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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), Valuation rings, Applications of tropical 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 Symbolic computation and algebraic computation, Global theory and resolution of singularities (algebro-geometric aspects), 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 Basu, S.: Efficient algorithm for computing the Euler-Poincaré characteristic of a semi- algebraic set defined by few quadratic inequalities. Comput. Complexity 15, 236-251 (2006) Semialgebraic sets and related spaces, Topology of real algebraic varieties, Effectivity, complexity and computational aspects of algebraic geometry, 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 Symbolic computation and algebraic computation, Toric varieties, Newton polyhedra, Okounkov bodies, Computational aspects of algebraic curves, Compact Riemann surfaces and uniformization
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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., Lombardi H., Schuster P.\(Spectral Schemes as Ringed Lattices\). Annals of Mathematics and Artificial Intelligence. 56, (2009), 339-360. Other constructive mathematics, Distributive lattices, 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 A. L. Chistov, ''Polynomial-time computation of the degree of a dominant morphism in zero characteristic. II,'' Zap. Nauchn. Semin. POMI, 325, 181--224 (2005). 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 Solving polynomial systems; resultants, Software, source code, etc. for problems pertaining to commutative algebra, Symbolic computation and algebraic computation, Singularities 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 Bronstein, M., Parallel Integration, J. Symbolic Computation (submitted). Differential algebra, Symbolic computation and algebraic computation, Algebraic functions and function fields 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 Mora, T., Solving polynomial equation systems, vol. IV, (2016), Cambridge University Press Research exposition (monographs, survey articles) pertaining to field theory, Computational aspects and applications of commutative rings, 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 José F. Fernando, On the Pythagoras numbers of real analytic rings, J. Algebra 243 (2001), no. 1, 321 -- 338. Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real 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 Fernando, JF, On the sustitution theorem for rings of semi-algebraic functions, J. Inst. Math. Jussieu, 14, 857-894, (2015) Semialgebraic sets and related spaces, 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 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Foundations of tropical geometry and relations with algebra, 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, Applications to coding theory and cryptography of arithmetic 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 C.A. Berenstein and A. Yger , Formules de représentation intégrale et problèmes de division , '' Diophantine Approximations and Transcendental Numbers ,'' P. Phillipon (ed.), Walter de Gruyter & Co., Berlin, 1992, 15-37. Integral representations; canonical kernels (Szegő, Bergman, etc.), Polynomials, factorization in 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 Ch. Ferrier, Hubert's 17th problem and best dual bounds in quadratic minimization. Cybernetics and System Analysis 5 ( 1998) 76-91. Zbl0972.13017 MR1712046 Real algebra, 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 Bürgisser, P.: Lower bounds and real algebraic geometry, Mathematics and computer science, 35-54 (2001) Symbolic computation and algebraic computation, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Real algebraic and real-analytic geometry, Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.), Computer graphics; computational geometry (digital and algorithmic 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 Andrews, G. E.; Baxter, R. J.: Scratchpad explorations for elliptic theta functions. Vol. 125 125, 17-33 (1990) Elliptic functions and integrals, Theta functions and curves; Schottky problem, 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 theory of quadratic forms; Witt groups and rings, Real-analytic and semi-analytic sets, 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 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 Symbolic computation and algebraic computation, Solving polynomial systems; resultants, Real algebraic sets, 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 Basu, S.: On bounding the Betti numbers and computing the euler characteristic of semi-algebraic sets. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 408-417. ACM, New York (1996) Semialgebraic sets and related spaces, Symbolic computation and algebraic computation, Analysis of algorithms and problem complexity, Étale and other Grothendieck topologies and (co)homologies, Software, source code, etc. for problems pertaining to algebraic geometry, 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 Whiteley W. Invariant computations for analytic projective geometry. J Symbolic Computation, 11: 549--578 (1991) Symbolic computation and algebraic computation, Computational aspects in algebraic geometry, Projective 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 Numerical aspects of computer graphics, image analysis, and computational geometry, Computational aspects of algebraic curves, Elliptic curves, 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 Green, M.L.: \textit{Generic initial ideals}, Six lectures on commutative algebra (Bellaterra, 1996), Progr. Math., vol. 166. Birkhäuser, Basel, 1998, pp. 119-186 Parametrization (Chow and Hilbert schemes), Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Polynomial rings and ideals; rings of integer-valued polynomials, 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 Huber B., SIAM J. Control Optim. 