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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Helmer, M.; Sturmfels, B., Nearest points on toric varieties, Math. Scand., 122, 213-238, (2018) Toric varieties, Newton polyhedra, Okounkov bodies, Effectivity, complexity and computational aspects of algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Divisors, linear systems, invertible sheaves, Fibrations, degenerations in algebraic geometry, Minimal model program (Mori theory, extremal rays), Effectivity, complexity and computational aspects of algebraic geometry, Singularities of surfaces or higher-dimensional varieties
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Numerical computation of solutions to systems of equations, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Symbolic computation and algebraic computation, Computational aspects of higher-dimensional varieties
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Isogeny, Theta functions and abelian varieties, Computational aspects of algebraic curves, Effectivity, complexity and computational aspects of algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Heier ( G. ) .- Finite type and the effective Nullstellensatz , ArXiv : Math/AG 0603666. arXiv | MR 2440293 | Zbl 1149.14047 Effectivity, complexity and computational aspects of algebraic geometry, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Invariants of analytic local rings, Finite-type domains
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Computer-aided design (modeling of curves and surfaces), Symbolic computation and algebraic computation, Computational aspects of algebraic curves
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Computational aspects of algebraic curves, Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain, Plane and space curves, Abstract differential equations, Formal solutions and transform techniques for ordinary differential equations in the complex domain, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Landsberg, J.M.: Geometry and the complexity of matrix multiplication. Bull. Am. Math. Soc. (N.S.) \textbf{45}(2), 247-284 (2008) Symbolic computation and algebraic computation, Computational aspects of higher-dimensional varieties, Multilinear algebra, tensor calculus, Analysis of algorithms and problem complexity
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Lubicz, D; Robert, D, Computing isogenies between abelian varieties, Compos. Math., 148, 1483-1515, (2012) Isogeny, Theta functions and abelian varieties, Effectivity, complexity and computational aspects of algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Effectivity, complexity and computational aspects of algebraic geometry, Topology of real algebraic varieties
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Tomasz Rodak and Stanisław Spodzieja, Effective formulas for the Łojasiewicz exponent at infinity, J. Pure Appl. Algebra 213 (2009), no. 9, 1816 -- 1822. Effectivity, complexity and computational aspects of algebraic geometry, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Theory of computing
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic sets
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Bröcker L.: Minimal generation of basic semialgebraic sets. Rky. Mtn. J. Math. 14, 935--938 (1984) Real algebraic and real-analytic geometry, Polynomials in real and complex fields: location of zeros (algebraic theorems), Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Enumerative problems (combinatorial problems) in algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Singularities in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Arcs and motivic integration, Computational aspects of algebraic curves, Computational aspects of higher-dimensional varieties, Effectivity, complexity and computational aspects of algebraic geometry, Local complex singularities
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation J. D. Hauenstein, C. Ikenmeyer, and J. M. Landsberg, \textit{Equations for lower bounds on border rank}, Exp. Math., 22 (2013), pp. 372--383. Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Determinantal varieties, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation de Rham cohomology and algebraic geometry, Computational aspects of algebraic surfaces, Symbolic computation and algebraic computation
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Bates, DJ; Oeding, L, Toward a salmon conjecture, Exp Math, 20, 358-370, (2011) Group actions on varieties or schemes (quotients), Actions of groups on commutative rings; invariant theory, Determinantal varieties, Representation theory for linear algebraic groups, Vector and tensor algebra, theory of invariants, Multilinear algebra, tensor calculus, Numerical computation of solutions to systems of equations, Symbolic computation and algebraic computation, Computational aspects in algebraic geometry
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Dongming Wang, Decomposing algebraic varieties, Automated deduction in geometry (Beijing, 1998) Lecture Notes in Comput. Sci., vol. 1669, Springer, Berlin, 1999, pp. 180 -- 206. Computational aspects of higher-dimensional varieties, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, Polynomials, factorization in commutative rings
