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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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. Sombra, ''Bounds for the Hilbert function of polynomial ideals and for the degrees in the Nullstellensatz,'' \textit{J. Pure Appl. Algebra}, \textbf{117/118}, 565-599 (1996). Relevant commutative algebra, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, 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 Linear programming, 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 Software, source code, etc. for problems pertaining to 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 S. Baktir and B. Sunar, ''Optimal Tower Fields,'' IEEE Trans. Comp. 53(10), 1231 (2004). Mathematical problems of computer architecture, Algebraic coding theory; cryptography (number-theoretic aspects), Symbolic computation and algebraic computation, Cryptography, 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 Geometric invariant theory, Effectivity, complexity and computational aspects of algebraic geometry, Linear preserver problems, Lie algebras of linear algebraic groups, Representations of quivers and partially ordered sets, Analysis of algorithms and problem complexity, Algebraic systems of matrices, Actions of groups on commutative rings; invariant theory, 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 Grasegger, G.; Lastra, A.; Sendra, J. R.; Winkler, F., A solution method for autonomous first-order algebraic partial differential equations, J. Comput. Appl. Math., 300, 119-133, (2016) Symbolic computation and algebraic computation, Hypersurfaces and algebraic geometry, Geometric theory, characteristics, transformations in context of PDEs
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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. Keyser, T. Culver, D. Manocha, and S. Krishnan, Efficient and Exact Manipulation of Algebraic Points and Curves, Comput. Aided. Geom. Design, 2000, 32(11): 649--662. Numerical interpolation, Computational aspects of higher-dimensional varieties, Symbolic computation and algebraic computation, Computer science aspects of computer-aided design, 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 \(4\)-folds, Fano varieties, Computational aspects of algebraic 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 Pérez-Díaz, S.; Sendra, J. R.; Villarino, C., Computing the Singularities of Rational Surfaces, Math. Comput., 84, 294, 1991-2021, (2015) Computational aspects of algebraic surfaces, Singularities of surfaces or 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 Andradas, C.; Gamboa, J. M., On projections of real algebraic varieties, Pacific J. Math., 121, 2, 281-291, (1986) Real algebraic and real-analytic geometry, Real-analytic and Nash manifolds, 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 Projective techniques in algebraic geometry, Multilinear algebra, tensor calculus, Real algebraic sets, Computational aspects of higher-dimensional varieties, Polynomials, factorization in commutative rings, 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 Computer graphics; computational geometry (digital and algorithmic aspects), Effectivity, complexity and computational aspects of algebraic geometry, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Combinatorial complexity of geometric structures
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Toshinori Oaku, Nobuki Takayama, and Uli Walther, A localization algorithm for \?-modules, J. Symbolic Comput. 29 (2000), no. 4-5, 721 -- 728. Symbolic computation in algebra, analysis, and geometry (Berkeley, CA, 1998). Modules of differentials, Symbolic computation and algebraic computation, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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. Kapur, Y. Cai, An algorithm for computing a Gröbner basis of a polynomial ideal over a ring with zero divisors. Math. Comput. Sci. 2, 601--634 (2009) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), 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 Hyperfunctions, Holomorphic functions of several complex variables, Toric varieties, Newton polyhedra, Okounkov bodies, Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions), Combinatorial aspects of matroids and geometric lattices, 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 Number-theoretic algorithms; complexity, Symbolic computation and algebraic computation, Polynomials in number theory, Polynomials in real and complex fields: factorization, Parametrization (Chow and Hilbert 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 Fekak ( A. ) .- Exposants de Łojasiewicz pour les fonctions semi-algébriques , C.R.A.S. Paris, t. 310, Série 1, 193 - 196 ( 1990 ). Zbl 0706.14036 Real algebraic 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 Complex multiplication and abelian varieties, Effectivity, complexity and computational aspects of algebraic geometry, Number-theoretic algorithms; complexity, Complex multiplication and moduli of abelian varieties
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Schemes and morphisms, Combinatorial aspects of matroids and geometric lattices, Foundations of tropical geometry and relations with algebra, Ordered fields, Rigid 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 Stengle, G., Yousef, H.: The spherical spectrum of a graded ring. Geom. Dedic. 52, 195--208 (1994) Relevant commutative algebra, Semialgebraic sets and related spaces, Ordered rings, algebras, modules, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Graded 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 Mehlhorn, K.; Sagraloff, M.; Wang, P.: From approximate factorization to root isolation, 283-290 (2013) Symbolic computation and algebraic computation, Computational aspects of algebraic curves, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Numerical computation of roots of polynomial equations, Analysis of algorithms