38 (4) pp 1265-- (2000) Enumerative problems (combinatorial problems) in algebraic geometry, Pole and zero placement problems, Numerical computation of solutions to systems of equations, Symbolic computation and algebraic computation, Geometric methods, Grassmannians, Schubert varieties, flag 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 Dahan, X., Schost, É: Sharp estimates for triangular sets. In: Proceedings of ISSAC 2004, pp. 103-110. ACM Press (2004) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Heights, 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 Solving polynomial systems; resultants, Geometric aspects of numerical algebraic geometry, 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 Mora, T.: An algorithm to compute the equations of tangent cones. In: Calmet, J.(ed.) Proc. EUROCAM '82. Lecture Notes in Computer Science, vol. 144, pp. 158--165. Springer, Berlin (1982) Symbolic computation and algebraic computation, Singularities in 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 Computational aspects of higher-dimensional varieties, Global theory and resolution of singularities (algebro-geometric aspects), Positive characteristic ground fields in algebraic geometry, Symbolic computation and algebraic computation, Toric varieties, Newton polyhedra, Okounkov bodies
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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 Actions of groups on commutative rings; invariant theory, Solving polynomial systems; resultants, 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 Brown, C.W.: QEPCAD B--a program for computing with semi-algebraic sets using CADs. ACM SIGSAM Bulletin 37(4), 97--108 (2003). http://www.cs.usna.edu/\(\sim\)qepcad/B/QEPCAD.html Symbolic computation and algebraic computation, Semialgebraic sets and related spaces, 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 Greuel, G. -M.; Pfister, G.; Schönemann, H.: Singular - a computer algebra system for polynomial computations. (2009) 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 Effectivity, complexity and computational aspects of algebraic geometry, 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 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Parametrization (Chow and Hilbert schemes), 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, Effectivity, complexity and computational aspects of algebraic geometry, 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 Applications of methods of algebraic \(K\)-theory in algebraic geometry, Algebraic moduli problems, moduli of vector bundles, Vector bundles on curves and their moduli, Computational aspects of higher-dimensional varieties, \(K\)-theory of 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 Symbolic computation and algebraic computation, Proceedings, conferences, collections, etc. pertaining to computer science, Proceedings, conferences, collections, etc. pertaining to number theory, Proceedings, conferences, collections, etc. pertaining to field theory, Proceedings, conferences, collections, etc. pertaining to commutative algebra, Proceedings, conferences, collections, etc. 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 P. Bürgisser, J. M. Landsberg, L. Manivel and J. Weyman, An Overview of Mathematical Issues Arising in the Geometric Complexity Theory Approach to VP{\currency}VNP. \textit{SIAM Journal on Computing }40 (2011), 1179-- 1209.arXiv:0907.2850.Zbl 1252.68134 MR 2861717 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Effectivity, complexity and computational aspects of algebraic geometry, Symmetric groups, Geometric invariant 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 T. Lickteig, On semialgebraic decision complexity, Technical Report TR-90-052, International Computer Science Institute, Berkeley, and Universität Tübingen, Habilitationsschrift, to appear. Analysis of algorithms and problem complexity, 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 Jeronimo, G.; Perrucci, D., A probabilistic symbolic algorithm to find the minimum of a polynomial function on a basic closed semialgebraic set, Discrete comput. geom., 52, 2, 260-277, (2014) Nonlinear programming, Semialgebraic sets and related spaces, Abstract computational complexity for mathematical programming problems, Symbolic computation and algebraic computation, Software, source code, etc. for problems pertaining to algebraic 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 Zhonggang Zeng, The closedness subspace method for computing the multiplicity structure of a polynomial system, Interactions of classical and numerical algebraic geometry, Contemp. Math., vol. 496, Amer. Math. Soc., Providence, RI, 2009, pp. 347 -- 362. Numerical