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Computer graphics; computational geometry (digital and algorithmic aspects), Effectivity, complexity and computational aspects of algebraic geometry, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Combinatorial complexity of geometric structures
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Mohamed Elkadi and Bernard Mourrain. \textit{Introduction à la résolution des systèmes polynomiaux}, volume~59 of \textit{Mathématiques & Applications}. Springer, Berlin, 2007. Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Effectivity, complexity and computational aspects of algebraic geometry, Numerical computation of eigenvalues and eigenvectors of matrices, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general algebraic systems, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Joos Heintz, Marie-Françoise Roy, and Pablo Solernó, Single exponential path finding in semialgebraic sets. I. The case of a regular bounded hypersurface, Applied algebra, algebraic algorithms and error-correcting codes (Tokyo, 1990) Lecture Notes in Comput. Sci., vol. 508, Springer, Berlin, 1991, pp. 180 -- 196. Effectivity, complexity and computational aspects of algebraic geometry, Semialgebraic sets and related spaces, Analysis of algorithms and problem complexity
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation J. William Helton and Mihai Putinar, Positive polynomials in scalar and matrix variables, the spectral theorem, and optimization, Operator theory, structured matrices, and dilations, Theta Ser. Adv. Math., vol. 7, Theta, Bucharest, 2007, pp. 229 -- 306. Research exposition (monographs, survey articles) pertaining to operator theory, Several-variable operator theory (spectral, Fredholm, etc.), Linear operator methods in interpolation, moment and extension problems, Moment problems, Semialgebraic sets and related spaces, Real algebra, Linear systems in control theory, Positive matrices and their generalizations; cones of matrices, Linear operator inequalities, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Clémence Durvye and Grégoire Lecerf, A concise proof of the Kronecker polynomial system solver from scratch, Expo. Math. 26 (2008), no. 2, 101 -- 139. Computational aspects of higher-dimensional varieties, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Collections of abstracts of lectures, Proceedings of conferences of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Real algebraic and real-analytic geometry, Proceedings, conferences, collections, etc. pertaining to commutative algebra, Real algebra, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Solving polynomial systems; resultants, Determinantal varieties, Computational aspects of algebraic curves, Combinatorial optimization
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Reznick, B.; Tokcan, N., Binary forms with three different relative ranks, arXiv preprint Forms of degree higher than two, Waring's problem and variants, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Enumerative problems (combinatorial problems) in algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Campillo, A.; Farrán, J.: Adjoints and codes, Rend. sem. Mat. univ. Politec. Torino 62, 209-223 (2004) Computational aspects of algebraic curves, Applications to coding theory and cryptography of arithmetic geometry, Symbolic computation and algebraic computation, Geometric methods (including applications of algebraic geometry) applied to coding theory
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Bernardi, A.; Gimigliano, A.; Idà, M., Singularities of plane rational curves via projections, J. Symb. Comput., 86, 189-214, (2018) Computational aspects of algebraic curves, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Pérez-Díaz, S.; Sendra, J.; Sendra, J. R.: Parametrizations of approximate algebraic curves by lines. Theoret. comput. Sci. 315, No. 2 -- 3, 627-650 (2004) Symbolic computation and algebraic computation, Computational aspects of algebraic curves, Numerical aspects of computer graphics, image analysis, and computational geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Computational aspects of higher-dimensional varieties, Semialgebraic sets and related spaces, Topology of real algebraic varieties, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation P. PISÓN-CASARES, A. VIGNERON-TENORIO, First Syzygies of Toric Varieties and Diophantine Equations in Congruence. Communications in Algebra, 29, 4, (2001). Computational aspects and applications of commutative rings, Syzygies, resolutions, complexes and commutative rings, Symbolic computation and algebraic computation, Toric varieties, Newton polyhedra, Okounkov bodies, Computer solution of Diophantine equations, Ordinary and skew polynomial rings and semigroup rings
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Couveignes, J-M; Ezome, T, Computing functions on Jacobians and their quotients, LMS J. Comput. Math., 18, 555-577, (2015) Isogeny, Computational aspects of algebraic curves, Effectivity, complexity and computational aspects of algebraic geometry, Theta functions and abelian varieties
