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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 Bogart, T., Jensen, A., Speyer, D., Sturmfels, B., Thomas, R.: Computing tropical varieties. J. Symb. Comput. \textbf{42}(1-2), 54-73 (2007). Effective Methods in Algebraic Geometry (MEGA 2005) Computational aspects in algebraic geometry, Real algebraic and real-analytic 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 Computer graphics; computational geometry (digital and algorithmic aspects), Computational aspects of algebraic curves, Numerical aspects of computer graphics, image analysis, and computational 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 Bernd Bank, Marc Giusti, Joos Heintz & Guy Merlin Mbakop, ``Polar varieties and efficient real elimination'', Math. Z.238 (2001) no. 1, p. 115-144 Real algebraic sets, Computational aspects in 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 Heintz, J.; Roy, M. -F.; Solernó, P.: Description des composantes connexes d'un ensemble semialgébrique en temps simplement exponential. C. R. Math. acad. Sci. 313, 167-170 (1991) Effectivity, complexity and computational aspects of algebraic geometry, Semialgebraic sets and related spaces, Analysis of algorithms and problem complexity, Quantifier elimination, model completeness, and related topics
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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, A computer program for the resolution of singularities, Resolution of singularities (Obergurgl, 1997) Progr. Math., vol. 181, Birkhäuser, Basel, 2000, pp. 231 -- 238. Computational aspects of algebraic surfaces, Symbolic computation and algebraic computation, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Global theory and resolution of singularities (algebro-geometric aspects)
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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 Huber, B; Sottile, F; Sturmfels, B, Numerical Schubert calculus, J. Symb. Comp., 26, 767-788, (1998) Enumerative problems (combinatorial problems) in algebraic geometry, Configurations and arrangements of linear subspaces, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Global methods, including homotopy approaches to the numerical solution of nonlinear equations, 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 Seppälä, M.: Computation of period matrices of real algebraic curves. Discrete comput. Geom. 11, No. 1, 65-81 (1994) Computational aspects of algebraic curves, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Special algebraic curves and curves of low genus, Symbolic computation and algebraic computation, 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 (Langer, U.; Paule, P., Numerical and symbolic scientific computing, (2011), Springer Vienna (Austria)) Proceedings, conferences, collections, etc. pertaining to numerical analysis, Proceedings, conferences, collections, etc. pertaining to computer science, Software, source code, etc. for problems pertaining to numerical analysis, Collections of articles of miscellaneous specific interest, Symbolic computation and algebraic computation, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Computational aspects of algebraic curves, Computer-aided design (modeling of curves and 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 Nagao, K.: Improving group law algorithms for Jacobians of hyperelliptic curves, Lecture notes in comput. Sci. 1838, 439-448 (2000) Symbolic computation and algebraic computation, Jacobians, Prym varieties, Applications to coding theory and cryptography of arithmetic geometry, 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 Walther, U.: Algorithmic computation of local cohomology modules and the cohomological dimension of algebraic varieties. J. pure appl. Algebra 139, 303-321 (1999) Local cohomology and algebraic geometry, Computational aspects of higher-dimensional varieties, Local cohomology and commutative rings, Symbolic computation and algebraic computation, 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 DOI: 10.2140/jsag.2013.5.20 Software, source code, etc. for problems pertaining to commutative algebra, Software, source code, etc. for problems pertaining to algebraic geometry, Computational aspects in algebraic geometry, Multivariate analysis, Numerical computation of solutions to systems of 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 K. Kaspers, L. Mathelin, and H. Abou-Kandil, \textit{A machine learning approach for constrained sensor placement}, in Proceedings of the American Control Conference, 2015, pp. 4479--4484, http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=7172034. Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Semialgebraic sets and related spaces, Model-theoretic algebra, Model theory of ordered structures; o-minimality
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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, Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Multiplicity theory and related topics, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Divisors, linear systems, invertible sheaves, 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 Numerical aspects of computer graphics, image analysis, and computational geometry, Fibrations, degenerations in algebraic geometry, Singularities of curves, local rings, Plane and space curves, 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 Arnon, D. S.; Collins, G. E.; Mccallum, S.: Cylindrical algebraic decomposition i: Basic algorithm. Texts and monographs in symbolic computation, 136-151 (1998) 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 Van Hamel, J., \textit{divisors on real algebraic varieties without real points}, Manuscripta Math., 98, 409-424, (1999) Real algebraic sets, Picard groups, Forms over real fields, Other nonalgebraically closed ground fields in algebraic geometry, Divisors, linear systems, invertible sheaves, 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 