computation of solutions to systems of equations, Approximation algorithms, Symbolic computation and algebraic computation, Computational aspects in algebraic geometry, Multiplicity of solutions of equilibrium problems in solid mechanics, 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 F. Sottile, \textit{From enumerative geometry to solving systems of polynomial equations}, in Computations in Algebraic Geometry with Macaulay 2, ACM, New York, 2002, pp. 101--128. Enumerative problems (combinatorial problems) in algebraic geometry, Numerical computation of solutions to systems of equations, Polynomial rings and ideals; rings of integer-valued polynomials, 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 Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler, Numerical irreducible decomposition using PHCpack, Algebra, geometry, and software systems, Springer, Berlin, 2003, pp. 109 -- 129. Numerical computation of solutions to systems of equations, Packaged methods for numerical algorithms, Polynomials, factorization in commutative rings, Computational aspects of higher-dimensional varieties, Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.), 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 Burési J., Mahé L.: Reducing inequalities with bounds. Math. Z. 227(2), 231--243 (1998) MR 98j:14073 Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Forms over real 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 Foundations of tropical geometry and relations with algebra, 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 Quadratic forms over general fields, Forms over real fields, Algebraic theory of quadratic forms; Witt groups and rings, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Algebraic cycles
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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 Cryptography, Computational aspects of algebraic surfaces, 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 M. Marshall, \textit{Positive Polynomials and Sums of Squares}, Math. Surveys Monogr. 146, American Mathematical Society, Providence, RI, 2008, . Research exposition (monographs, survey articles) pertaining to commutative algebra, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Real algebra, Research exposition (monographs, survey articles) pertaining to field theory, Valued fields, Ordered fields, 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 Plaumann, D., Sturmfels, B., Vinzant, C.: Quartic curves and their bitangents. J. Symb. Comput. \textbf{46}(6), 712-733 (2011) (14H50 (14N05)) Computational aspects of algebraic curves, Plane and space curves, Projective 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 Gu, N.; Lazard, D.; Rouillier, F.; Xiang, Y.: Using computer algebra to certify the global convergence of a numerical optimization process, Mathematics in computer science 1, No. 2, 291-304 (2007) Signal theory (characterization, reconstruction, filtering, etc.), Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Semialgebraic sets and related spaces, Numerical methods for mathematical programming, optimization and variational techniques, 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 History of algebraic geometry, History of mathematics in the 20th century, History of mathematics in the 21st century, Computational aspects of algebraic curves, Geometric aspects of numerical algebraic geometry, Computer-aided design (modeling of curves and surfaces), Computer science aspects of computer-aided design, 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 Nonstandard models in mathematics, Semialgebraic sets and related spaces, Real-analytic and semi-analytic sets, Foundations: limits and generalizations, elementary topology of the line, Asymptotic approximations, asymptotic expansions (steepest descent, etc.), 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 Draisma, J., Horobet, E., Ottaviani, G., Sturmfels, B., Thomas, R.R.: The euclidean distance degree. In: Proceedings of the 2014 Symposium on Symbolic-Numeric Computation, pp. 9-16 (2014) Symbolic computation and algebraic computation, Real algebraic sets, 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 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 Semialgebraic sets and related spaces, 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 Quantum state spaces, operational and probabilistic concepts, Applications of differential geometry to physics, Dynamic and nonequilibrium phase transitions (general) in statistical mechanics, Effectivity, complexity and computational aspects of algebraic geometry, Quantum chaos