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Volcheck, E., 1997. On computing the dual of a plane algebraic curve. In: Proceedings of ISSAC'97. pp.~356--358 Symbolic computation and algebraic computation, Computational aspects of algebraic curves
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation 10. O. SIMON, Aspects quantitatifs de Nullstellensätze et de Positivstellensätze. Nombres de Pythagore, Communications in Algebra, 1989, 17, (3), p. 637-667. Zbl0668.14001 MR981475 Relevant commutative algebra, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic and real-analytic geometry, Quadratic forms over general fields
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Effectivity, complexity and computational aspects of algebraic geometry, Explicit solutions, first integrals of ordinary differential equations, Abstract differential equations
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Giusti, M.; Heintz, J., La détermination des points isolés et de la dimension d'une variété algébrique peut se faire en temps polynomial, (), To appear Computational aspects of higher-dimensional varieties, Symbolic computation and algebraic computation, Relevant commutative algebra
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Gräbe, H-G, The tangent cone algorithm and homogenization, J. Pure Appl. Algebra, 97, 303-312, (1994) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Computational aspects in algebraic geometry, Symbolic computation and algebraic computation, Analysis of algorithms and problem complexity
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation J. B. Lasserre, \textit{A sum of squares approximation of nonnegative polynomials}, SIAM J. Optim., 16 (2006), pp. 751--765. Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Semialgebraic sets and related spaces, Semidefinite programming
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation I.Z. Emiris, T. Kalinka, C. Konaxis, T. Luu Ba, Sparse implicitization by interpolation: Characterizing non-exactness and an application to computing discriminants, in: Proc. ACM Symp. Solid & Phys. Modeling, Dijon, France, 2012, submitted. Symbolic computation and algebraic computation, Solving polynomial systems; resultants, Computational aspects of algebraic curves, Computational aspects of algebraic surfaces
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Quantifier elimination, model completeness, and related topics, Symbolic computation and algebraic computation, Real algebraic and real-analytic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Singularities of curves, local rings, Rational and birational maps, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Étale and other Grothendieck topologies and (co)homologies, Computational aspects of algebraic curves, Effectivity, complexity and computational aspects of algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation J. Bochnak, M. Coste, and M.-F. Roy, \textit{Real Algebraic Geometry}, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 36, Springer-Verlag, Berlin, 1998. Real algebraic and real-analytic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Ordered fields, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Algebraic theory of quadratic forms; Witt groups and rings, \(K\)-theory in geometry, Witt groups of rings, Real-analytic manifolds, real-analytic spaces, Stable classes of vector space bundles in algebraic topology and relations to \(K\)-theory, Stratifications in topological manifolds, Real-analytic and Nash manifolds, Stratified sets
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Rational points, Finite ground fields in algebraic geometry, Applications to coding theory and cryptography of arithmetic geometry, Special algebraic curves and curves of low genus, Computational aspects of algebraic curves, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Bradford, R.J., Davenport, J.H., England, M., McCallum, S., Wilson, D.J.: Truth Table Invariant Cylindrical Algebraic Decomposition (2014). Symbolic computation and algebraic computation, Real algebraic and real-analytic geometry, Computational aspects in algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Soliton equations, Soliton solutions, Symbolic computation and algebraic computation, Periodic solutions to PDEs, Water waves, gravity waves; dispersion and scattering, nonlinear interaction, Solitary waves for incompressible inviscid fluids, Theta functions and curves; Schottky problem
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Semidefinite programming, Real algebraic sets, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry)
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation C. Bogner and F. Brown, \textit{Feynman integrals and iterated integrals on moduli spaces of curves of genus zero}, arXiv:1408.1862 [INSPIRE]. Feynman integrals and graphs; applications of algebraic topology and algebraic geometry, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Families, moduli of curves (algebraic), Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Relevant commutative algebra, Effectivity, complexity and computational aspects of algebraic geometry, Ideals and multiplicative ideal theory in commutative rings, Polynomials in number theory
