac Mixtures, Algebraic Matroids in Action, Normality and short exact sequences of Hopf-Galois structures, Gröbner–Shirshov bases for commutative dialgebras, Khovanskii Bases, Higher Rank Valuations, and Tropical Geometry, A linear algebra method to decompose forms whose length is lower than the number of variables into weighted sum of squares, Differential algebraic dependence and Novikov dependence, Toda lattice hierarchy and soliton equations on square lattice, The case of a constant absolute invariant for the Liénard system, Evaluating and Differentiating a Polynomial Using a Pseudo-witness Set, On the complexity of quadratic programming with two quadratic constraints, Higher-distance commuting varieties, Funciones booleanas, bases de Grobner y cuasigrupos, Classification of four qubit states and their stabilisers under SLOCC operations, Four-Dimensional Homogeneous Generalizations of Einstein Metrics, Stickelberger and the Eigenvalue Theorem, AN EFFECTIVE ANALYTIC FORMULA FOR THE NUMBER OF DISTINCT IRREDUCIBLE FACTORS OF A POLYNOMIAL, Real forms of embeddings of maximal reductive subalgebras of the complex simple Lie algebras of rank up to 8, Solving p-adic polynomial systems via iterative eigenvector algorithms, Hausdorff moment problem and nonlinear time optimality, Elementary construction of residue currents associated to Cohen–Macaulay ideals, Smooth mixed projective curves and a conjecture, Filtering cohomology of ordinary and Lagrangian Grassmannians, The regularity conjecture for prime ideals in polynomial rings, Approximate super-resolution of positive measures in all dimensions, Qualification Conditions in Semialgebraic Programming, On compact packings of the plane with circles of three radii, Centralizers and normalizers of local analytic and formal vector fields, Gröbner bases of neural ideals, Dead‐beat regulation of mechanical juggling systems, Algorithms and programs for calculating the roots of polynomial of one or two variables, Local integrability and linearizability of a \((1:-1:-1)\) resonant quadratic system, A locally convergent continuous-time algorithm to find all the roots of a time-varying polynomial, On bipartite distinct distances in the plane, An insertion algorithm on multiset partitions with applications to diagram algebras, Universal Gröbner bases of toric ideals of combinatorial neural codes, On the distance of stabilizer quantum codes from \(J\)-affine variety codes, Relative generalized Hamming weights of affine Cartesian codes, When Is a Formula a Loop Invariant?, Learning algebraic decompositions using Prony structures, From standard monomial theory to semi-toric degenerations via Newton–Okounkov bodies, Boolean network analysis through the joint use of linear algebra and algebraic geometry, Symmetry in multivariate ideal interpolation, The center problem and time-reversibility with respect to a quadratic involution for a class of polynomial differential systems with order 2 or 3, Path planning in formation and collision avoidance for multi-agent systems, Standard bases for tensor products of exterior powers, In-depth comparison of the Berlekamp-Massey-Sakata and the Scalar-FGLM algorithms: the adaptive variants, Torus partition function of the six-vertex model from algebraic geometry, Lonely points in simplices, On \(f\)- and \(h\)-vectors of relative simplicial complexes, Nivat's conjecture and pattern complexity in algebraic subshifts, On the factorization of non-commutative polynomials (in free associative algebras), Gröbner bases of reaction networks with intermediate species, Feynman integrals in dimensional regularization and extensions of Calabi-Yau motives, Algebraic invariants and local stability of planar differential systems, Algebraic properties of HTC-identifiable graphs, Detecting truth, just on parts, Computation of the expected Euler characteristic for the largest eigenvalue of a real non-central Wishart matrix, Betti numbers of Koszul algebras defined by four quadrics, A new algorithm for computing staggered linear bases, Hodge dual operators and model algebras for rational representations of the general linear group, Unnamed Item, Unconditional reflexive polytopes, Combining realization space models of polytopes, Unnamed Item, On affine tropical F5 algorithms, Locating and Counting Equilibria of the Kuramoto Model with Rank-One Coupling, Uniform Yomdin-Gromov parametrizations and points of bounded height in valued fields, Ansätze for scattering amplitudes from \(p\)-adic numbers and algebraic geometry, Minimal presentations of shifted numerical monoids, Classification of nilpotent associative algebras of small dimension, Koszul Algebras and Computations, Recursive