Briales, A., Campillo, A., Pisón, P., Vignerón, A.: Minimal resolution of lattices and integer linear programing. Revista Matemática Iberoamericana 19(2), 287-306 (2003) Syzygies, resolutions, complexes and commutative rings, Toric varieties, Newton polyhedra, Okounkov bodies, 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 A. Sommese, J. Verschelde and C. Wampler, \textit{Numerical factorization of multivariate complex polynomials}, Theoret. Comput. Sci. 315 (2004), 651-669. Polynomials, factorization in commutative rings, Computational aspects in algebraic geometry, Numerical computation of solutions to systems of 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 Sendra, J.; Winkler, F.: Real parametrization of algebraic curves, artificial intelligence and symbolic computation. (1998) Computational aspects of algebraic curves, Arithmetic ground fields for curves, Symbolic computation and algebraic computation, 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 Special divisors on curves (gonality, Brill-Noether theory), Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes, 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 Marinari, M.G., Ramella, L.: Criteria for stability and Borelness. In: Zero-dimensional schemes and applications. Proceedings of the workshop Naples 2000, Queen's Papers Pure Appl. Math. 123, (2002) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Computational aspects in 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 Möller, H. M., On decomposing systems of polynomial equations with finitely many solutions, Appl. Algebra Eng. Commun. Comput., 4, 4, 217-230, (1993) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Computational aspects of higher-dimensional varieties, 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 Monnier, J. P.: Unramified cohomology and quadratic forms. Math. Z. 235, 455-478 (2000) Algebraic theory of quadratic forms; Witt groups and rings, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Rational and ruled surfaces, \(4\)-folds, Witt groups of rings, \(K3\) surfaces and Enriques surfaces, Real algebraic sets
| 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 Polynomials, factorization in commutative rings, Real algebraic sets, 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 Proceedings of conferences of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Proceedings, conferences, collections, etc. pertaining to commutative algebra, Proceedings, conferences, collections, etc. pertaining to nonassociative rings and algebras, 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 Computational aspects of algebraic curves, Computer graphics; computational geometry (digital and algorithmic aspects), Computer science aspects of computer-aided design, 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 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Germs of analytic sets, local parametrization, Group actions on varieties or schemes (quotients), Semi-analytic sets, subanalytic sets, and generalizations, Real algebraic and real-analytic geometry, Real-analytic manifolds, real-analytic spaces
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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 L. Ramero, Effective estimates for unirationality , Manuscripta Math. 68 (1990), no. 4, 435-445. Rational and unirational varieties, Effectivity, complexity and computational aspects of algebraic geometry, Complete intersections
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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 Dahan, X.; Jin, X.; Maza, M. Moreno; Schost, É.: Change of order for regular chains in positive dimension, Theoret. comput. Sci. 392, No. 1--3, 37-65 (2008) Computational aspects in algebraic geometry, Computational aspects and applications of commutative rings, 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 Computational aspects in 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 Computer science aspects of computer-aided design, Geometric aspects of numerical algebraic geometry, Computer-aided design (modeling of curves and surfaces), 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 Schultz T, Jüttler B.Envelope computation in the plane by approximate implicitization. Appl Algebra Eng Comm Comput. 2011;22(4):265-288. Computer-aided design (modeling of curves and surfaces), Effectivity, complexity and computational aspects of algebraic geometry, Spline approximation
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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 Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.), Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), 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 Shaska T., ''Determining the automorphism group of a hyperelliptic curve,'' in: Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, ACM Press, New York, 2003, pp. 248--254. Symbolic computation and algebraic computation, Families, moduli of curves (algebraic), Automorphisms of curves, Computational aspects of algebraic curves, Infinite automorphism groups
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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, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Moment problems, Nonconvex programming, global optimization, Real algebra, Semialgebraic sets and related spaces
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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 General valuation theory for fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Field arithmetic, Valued fields, 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 Symbolic computation and algebraic computation, Toric varieties, Newton polyhedra, Okounkov bodies, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Computational aspects related to convexity