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Grassmannians, Schubert varieties, flag manifolds, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Basu, S.; Pollack, R.; Roy, M. -F.: Computing the first Betti number and the connected components of semi-algebraic sets. (2005) Software, source code, etc. for problems pertaining to algebraic geometry, Semialgebraic sets and related spaces, Analysis of algorithms and problem complexity, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Dupont, L., Lazard, D., Lazard, S., Petitjean, S.: Near-optimal parameterization of the intersection of quadrics: II. A classification of pencils. J. Symb. Comput. 43(3), 192--215 (2008) Computational aspects of algebraic curves, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Arithmetic ground fields for curves, Divisors, linear systems, invertible sheaves, Symbolic computation and algebraic computation, Special surfaces, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry, History of algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Jia, X.; Wang, W.; Choi, Y.-K.; Mourrain, B.; Tu, C., Continuous detection of the variations of the intersection curve of two moving quadrics in 3-dimensional projective space, J. symb. comput., 73, C, 221-243, (2016) Symbolic computation and algebraic computation, Projective techniques in algebraic geometry, Real algebraic sets, Computational aspects of algebraic curves
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Parametrization (Chow and Hilbert schemes), Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Special algebraic curves and curves of low genus, Configurations and arrangements of linear subspaces, \(p\)-adic cohomology, crystalline cohomology, Compact Riemann surfaces and uniformization, Symbolic computation and algebraic computation, Proceedings of conferences of miscellaneous specific interest
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Andradas, C; Recio, T; Sendra, JR; Tabera, LF, On the simplification of the coefficients of a parametrization, J. Symb. Comput., 44, 192-210, (2009) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Computational aspects in algebraic geometry, Computational aspects of higher-dimensional varieties, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation \textsc{D.~Bates, J.~Hauenstein, A.~Sommese, and C.~Wampler}, \textit{Numerically solving polynomial systems with Bertini}, vol.~25 of Software, Environments, and Tools, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2013. Research exposition (monographs, survey articles) pertaining to numerical analysis, Computational aspects of higher-dimensional varieties, Numerical computation of roots of polynomial equations, Numerical computation of solutions to systems of equations, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Packaged methods for numerical algorithms, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Chardin, M.: Applications of some properties of the canonical module in computational projective algebraic geometry. J. symbolic comput. 29, 527-544 (2000) Computational aspects in algebraic geometry, Symbolic computation and algebraic computation, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Real-analytic and semi-analytic sets, Commutative rings and modules of finite generation or presentation; number of generators, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ideals and multiplicative ideal theory in commutative rings
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Sums of squares and representations by other particular quadratic forms, Convexity of real functions of several variables, generalizations
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, Integral closure of commutative rings and ideals, Algebraic number theory computations, Software, source code, etc. for problems pertaining to commutative algebra, Algebraic functions and function fields in algebraic geometry, Computational aspects of algebraic curves
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Computational real algebraic geometry, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation B. Reznick, \textit{Some concrete aspects of Hilbert's 17th problem}, in Real Algebraic Geometry and Ordered Structures, Contemp. Math. 253, American Mathematical Society, Providence, RI, 2000, pp. 251--272. Forms over real fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Research exposition (monographs, survey articles) pertaining to number theory, History of number theory, Forms of degree higher than two, History of mathematics in the 20th century, Real algebraic and real-analytic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation H. G. Folz and H. G. Zimmer, What is the rank of the Demjanenko matrix?, J. Symbolic Comput. 4 (1987), no. 1, 53 -- 67. Software, source code, etc. for problems pertaining to algebraic geometry, Symbolic computation and algebraic computation, Software, source code, etc. for problems pertaining to linear algebra