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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, 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 Arslan, F.; Sipahi, N.; Şahin, N., Monomial curve families supporting Rossi's conjecture, J. symbolic comput., 55, 10-18, (2013) Singularities of curves, local rings, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Semigroups, 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 Wu, X.; Zhi, L., Determining singular solutions of polynomial systems via symbolic--numeric reduction to geometric involutive forms, Journal of Symbolic Computation, 47, 3, 227-238, (2012) Solving polynomial systems; resultants, Complexity and performance of numerical algorithms, 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 Wu W T, \textit{Mathematics Mechanization}, Science Press and Kluwer Academic Publishers, Beijing, 2000. Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science, History of Chinese mathematics, Polynomials in real and complex fields: location of zeros (algebraic theorems), Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Computational aspects of algebraic curves, Elementary problems in Euclidean geometries, Error analysis and interval analysis, Artificial intelligence for robotics, 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 Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Complexity and performance of 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 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 Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Valuations and their generalizations for 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 Sabeti, R, Numerical-symbolic exact irreducible decomposition of cyclic-12, LMS J. Comput. Math., 14, 155-172, (2011) Numerical computation of solutions to systems of equations, Symbolic computation and algebraic computation, Computational aspects in algebraic geometry, Polynomials, factorization in commutative rings, Numerical computation of roots of polynomial 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 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Complex spaces, 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 M Lederer. The vanishing ideal of a finite set of closed points in affine space, J Pure Appl Algebra, 2008, 212: 1116--1133. Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Effectivity, complexity and computational aspects of algebraic geometry, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Computational real 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 Dellière, S.: On the links between triangular sets and dynamic constructible closure. J. pure appl. Algebra 163, No. 1, 49-68 (2001) 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 Genetic algebras, Problems related to evolution, Geometric aspects of numerical algebraic geometry, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Divisors, linear systems, invertible sheaves, Real algebraic 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 A. Dickenstein and I. Z. Emiris, \textit{Solving Polynomial Equations: Foundations, Algorithms, and Applications}, Algorithms Comput. Math. 14, Springer, New York, 2005. Proceedings, conferences, collections, etc. pertaining to field theory, Computational aspects in algebraic geometry, Proceedings, conferences, collections, etc. pertaining to commutative algebra, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Proceedings, conferences, collections, etc. pertaining to computer science, Collections of articles of miscellaneous specific interest, Computational aspects and applications of commutative rings, Symbolic computation and algebraic computation, Separable extensions, Galois 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 Fibrations, degenerations in algebraic geometry, Local complex singularities, Topology of real algebraic varieties, 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, Topological properties of mappings on 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 Ramsey theory, Generalized Ramsey theory, Semialgebraic sets and related spaces, Fixed points and coincidences in algebraic topology, Combinatorial aspects of 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 Halfpap, Jennifer; Lebl, Jiří, Signature pairs of positive polynomials, Bull. Inst. Math. Acad. Sin. (N.S.), 2304-7909, 8, 2, 169-192, (2013) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Semialgebraic sets and related spaces, Quadratic and bilinear forms, inner products, Holomorphic functions of several complex variables
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Riemann-Roch theorems, 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 Foundations of tropical geometry and relations with algebra, 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 N. Vorobjov, Deciding consistency of systems of polynomial in exponent inequalities in subexponential time. InEffective Methods in Algebraic Geometry, Birkhäuser, Boston, 1991, 491-501. Decidability of theories and sets of sentences, 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 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Computational aspects in algebraic geometry, Symbolic computation and algebraic computation, Software, source code, etc. for problems pertaining to commutative algebra
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation M. V. Catalisano, L. Chiantini, A. V. Geramita, and A. Oneto Waring-like decompositions of polynomials, 1, Linear Algebra Appl. 533 (2017), 311--325. Projective techniques in algebraic geometry, Computational aspects of higher-dimensional varieties, Effectivity, complexity and computational aspects of algebraic geometry, Polynomials, factorization in commutative rings, Special 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 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Semialgebraic sets and related spaces, Topology of real algebraic 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 Andradas, C.; Bröcker, L.; Ruiz, J.-M., \textit{Constructible Sets in Real Geometry}, 33, (1996), Springer-Verlag, Berlin Real algebraic and real-analytic geometry, Analytical algebras and rings, Research exposition (monographs, survey articles) pertaining to field theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to commutative algebra, 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 Berr, R.: Null- and positivstellensätze for generalized real closed fields. J. pure appl. Algebra 125, 19-53 (1998) Ordered fields, Real algebraic sets, General valuation theory for fields, Model theory of 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 Efremenko, K., Landsberg, J. M., Schenck, H., Weyman, J. (2015). On minimal free resolutions and the method of shifted partial derivatives in complexity theory (CoRR abs/1504.05171). Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Syzygies, resolutions, complexes and commutative rings, Solving polynomial systems; resultants, Group actions on varieties or schemes (quotients), Symmetric groups, 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 Huang, Y.; Ngô, L. X C.; Winkler, F., Rational general solutions of trivariate rational differential systems, Mathematics in Computer Science, 6, 361-374, (2012) Symbolic computation and algebraic computation, Plane and space curves, Explicit solutions, first integrals of ordinary differential equations