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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 Combinatorial aspects of matroids and geometric lattices, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Relations with arrangements of hyperplanes, 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.~M.~Landsberg 2014 New lower bounds for the rank of matrix multiplication \textit{SIAM J.~Comput.} 43 1 144--149 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Analysis of algorithms and problem complexity, Effectivity, complexity and computational aspects of algebraic geometry, Computational aspects and applications of 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 J. Böhm, A. Frühbis-Krüger, A smoothness test for higher codimension. J. Symb. Comput. 86, 153-165 (2018) 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 Computational aspects related to convexity, Semirings, 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 Actions of groups on commutative rings; invariant theory, 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 Singularities of curves, local rings, Singularities of surfaces or higher-dimensional varieties, Symbolic computation and algebraic computation, Rational and ruled surfaces, 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 SCHMID, J.:Eine Bemerkung zu den höheren Pythagoraszahlen reeller Körper, manuscripta math. 61, (1988)195--202 Forms over real fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), 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 S Y Orevkov, Quasipositivity problem for \(3\)-braids, Turkish J. Math. 28 (2004) 89 Braid groups; Artin groups, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), Generators, relations, and presentations of groups, Plane and space 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 Decoding, Geometric methods (including applications of algebraic geometry) applied to coding theory, Symbolic computation and algebraic computation, Applications to coding theory and cryptography of arithmetic 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 Algebraic geometry, Mechanization of proofs and logical operations, Transcendental methods of algebraic geometry (complex-analytic aspects), Functor categories, comma categories
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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.), Real algebra, Real-analytic and semi-analytic 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 Computational aspects in algebraic geometry, 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 Fibrations, degenerations in algebraic geometry, Effectivity, complexity and computational aspects of algebraic geometry, Critical points of functions and mappings on manifolds, Singularities of differentiable mappings in differential topology, Semialgebraic sets and related spaces, Global theory of complex singularities; cohomological properties, Topology of real algebraic varieties
| 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 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 Sonia Pérez-Díaz and J. Rafael Sendra, Computation of the degree of rational surface parametrizations, J. Pure Appl. Algebra 193 (2004), no. 1-3, 99 -- 121. Computational aspects of algebraic surfaces, 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 Ramella, I.: Ideals of points in generic position: a polynomial algorithm for computing a minimal set of generators. Ricerche di matematica 43, 205-217 (1994) Symbolic computation and algebraic computation, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Analysis of algorithms and problem complexity, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
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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, Sums of squares and representations by other particular quadratic forms, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real 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 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.), Software, source code, etc. for problems pertaining to commutative algebra, 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 Carlos Andradas and Jesús M. Ruiz, On local uniformization of orderings, Recent advances in real algebraic geometry and quadratic forms (Berkeley, CA, 1990/1991; San Francisco, CA, 1991) Contemp. Math., vol. 155, Amer. Math. Soc., Providence, RI, 1994, pp. 19 -- 46. Real algebraic and real-analytic geometry, Valuations and their generalizations for commutative rings, 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 Effectivity, complexity and computational aspects of algebraic geometry, Secant varieties, tensor rank, varieties of sums of powers
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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, Formal power series rings, 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 Geometric aspects of tropical varieties, Combinatorial aspects of tropical 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 Bernd Bank, Marc Giusti & Joos and Heintz, ``Generalized polar varieties: geometry and algorithms'', J. Complexity21 (2005) no. 4, p. 377-412 Real algebraic sets, Singularities in algebraic geometry, Computational aspects in algebraic geometry, Analysis of algorithms and problem complexity, 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 Krone, Robert: Numerical algorithms for dual bases of positive-dimensional ideals. J. algebra appl. 12, No. 06, 1350018 (2013) 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 Finite ground fields in algebraic geometry, Symbolic computation and algebraic computation, Algebraic coding theory; cryptography (number-theoretic aspects), Analysis of algorithms and problem complexity, Toeplitz operators, Hankel operators, Wiener-Hopf operators, Rational and birational maps, Computational aspects in algebraic geometry, Applications to coding theory and cryptography of arithmetic 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, Projective techniques in algebraic geometry, Computational aspects of higher-dimensional varieties, Effectivity, complexity and computational aspects of algebraic geometry, Multilinear algebra, tensor calculus, Vector and tensor algebra, theory of invariants