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Effectivity, complexity and computational aspects of algebraic geometry, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Max-plus and related algebras, Foundations of tropical geometry and relations with algebra, Analysis of algorithms and problem complexity
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Computational real algebraic geometry, Sums of squares and representations by other particular quadratic forms, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Kucharz, W.: Invertible ideals in real holomorphy rings. J. reine angew. Math. 395, 171-185 (1989) Ideals and multiplicative ideal theory in commutative rings, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic and real-analytic geometry, Divisibility and factorizations in commutative rings
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Solving polynomial systems; resultants, History of commutative algebra, History of mathematics in the 20th century, History of mathematics in the 21st century, Effectivity, complexity and computational aspects of algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Formally \(p\)-adic fields, Local ground fields in algebraic geometry, Other constructive mathematics
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Elliptic curves, Isogeny, Effectivity, complexity and computational aspects of algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Solving polynomial systems; resultants, Symbolic computation and algebraic computation, Classical problems, Schubert calculus, Computational real algebraic geometry
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Software, source code, etc. for problems pertaining to commutative algebra, Computational real algebraic geometry, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Schicho J., Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation pp 292-- (2000) Symbolic computation and algebraic computation, Computational aspects of algebraic surfaces
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Symbolic computation and algebraic computation, Software, source code, etc. for problems pertaining to algebraic geometry, Homotopy theory and fundamental groups in algebraic geometry
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation M. Michalska, Curves testing boundedness of polynomials on subsets of the real plane. \textit{J. Symbolic Comput}. \textbf{56} (2013), 107-124. MR3061711 Zbl 1304.14072 Semialgebraic sets and related spaces, Nash functions and manifolds, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation S. Arnborg and H. Feng, Algebraic decomposition of regular curves, J. Symbolic Comput. 5 (1988) 131--140. Families, moduli of curves (algebraic), Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Orecchia F., J. Symbolic Computation 31 pp 343-- (2001) Computational aspects of higher-dimensional varieties, Analysis of algorithms, Symbolic computation and algebraic computation, Software, source code, etc. for problems pertaining to algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation S. Basu, Computing the top Betti numbers of semi-algebraic sets defined by quadratic inequalities in polynomial time. Preprint math.AG/0603262 Software, source code, etc. for problems pertaining to algebraic geometry, Semialgebraic sets and related spaces, Analysis of algorithms and problem complexity, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation A. J. Wilkie, \textit{Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function}, J. Amer. Math. Soc., 9 (1996), pp. 1051--1094, . Model-theoretic algebra, Model theory of fields, Semi-analytic sets, subanalytic sets, and generalizations, Real-analytic and semi-analytic sets, Valued fields, Ordered fields
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Software, source code, etc. for problems pertaining to algebraic geometry, Real algebraic sets, Geometric aspects of numerical algebraic geometry, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Garcia-Puente, L; Petrovic, S; Sullivant, S, Graphical models, J Softw Algebra Geom, 5, 1-7, (2013) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Software, source code, etc. for problems pertaining to commutative algebra, Multivariate analysis, Symbolic computation and algebraic computation, Computational aspects in algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Computer-aided design (modeling of curves and surfaces), Computational aspects of algebraic curves, Numerical computation of roots of polynomial equations, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Lickteig, T. M.; Werther, K.: How can a complex square root be computed in an optimal way?. Comput. complexity 5, 222-236 (1995) Analysis of algorithms and problem complexity, Symbolic computation and algebraic computation, Semialgebraic sets and related spaces, Nash functions and manifolds