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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, 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 Batkhin, A-B; Bruno, A-D, Investigation of a real algebraic surface, Program Comput Softw, 41, 74-83, (2015) Real algebraic sets, Computational aspects of algebraic surfaces, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Surfaces in Euclidean 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 D. Eisenbud, F.-O. Schreyer, Relative Beilinson monad and direct image for families of coherent sheaves. Trans. Am. Math. Soc. 360(10), 5367-5396 (2008). arXiv:math/0506391. MR 2415078 (2009f:14030) Syzygies, resolutions, complexes and commutative rings, 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.D. Hauenstein and A.J. Sommese, \textit{Witness sets of projections}, Appl. Math. Comput., 217 (2010), pp. 3349--3354. Computational aspects of higher-dimensional 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 Computational aspects in algebraic geometry, 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 CHUDNOVSKY, D. V., and CHUDNOVSKY, G. V., Editors, Search Theory, Marcel Dekker, New York, New York, 1988. Formal groups, \(p\)-divisible groups, Arithmetic ground fields for curves, Symbolic computation and algebraic computation, Abstract differential equations, Finite ground fields in algebraic geometry, Power series rings, Bordism and cobordism theories and formal group laws in algebraic topology
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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 Sakkalis T.: The topological configuration of a real algebraic curve. Bull. Aust. Math. Soc. 43, 37--50 (1991) Topology of real algebraic varieties, Computational aspects of algebraic curves, Symbolic computation and algebraic computation, Special algebraic curves and curves of low genus, Topological properties 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 Gatellier, G.; Labrouzy, A.; Mourrain, B.; Técourt, J.: Computing the topology of three-dimensional algebraic curves. Computational methods for algebraic spline surfaces, 27-43 (2003) 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 Scheiderer, C.,Stability index of real varieties. Invent. Math.97 (1989), 467--483. Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real polynomials: analytic properties, 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 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Effectivity, complexity and computational aspects of algebraic geometry, Word problems, etc. in computability and recursion theory, Word problems (aspects of algebraic structures), Thue and Post systems, etc., Lattice ideals, congruence relations
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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 Jacobians, Prym varieties, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Rational points, 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 Beltrán, C.; Leykin, A., Certified numerical homotopy tracking, Exp. math., 21, 1, 69-83, (2012) Effectivity, complexity and computational aspects of algebraic geometry, Numerical computation of solutions to systems of equations, Global methods, including homotopy approaches to the numerical solution of nonlinear 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 Computational aspects of algebraic surfaces, Local complex singularities, Singularities of holomorphic vector fields and foliations, 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 Stability of topological dynamical systems, Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems, Computational real algebraic geometry, Geometric methods in ordinary differential equations, Asymptotic properties of solutions to ordinary differential equations, Computational methods for invariant manifolds of dynamical systems, Symbolic computation and algebraic computation, Semidefinite programming
| 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 Helmer, M.: Computing characteristic classes of subschemes of smooth toric varieties. J. algebra (2017) Toric varieties, Newton polyhedra, Okounkov bodies, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Enumerative problems (combinatorial problems) in algebraic geometry, Computational aspects of higher-dimensional varieties, 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 Gabriela Jeronimo, Teresa Krick, Juan Sabia, and Martín Sombra, The computational complexity of the Chow form, Found. Comput. Math. 4 (2004), no. 1, 41 -- 117. Computational aspects of higher-dimensional varieties, 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 Alonso M.E., Gamboa J.M., Ruiz J.M.: On orderings in real surfaces. J. Pure Appl. Algebra 36, 1--14 (1985) Real algebraic and real-analytic geometry, Arithmetic ground fields for surfaces or higher-dimensional varieties, 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 L. González-Vega, F. Rouillier, M.-F. Roy, G. Trujillo, Symbolic recipes for real solutions, vol. 4 of Algorithms and Computations in Mathematics, Springer-Verlag, 1999, pp. 121--167 (Chapter 6) Nonlinear algebraic or transcendental equations, Computational aspects in 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 Packaged methods for numerical algorithms, Software, source code, etc. for problems pertaining to commutative algebra, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Toric varieties, Newton polyhedra, Okounkov bodies, Effectivity, complexity and computational aspects of 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 Alonso, M. E.; Gamboa, J. M.; Ruiz, J. M.: Ordres sur LES surfaces réelles. C. R. Acad. sci. Paris ser. I 298, No. No. 1, 17-19 (1984) Real algebraic and real-analytic geometry, Real-analytic manifolds, real-analytic spaces, Ordered rings, algebras, modules, 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 Bodnár, G.: Algorithmic tests for the normal crossings property. Preprint, Univ. Linz. Global theory and resolution of singularities (algebro-geometric aspects), Computational aspects of higher-dimensional varieties, 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 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic and real-analytic geometry, Relevant commutative algebra