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Software, source code, etc. for problems pertaining to algebraic geometry, Geometric aspects of numerical algebraic geometry, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), 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 Computational real algebraic geometry, Semialgebraic sets and related spaces, 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.), 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 Algebraic coding theory; cryptography (number-theoretic aspects), Elliptic 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 Computational aspects in algebraic geometry, Germs of analytic sets, local parametrization, Real-analytic sets, complex Nash functions, 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 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 Toric varieties, Newton polyhedra, Okounkov bodies, Lattice polytopes in convex geometry (including relations with commutative algebra and 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 Becher K.J., Van Geel J.: Sums of squares in function fields of hyperelliptic curves. Math. Z. 209, 829--844 (2009) Sums of squares and representations by other particular quadratic forms, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), 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 DOI: 10.1007/s00037-003-0180-0 Effectivity, complexity and computational aspects of algebraic geometry, Elliptic curves, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Elliptic curves over global fields, Global ground 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 N. Vorobjov. The complexity of deciding consistency of systems of polynomial in exponent inequalities.J. Symbolic Comput.,13, 139--173, 1992. Analysis of algorithms and problem complexity, Symbolic computation and algebraic computation, Computational aspects in algebraic geometry, Real algebraic sets, Nonstandard models of arithmetic, 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 Rational and birational maps, Finite ground fields in algebraic geometry, Applications to coding theory and cryptography of arithmetic geometry, Effectivity, complexity and computational aspects of algebraic geometry, Isogeny, Elliptic curves
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation M. Marshall, ''Real Reduced Multirings and Multifields,'' J. Pure Appl. Algebra 205, 452--468 (2006). Semialgebraic sets and related spaces, Real algebra, 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 Michael Shub and Steve Smale, On the intractability of Hilbert's Nullstellensatz and an algebraic version of ''\?\?\?=\??'', Duke Math. J. 81 (1995), no. 1, 47 -- 54 (1996). A celebration of John F. Nash, Jr. Complexity of computation (including implicit computational complexity), Relevant commutative algebra, Decidability (number-theoretic aspects), Analysis of algorithms and problem complexity, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Eberhard Becker, On the real spectrum of a ring and its application to semialgebraic geometry, Bull. Amer. Math. Soc. (N.S.) 15 (1986), no. 1, 19-60. Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Varieties and morphisms, Other model constructions, Relevant commutative algebra
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation M. Elkadi, Une version effective du thèoréme de Briancon Skoda dans le cas algébrique discret, Acta Arith., To appear. Analytic algebras and generalizations, preparation theorems, Integral representations; canonical kernels (Szegő, Bergman, etc.), Effectivity, complexity and computational aspects of algebraic geometry, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation [9]Z. Jelonek, On the generalized critical values of a polynomial mapping, Manuscripta Math. 110 (2003), 145--157. Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Effectivity, complexity and computational aspects of algebraic geometry, Affine analytic geometry, Euclidean analytic geometry, Linear transformations, semilinear transformations
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Parametrization (Chow and Hilbert schemes), Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Petitjean, S. 1994a. Automating the construction of stationary multiple-point classes. In Proceedings of ISSAC'94 (International Symposium on Symbolic and Algebraic Computation), Oxford, United Kingdom, ACM Press, pp. 9-14. Computer graphics; computational geometry (digital and algorithmic aspects), Enumerative problems (combinatorial problems) 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 Bertone, C., Quasi-stable ideals and Borel-fixed ideals with a given Hilbert polynomial, Appl. Algebra Engrg. Comm. Comput., 26, 6, 507-525, (2015) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Effectivity, complexity and computational aspects of algebraic geometry, Combinatorial aspects of 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 Martin del Campo, A.; Rodriguez, J.I., Critical points via monodromy and local methods, J. symb. comput., 79, 3, 559-574, (2017) Algebraic 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 [10]J. Kollár, Effective Nullstellensatz for arbitrary ideals, J. Eur. Math. Soc. 1 (1999), 313--337. Effectivity, complexity and computational aspects of algebraic geometry, Relevant commutative algebra, Polynomials in number theory, Polynomials over commutative rings, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Formal methods and deformations 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 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 Computer-aided design (modeling of curves and surfaces), Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Computational aspects of algebraic curves, Symbolic computation and algebraic computation, Numerical computation of roots of polynomial equations, Numerical computation of solutions to systems of equations