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Semidefinite programming, Numerical mathematical programming methods, Nonconvex programming, global optimization, Coloring of graphs and hypergraphs, Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation G. Comte and Y. Yomdin, \textit{Tame Geometry with Application in Smooth Analysis}, Lecture Notes in Mathematics, Vol. 1834, Springer, Berlin, 2004. Semialgebraic sets and related spaces, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Effectivity, complexity and computational aspects of algebraic geometry, Integration of real functions of several variables: length, area, volume, Equisingularity (topological and analytic)
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation G. V. Chudnovsky, \textit{Singular points on complex hypersurfaces and multidimensional Schwarz} \textit{lemma}, in: Seminar on Number Theory, Paris 1979--80, Progr. Math. 12, Birkhäuser, Boston, Mass., 1981, 29--69. [14] C. Ciliberto, A. L. Knutsen, J. Lesieutre, V. Lozovanu, R. Miranda, Y. Mustopa, D. Testa, \textit{A few questions about curves on surfaces}, Rend. Circ. Mat. Palermo (2) 66 (2017), 195--204. [15] C. Ciliberto, R. Miranda, \textit{Nagata's conjecture for a square or nearly-square number of} \textit{points}, Ric. Mat. 55 (2006), 71--78. Special surfaces, Rational and ruled surfaces, Divisors, linear systems, invertible sheaves, Vanishing theorems in algebraic geometry, Effectivity, complexity and computational aspects of algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation DOI: 10.1016/j.cagd.2009.03.006 Computer-aided design (modeling of curves and surfaces), Effectivity, complexity and computational aspects of algebraic geometry, Numerical computation using splines
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Andres, D.; Levandovskyy, V.; Martín-Morales, J.: Principal intersection and Bernstein-Sato polynomial of an affine variety, (2009) Software, source code, etc. for problems pertaining to algebraic geometry, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Affine geometry, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Basu, S., Zell, T.: On projections of semi-algebraic sets defined by few quadratic inequalities. Arxiv: AG/0602398 Semialgebraic sets and related spaces, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Coquand, T., \textit{space of valuations}, Annals of Pure and Applied Logic, 157, 97-109, (2009) Other constructive mathematics, Frames, locales, Valuations and their generalizations for commutative rings, Applications of logic to commutative algebra, Schemes and morphisms
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Vaccon, Tristan, Matrix-F5 algorithms and tropical Gröbner bases computation, (Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC 2015, Bath, United Kingdom, (2015)), 355-362 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), \(p\)-adic theory, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation A. L. Chistov, ''Polynomial-time computation of the degree of a dominant morphism in zero-characteristic. IV,'' J. Math. Sci., 158, No. 6, 912--927 (2009). Effectivity, complexity and computational aspects of algebraic geometry, Rational and birational maps
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Gábor Bodnár and Josef Schicho, Two computational techniques for singularity resolution, J. Symbolic Comput. 32 (2001), no. 1-2, 39 -- 54. Computer algebra and mechanized reasoning (St. Andrews, 2000). Global theory and resolution of singularities (algebro-geometric aspects), Computational aspects of higher-dimensional varieties, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation M. VAN HOEIJ, Computing parametrizations of rational algebraic curves, ISSAC '94 Proceedings (1994), 187-190. Computational aspects of algebraic curves, Symbolic computation and algebraic computation, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Software, source code, etc. for problems pertaining to algebraic geometry
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Polynomials in general fields (irreducibility, etc.), Real algebra, Moment problems
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation A. Galligo, L. Gonzalez-Vega, H. Lombardi, Continuity properties for flat families of polynomials (II) A metric point of view, in preparation. Polynomials, factorization in commutative rings, Real algebraic and real-analytic geometry, Relevant commutative algebra, Numerical computation of solutions to systems of equations, Symbolic computation and algebraic computation, Computational aspects in algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Sommese, A. J.; Verschelde, J.; Wampler, C. W.: A method for tracking singular paths with application to the numerical irreducible decomposition. Algebraic geometry, A volume in memory of paolo francia, vol. 286 286, 329-345 (2002) Numerical computation of solutions to systems of equations, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Computational aspects of higher-dimensional varieties, Real polynomials: location of zeros, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Deformations of complex singularities; vanishing cycles, Effectivity, complexity and computational aspects of algebraic geometry, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Group actions on varieties or schemes (quotients), Symbolic computation and algebraic computation
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