structures in involutive bases theory, Polynomial solutions of algebraic difference equations and homogeneous symmetric polynomials, Computing the resolution regularity of bi-homogeneous ideals, Boolean network representation of a continuous-time system and finite-horizon optimal control: application to the single-gene regulatory system for the lac operon, On some configurations of oppositely charged trapped vortices in the plane, Gröbner Bases in D-Modules: Application to Bernstein-Sato Polynomials, Lévy-driven causal CARMA random fields, Computing unit groups of curves, Solving multivariate polynomial systems and an invariant from commutative algebra, Conformally Einstein and Bach-flat four-dimensional homogeneous manifolds, Unnamed Item, Unnamed Item, A general version of the Nullstellensatz for arbitrary fields, On powers of Plücker coordinates and representability of arithmetic matroids, A symbolic algorithm to compute immersions of polynomial systems into linear ones up to an output injection, Geronimus transformations of bivariate linear functionals, Cryptanalysis of elliptic curve hidden number problem from PKC 2017, Tropical varieties associated to ideal triangulations: The Whitehead link complement, The Many Lives of the Twisted Cubic, Solutions of the Yang–Baxter equation for (n + 1) (2n + 1)-vertex models using a differential approach, On pseudo-Frobenius elements of submonoids of \(\mathbb{N}^d\), Rational solutions of first-order algebraic ordinary difference equations, Size-degree trade-offs for sums-of-squares and positivstellensatz proofs, Algebraic geometric codes on minimal Hirzebruch surfaces, Analytic form of the planar two-loop five-parton scattering amplitudes in QCD, The slack realization space of a matroid, Algebraic characterization of \(\mathbb{C}\)-regular fractions under level permutations, Whitney's theorem, triangular sets, and probabilistic descent on manifolds, Nœther bases and their applications, Method of moments for 3D single particleab initiomodeling with non-uniform distribution of viewing angles, Typical and generic ranks in matrix completion, Level curve portraits of rational inner functions, Maximal directional operators along algebraic varieties, General remainder theorem and factor theorem for polynomials over non-commutative coefficient rings, On the uniform algebraic observability of multi-switching linear systems, Control analysis and design via randomised coordinate polynomial minimisation, Sums of squares and quadratic persistence on real projective varieties, Algorithmic problems for differential polynomial algebras, Polynomial-division-based algorithms for computing linear recurrence relations, Rough ideals under relations associated to fuzzy ideals, Ricci solitons on four-dimensional Lorentzian Lie groups, Solving systems of polynomial equations -- a tensor approach, Linear random walks on the torus, Level lines of a polynomial on a plane, Solving and classifying the solutions of the Yang-Baxter equation through a differential approach. Two-state systems, Characterizing positively invariant sets: inductive and topological methods, Two algorithms for computing the general component of jet scheme and applications, Rank computation in Euclidean Jordan algebras, Classification of real trivectors in dimension nine, Challenging theorem provers with Mathematical Olympiad problems in solid geometry, Finite sets of \(d\)-planes in affine space, Covering symmetric sets of the Boolean cube by affine hyperplanes, Optimization over the Boolean hypercube via sums of nonnegative circuit polynomials, Packed words and quotient rings, Pegasus: sound continuous invariant generation, An extension of Wilf's conjecture to affine semigroups, Gaussoids are two-antecedental approximations of Gaussian conditional independence structures, Book review of: D. Maclagan and B. Sturmfels, Introduction to tropical geometry, Pseudorandom sequences derived from automatic sequences, Standard complexes of matroids and lattice paths, Multivariate volume, Ehrhart, and \(h^\ast \)-polynomials of polytropes, On polynomial feedback Nash equilibria for two-player scalar differential games, On non-binomial structure of cyclic 8-roots, Many faces of symmetric edge polytopes, On the role of the overall effect in exponential families, Representations of positive polynomials on noncompact semialgebraic sets via KKT ideals, Interior and exterior curves of finite Blaschke products, A non-commutative cryptosystem based on quaternion algebras, \(t\)-unique reductions for Mészáros's subdivision algebra, The set of unattainable points for the rational Hermite interpolation problem, Keplerian integrals, elimination theory and