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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. Dupont, D. Lazard, S. Lazard, and S. Petitjean, A new algorithm for the robust intersection of two general quadrics, in: Proc. 19th Annu. ACM Sympos. Comput. Geom. 2003, pp. 246 -- 255 Computer graphics; computational geometry (digital and algorithmic aspects), 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 Caruso, F.: The SARAG library. In: Proceedings of the ICMS '06. Springer, Berlin (2006). Stable version included in maxima: http://maxima.sourceforge.net/, last version online at http://perso.univ-rennes1.fr/marie-francoise.roy/bpr-posted1.html Software, source code, etc. for problems pertaining to algebraic geometry, Real algebraic and real-analytic geometry, Symbolic computation and algebraic computation, Software, source code, etc. for problems pertaining to computer science, Software, source code, etc. for problems pertaining to field 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 Lazard, Daniel, Thirty years of polynomial system solving, and now? J, Symb. Comput., 44, 222-231, (2009) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, Computational aspects in algebraic geometry, 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 A. L. Chistov, ''Polynomial-time computation of the degree of algebraic varieties in zero characteristic and its applications,'' Zap. Nauchn. Semin. POMI, 258, 7--59 (1999). Computational aspects of higher-dimensional varieties, Real algebraic sets, 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 J. Ponce, B. Sturmfels, and M. Trager, \textit{Congruences and concurrent lines in multi-view geometry}, Avd. Appl. Math., 88 (2017), pp. 62--91, . Computational aspects of higher-dimensional varieties, Projective analytic geometry, 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 Cioffi, F., Lella, P., Marinari, M.G., Roggero, M.: Minimal Castelnuovo-Mumford regularity fixing the Hilbert polynomial. arXiv:1307.2707 [math.AG] Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Syzygies, resolutions, complexes and commutative rings, Symbolic computation and algebraic computation, Calculation of integer sequences, 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 Ludwig Bröcker, Minimale Erzeugung von Positivbereichen, Geom. Dedicata 16 (1984), no. 3, 335 -- 350 (German). Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Forms over real 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 Computational aspects of algebraic curves, Symbolic computation and algebraic computation, Riemann surfaces; Weierstrass points; gap sequences
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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 articles of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Proceedings, conferences, collections, etc. pertaining to numerical analysis, 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 L. Bröcker, On the reduction of semialgebraic sets by real valuations, in: ``Recent advances in real algebraic geometry and quadratic forms'', Contemp. Math., 155, Amer. Math. Soc., Providence, RI, 1994, pp. 75-95. Zbl0826.14038 MR1260702 Semialgebraic sets and related spaces, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Non-Archimedean valued fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Valuation 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, 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 Delzell, C. N.: Non-existence of analytically varying solutions to Hilbert's 17th problem. Contemp. math. 155, No. 73, 107-117 (1994) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real-analytic and semi-analytic sets, Sums of squares and representations by other particular quadratic forms
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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 ordinary differential equations, Computational aspects of algebraic curves, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, 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 Kytmanov, A.A.; Shchuplev, A.V., An algorithm for constructing toric compactifications, Program. Comput. Software, 39, 207-211, (2013) Symbolic computation and algebraic computation, Toric varieties, Newton polyhedra, Okounkov bodies, Compactification of 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 Fortuna, E.; Gianni, P.; Parenti, P.: Some constructions for real algebraic curves. Pubbl. dip. Mat. univ. Pisa, 1.285.1441 (2003) Real algebraic sets, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, 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 S. Basu. A complex analogue of Toda's theorem. \textit{Found. Comput. Math}., 12(3):327-362, 2012. Classical real and complex (co)homology in algebraic geometry, Effectivity, complexity and computational aspects of algebraic geometry, Complexity classes (hierarchies, relations among complexity classes, 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 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 Effectivity, complexity and computational aspects of algebraic geometry, Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions
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