| 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 Polynomial optimization, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Semialgebraic sets and related spaces, Computational real algebraic geometry, Semidefinite programming
| 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 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Computational aspects in algebraic geometry, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Symbolic computation and algebraic computation, Operator ideals
| 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 Andersson M., Wulcan E., \textit{Global effective versions of the Brian\c{}}\textit{con--Skoda--} \textit{Huneke theorem}, Invent. Math. 200 (2015), 607--651. Residues for several complex variables, Effectivity, complexity and computational aspects of algebraic geometry, Polynomials in number theory, Vanishing theorems in algebraic geometry, Germs of analytic sets, local parametrization, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Integration on analytic sets and spaces, currents
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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 Prestel, Alexander, Bounds for representations of polynomials positive on compact semi-algebraic sets.Valuation theory and its applications, Vol. I, Saskatoon, SK, 1999, Fields Inst. Commun. 32, 253-260, (2002), Amer. Math. Soc., Providence, RI Semialgebraic sets and related spaces, Real algebra, 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 Computational aspects of algebraic surfaces, Computational aspects of higher-dimensional varieties, Symbolic computation and algebraic computation, Rational and birational maps
| 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 DOI: 10.1016/S0022-4049(99)00015-8 Computational aspects in algebraic geometry, Geometric invariant 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 Software, source code, etc. for problems pertaining to commutative algebra, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Geometric aspects of numerical algebraic geometry, Nonlinear elasticity, Vibrations in dynamical problems in solid mechanics, Thermal effects in solid mechanics, 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 Lin, C.-S.; Wang, C. L., Mean field equations, hyperelliptic curves and modular forms, part II, J. Éc. Polytech. Math., 4, 557-593, (2017) Lamé, Mathieu, and spheroidal wave functions, Green's functions for elliptic equations, Singular elliptic equations, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions, Relationships between algebraic curves and integrable systems, Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\), 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 Software, source code, etc. for problems pertaining to algebraic geometry, Software, source code, etc. for problems pertaining to number theory, Applications to coding theory and cryptography of arithmetic geometry, 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 Hyodo N., Hong M., Yanami H., Hara S., Anai H.: Solving and visualizing nonlinear parametric constraints in control based on quantifier elimination. Appl. Algebra Eng. Commun. Comput. 18(6), 497--512 (2007) Symbolic computation and algebraic computation, Quantifier elimination, model completeness, and related topics, Real algebraic and real-analytic geometry, Numerical computation of solutions to systems of 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 Computational real algebraic geometry, Symbolic computation and algebraic computation, Connectivity
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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 Jaworski, P., Extensions of orderings on fields of quotients of rings of real analytic functions, Math. Nachr., 125, 329-339, (1986) Real-analytic and semi-analytic sets, Real-analytic manifolds, real-analytic spaces, Analytic algebras and generalizations, preparation theorems, 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 A. M. Cohen, S. Haller, and S. H. Murray, ''Computing in unipotent and reductive algebraic groups,'' LMS J. Comput. Math., 11, 343--366 (2008). Linear algebraic groups over arbitrary fields, Software, source code, etc. for problems pertaining to group theory, Symbolic computation and algebraic computation, Nilpotent groups, Group schemes
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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 Machura M., Marshall M., Osiak K., Metrizability of the space of R-places of a real function field, Math. Z., 2010, 266(1), 237--242 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 Zimmer H. G., ''SIMATH: a computer algebra system for number theoretic applications'' (1997) Algebraic number theory computations, Symbolic computation and algebraic computation, Computational aspects of algebraic curves, Cryptography, Elliptic curves over global fields, Computational 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 Computational aspects of algebraic curves, 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 Geometric methods (including applications of algebraic geometry) applied to coding theory, Symbolic computation and algebraic computation, Finite fields (field-theoretic aspects), Elementary questions 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 Mourrain, B., Wintz, J.: A subdivision method for arrangement computation of semi-algebraic curves. In: Nonlinear Computational Geometry, pp. 165-187, The IMA Volumes in Mathematics and its Applications, vol. 151, Springer, New York (2010) Symbolic computation and algebraic computation, Computer-aided design (modeling of curves and surfaces), Semialgebraic sets and related spaces