identification of very short arcs in a large database of optical observations, Blaschke products and circumscribed conics, Solving a binary puzzle, Optimization approaches to quadrature: new characterizations of Gaussian quadrature on the line and quadrature with few nodes on plane algebraic curves, on the plane and in higher dimensions, The one-dimensional line scheme of a family of quadratic quantum \(\mathbb{P}^3\)s, Revealing regions of multiple steady states in heterogeneous catalytic chemical reaction networks using Gröbner basis, Computing equilibria of semi-algebraic economies using triangular decomposition and real solution classification, On affine variety codes from the Klein quartic, Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat, Identifiability of phylogenetic parameters from \(k\)-mer data under the coalescent, Separation theorems for group invariant polynomials, Sign patterns requiring a unique inertia, Foreword to special issue, Generalized involutive symmetry and its application in integrability of differential systems, Generalized Hamming weights of affine Cartesian codes, A group action on multivariate polynomials over finite fields, Left-invariant Einstein metrics on \(S^3 \times S^3\), Algebraic geometry and Bethe ansatz. I: The quotient ring for BAE, Usage of modular techniques for efficient computation of ideal operations, Algebraic and geometric structures of analytic partial differential equations, The singular locus of semisimple Hessenberg varieties, Invariant algebraic sets and symmetrization of polynomial systems, Apparent singularities of D-finite systems, Generalized coinvariant algebras for \(G(r,1,n)\) in the Stanley-Reisner setting, qspray, Complexity bounds on Semaev's naive index calculus method for ECDLP, A comparison of unrestricted dynamic Gröbner basis algorithms, Autoregressive models for matrix-valued time series, Transforming ODEs and PDEs from radical coefficients to rational coefficients, Free field primaries in general dimensions: counting and construction with rings and modules, On the explicit solutions of separation of variables type for the incompressible 2D Euler equations, Generators for the \(C^m\)-closures of ideals, Learning algebraic varieties from samples, Algebras of symmetric holomorphic functions of several complex variables, A dynamical interval Newton method, Degree upper bounds for involutive bases, A logic based approach to finding real singularities of implicit ordinary differential equations, Homogeneous conformal \(C\)-spaces in dimension four, Algebraic invariants of projections of varieties and partial elimination ideals, Relative Gröbner and involutive bases for ideals in quotient rings, Identifying limits of ideals of points in the case of projective space, Detecting optimality and extracting solutions in polynomial optimization with the truncated GNS construction, A standard form in (some) free fields: how to construct minimal linear representations, The replenishment algorithm in algebras of sets, Guessing Gröbner bases of structured ideals of relations of sequences, Computation of Macaulay constants and degree bounds for Gröbner bases, On the structure of ternary Clifford algebras and their irreducible representations, State polytopes related to two classes of combinatorial neural codes, Enumerative Galois theory for cubics and quartics, Dealing with negative conditions in automated proving: tools and challenges. The unexpected consequences of Rabinowitsch's trick, Transfinite diameter on the graph of a polynomial mapping and the DeMarco-Rumely formula, Improved hitting set for orbit of ROABPs, The inverse of \(\chi\) and its applications to Rasta-like ciphers, Homogeneous four-manifolds with half-harmonic Weyl curvature tensor, Sparse interpolation in terms of multivariate Chebyshev polynomials, On hitting-set generators for polynomials that vanish rarely, Complementary decompositions of monomial ideals and involutive bases, On the base point locus of surface parametrizations: formulas and consequences, Group invariant operators and some applications to norm-attaining theory, Efficient localization at a prime ideal without producing unnecessary primary components, Disjunctive bases of applied algebras of sets and their use in problems of combinatorial geometry, Uniform bounds for the number of rational points on varieties over global fields, An explicit construction for \(n\)-contact curves to a smooth cubic via divisions of polynomials and Zariski tuples, On atomic density of numerical semigroup algebras, The Varchenko-Gel'fand ring of a cone, On a generalization of substitution-permutation networks: the HADES design strategy


Uses Software