| 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 Max-plus and related algebras, Linear equations (linear algebraic aspects), Semirings, 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 Sendra, J. Rafael; Sevilla, David; Villarino, Carlos, Covering rational ruled surfaces, Math. comp., 86, 308, 2861-2875, (November 2017) Computational aspects of algebraic 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 Model theory of ordered structures; o-minimality, Rational points, 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 Intersection theory, characteristic classes, intersection multiplicities in algebraic 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 Arcs and motivic integration, Computational aspects of algebraic curves, Symbolic computation and algebraic computation, Grothendieck topologies and Grothendieck topoi
| 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 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
| 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 Rational and ruled surfaces, Divisors, linear systems, invertible sheaves, Picard groups, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, 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 Polynomials, factorization in commutative rings, Algebraic numbers; rings of algebraic integers, Number-theoretic algorithms; complexity, Algebraic number theory computations, 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 Hermitian, skew-Hermitian, and related matrices, Matrices of integers, Grassmannians, Schubert varieties, flag manifolds, 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, Singularities of surfaces or higher-dimensional varieties, Computational aspects of algebraic surfaces
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Software, source code, etc. for problems pertaining to algebraic geometry, Arithmetic aspects of dessins d'enfants, Belyĭ theory, Dessins d'enfants theory, 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 Equations in general fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Special surfaces, Determinants, permanents, traces, other special matrix functions, Linear transformations, semilinear transformations, Euclidean analytic 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 Chen, C., Davenport, J.H., May, J., Moreno Maza, M., Xia, B., Xiao, R.: Triangular decomposition of semi-algebraic systems. In: Proceedings of ISSAC 2010, pp. 187--194. ACM, New York (2010) Symbolic computation and algebraic computation, Semialgebraic sets and related spaces
| 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, Polynomials, factorization in commutative rings, Interpolation in approximation theory, 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 Jacobian problem, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Effectivity, complexity and computational aspects of algebraic geometry, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
| 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 Becker, E.: Valuations and real places in the theory of formally real fields, in [10] Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Forms over real fields, Algebraic theory of quadratic forms; Witt groups and rings, Valued fields, 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 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Mixed Hodge theory of singular varieties (complex-analytic aspects), Characteristic classes and numbers in differential topology, 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, Ramification problems in algebraic geometry, Polynomial rings and ideals; rings of integer-valued polynomials
| 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 E. Becker: ?Extended Artin-Schreier theory of fields?, Rocky Mountain J. of Math., vol. 14, \# 4, Fall 1984 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Model theory of fields, Research exposition (monographs, survey articles) pertaining to field theory, Normed fields, Real algebraic and real-analytic geometry, Forms of degree higher than two, Separable extensions, Galois theory, Decidability and field theory, Model-theoretic 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 Symbolic computation and algebraic computation, Real algebraic sets, Analysis of 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 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, Ideals and multiplicative ideal theory in commutative rings, Relevant commutative algebra, Analysis of algorithms and problem complexity
| 0
|
Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Semialgebraic sets and related spaces, Sums of squares and representations by other particular quadratic forms, Forms over real fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Convex 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 DOI: 10.1016/j.jsc.2010.08.011 Computational aspects of algebraic curves, Symbolic computation and algebraic computation
| 0
|
Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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
| 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 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
| 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 Alexander Prestel, On the axiomatization of PRC-fields, Methods in mathematical logic (Caracas, 1983) Lecture Notes in Math., vol. 1130, Springer, Berlin, 1985, pp. 351 -- 359. Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Rational points, Real algebraic and real-analytic 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 Li, W.; Yuan, C. M.; Gao, X. S., Sparse differential resultant for Laurent differential polynomials, Found. Comput. Math., 15, 2, 451-517, (2015) Differential algebra, Symbolic computation and algebraic computation, Toric varieties, Newton polyhedra, Okounkov bodies, Computational aspects in algebraic geometry
| 0
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