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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 Fernando, On the spectra of rings of semialgebraic functions, Collect. Math. 63 (3) pp 299-- (2012) Semialgebraic sets and related spaces, Extension of maps, Real-valued functions in general topology, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Chain conditions, finiteness conditions in commutative ring 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 Fernando, J.F., Ueno, C.: On the complements of 3-dimensional convex polyhedra as polynomial images of \({\mathbb{R}}^3\). Int. J. Math. (2014). 10.1142/S0129167X14500712 Affine fibrations, Fibrations, degenerations 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 Canny, J.: Improved algorithms for sign determination and existential quantifier elimination. Comput. J. 36(5), 409--418 (1993) Symbolic computation and algebraic computation, Quantifier elimination, model completeness, and related topics, Semialgebraic sets and related spaces
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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, Real algebra, Ordered rings, Ordered fields
| 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 aspects of higher-dimensional varieties, 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 Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
| 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 Toric varieties, Newton polyhedra, Okounkov bodies, Effectivity, complexity and computational aspects of algebraic geometry, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Gale and other diagrams, Projective techniques 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 Bank, B.; Giusti, M.; Heintz, J.; Safey El Din, M., Intrinsic complexity estimates in polynomial optimization, J. complex., 30, 4, 430-443, (2014) Complexity and performance of numerical algorithms, Analysis of algorithms and problem complexity, Symbolic computation and algebraic computation, Abstract computational complexity for mathematical programming problems, Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Semialgebraic sets and related spaces, 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 Basu, S., Pollack, R., Roy, M.-F.: Computing roadmaps of semi-algebraic sets (extended abstract). In: STOC, pp. 168--173. ACM, New York (1996) Semialgebraic sets and related spaces, Analysis of algorithms and problem complexity, Symbolic computation and algebraic computation, Kinematics of mechanisms and robots
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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. Scheiblechner, On the complexity of counting irreducible components and computing Betti numbers of complex algebraic varieties, Ph.D. Thesis, Universität Paderborn, 2007. Research exposition (monographs, survey articles) pertaining to algebraic geometry, Effectivity, complexity and computational aspects of algebraic geometry, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, 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 Singularities of curves, local rings, Computational aspects of algebraic curves, Effectivity, complexity and computational aspects of algebraic geometry, Invariants of analytic local 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 V. Powers and B. Reznick, \textit{Polynomials that are positive on an interval}, Trans. Amer. Math. Soc., 352 (2000), pp. 4677--4692. Real polynomials: analytic properties, etc., Symbolic computation and algebraic computation, Semialgebraic sets and related spaces
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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.: Real places in function fields. Ph.d. dissertation (1983) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic and real-analytic geometry, Valued 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 Strong interaction, including quantum chromodynamics, Model quantum field theories, Statistical thermodynamics, Phase transitions (general) in equilibrium statistical mechanics, Effectivity, complexity and computational aspects of 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 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Subalgebras, congruence relations, Software, source code, etc. for problems pertaining to commutative algebra, Group actions on affine varieties, 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 Symbolic computation and algebraic computation, Computational real algebraic geometry, Learning and adaptive systems in artificial intelligence
| 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 J. Heintz, B. Kuijpers, A. Rojas Paredes, On the intrinsic complexity of elimination problems in effective algebraic geometry, arXiv:1201.4344v3. Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), 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 Computational aspects of algebraic curves, Plane and space curves, Topology of real algebraic varieties, 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 Numerical computation of solutions to systems of equations, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Toric varieties, Newton polyhedra, Okounkov bodies, Effectivity, complexity and computational aspects of algebraic geometry, Complexity and performance of numerical algorithms
| 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 Bürgisser, P.; Scheiblechner, P., On the complexity of counting components of algebraic varieties, J. Symbolic Comput., 44, 9, 1114-1136, (2009) Computational aspects of higher-dimensional varieties, Symbolic computation and algebraic computation, Parallel algorithms in 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 A. Poteaux and M. Rybowicz, Improving Complexity Bounds for the Computation of Puiseux Series over Finite Fields, Proceedings of ISSAC'15 (2015), 299-306. Symbolic computation and algebraic computation, Computational aspects of algebraic curves, 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 Real algebra, Semialgebraic sets and related spaces, 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 Effectivity, complexity and computational aspects of algebraic geometry, Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain, Affine algebraic groups, hyperalgebra constructions
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