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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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, Arithmetic ground fields for curves, Curves over finite and local fields, Symbolic computation and algebraic computation, Polynomials over finite fields, Matrices over special rings (quaternions, finite 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 Symbolic computation and algebraic computation, Ramification problems in algebraic geometry, Numerical computation of matrix norms, conditioning, scaling
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Santos, V., Quaresma, P., Campos, H., Marić, M.: Web Geometry Laboratory: case studies in Portugal and Serbia. In: Interactive Learning Environments, pp. 1-19 (Dec 2016) (online). 10.1080/10494820.2016.1258715 Computational aspects in algebraic geometry, Analytic and descriptive geometry, Symbolic computation and algebraic computation, 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 Software, source code, etc. for problems pertaining to algebraic geometry, Symbolic computation and algebraic computation, Geometric aspects of numerical algebraic geometry, Abstract computational complexity for mathematical programming problems
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Winkler, F., \textit{Polynomial Algorithms in Computer Algebra}, (1996), Springer, Vienna, Austria Symbolic computation and algebraic computation, Discrete mathematics in relation to computer science, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Computational aspects of algebraic curves, Number-theoretic algorithms; 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 I. E. Shparlinski, \textit{Finite Fields: Theory and Computation}, Kluwer Academic Publ., Dordrecht, 1999 (to appear). Finite fields and commutative rings (number-theoretic aspects), Research exposition (monographs, survey articles) pertaining to number theory, Number-theoretic algorithms; complexity, Algebraic coding theory; cryptography (number-theoretic aspects), Cryptography, Geometric methods (including applications of algebraic geometry) applied to coding theory, Polynomials over finite fields, Exponential sums, Arithmetic theory of polynomial rings over finite fields, Random number generation in numerical analysis, Analysis of algorithms and problem complexity, Symbolic computation and algebraic computation, Algebraic number theory computations, Rational points, Curves over finite and local fields, Factorization, Primality
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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, Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Geometric invariant theory, Symmetric groups, Representations of finite symmetric groups, Symbolic computation and algebraic computation, Image processing (compression, reconstruction, etc.) in information and communication theory, Biomedical imaging and signal processing
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Lickteig, T.; Meer, K.: Semi-algebraic complexity--additive complexity of diagonalization of quadratic forms. Revista matemática de la universidad complutense de Madrid 10 (1997, to appear) Analysis of algorithms and problem complexity, Symbolic computation and algebraic computation, Semialgebraic sets and related spaces, Nash functions and manifolds
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Krick, T.; Pardo, L. M.: Une approche informatique pour l'approximation diophantienne. C. R. Acad. sci. Paris sér. I 318, 407-412 (1994) Effectivity, complexity and computational aspects of algebraic geometry, Number-theoretic algorithms; complexity, Analysis of algorithms and problem complexity, 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 Kim, M.: Relating decision and search algorithms for rational points on curves of higher genus. Arch. Math. Logic 42, 563-568 (2003) Decidability (number-theoretic aspects), Rational points, Decidability of theories and sets of sentences, Global ground fields 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 Effectivity, complexity and computational aspects of algebraic geometry, Syzygies, resolutions, complexes and commutative rings, Computational homological algebra, Projective techniques 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 Symbolic computation and algebraic computation, Computational aspects of algebraic surfaces
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Power series rings, Effectivity, complexity and computational aspects of algebraic geometry, Valuations, completions, formal power series and related constructions (associative rings and algebras), Algebras of analytic functions of one complex variable, Power series, series of functions of several complex variables, Algebras of 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 B. Dong, B. Yu, and Y. Yu, \textit{A symmetric homotopy and hybrid polynomial system solving method for mixed trigonometric polynomial systems}, Math. Comp., 83 (2014), pp. 1847--1868, http://dx.doi.org/10.1090/S0025-5718-2013-02763-9. Solving polynomial systems; resultants, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Numerical computation of solutions to systems of equations, Computational aspects in algebraic geometry, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation McCallum, S.; Hong, H., On using Lazard's projection in CAD construction, J. Symb. Comput., 72, 65-81, (2016) Polynomials, factorization in commutative rings, Symbolic computation and algebraic computation, Cylindric and polyadic algebras; relation algebras, 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 External book reviews, Research exposition (monographs, survey articles) pertaining to numerical analysis, Computational aspects of higher-dimensional varieties, Numerical computation of roots of polynomial equations, Numerical computation of solutions to systems of equations, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Packaged methods for numerical algorithms, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Toric varieties, Newton polyhedra, Okounkov bodies, 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 Hauenstein, J. D.; Levandovskyy, V.: Certifying solutions to square systems of polynomial-exponential equations. (Sept. 2011) Computational aspects of higher-dimensional varieties, Symbolic computation and algebraic computation, Numerical computation of solutions to systems of equations
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Numerical computation of solutions to systems of equations, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Structure of families (Picard-Lefschetz, monodromy, etc.), Computational real algebraic geometry, Symbolic computation and algebraic computation, Geometric aspects of numerical 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
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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, Georg, Radical solutions of algebraic ordinary differential equations, (Nabeshima, K., Proceedings of the 2014 international symposium on symbolic and algebraic computation (ISSAC), (2014), ACM Press New York), 217-223 Symbolic computation and algebraic computation, Abstract differential equations, Computational aspects of algebraic 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 Computational aspects in algebraic geometry, Configuration theorems in linear incidence 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 Alcázar, J. G.; Sendra, J. R.: Local shape of offsets to algebraic curves, J. symbolic. Comput. 42, 338-351 (2007) Computational aspects of algebraic curves, Symbolic computation and algebraic computation, Singularities of curves, local rings, Plane and space 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 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, Software, source code, etc. for problems pertaining to convex and discrete geometry, Computational aspects related to convexity
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Polynomial optimization, Semialgebraic sets and related spaces, Semidefinite programming, Nonconvex programming, global optimization, 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 S. Beck and M. Kreuzer, ``How to compute the canonical module of a set of points'' in Algorithms in Algebraic Geometry and Applications (Santander, Spain, 1994) , Progr. Math. 143 , Birkhäuser, Basel, 1996, 51--78. Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Relevant commutative 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 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Skew fields, division rings, Brauer groups of schemes, Brauer groups (algebraic 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 E. Gross and J. I. Rodriguez, \textit{Maximum likelihood geometry in the presence of data zeros}, in Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, ISSAC '14, ACM, New York, 2014, pp. 232--239, . Symbolic computation and algebraic computation, Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Varieties and morphisms, Point estimation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Duval D (1991) Absolute factorization of polynomials: a geometric approach. SIAM J Comput 20:1--21 Symbolic computation and algebraic computation, Polynomials in real and complex fields: factorization, Algebraic functions and function fields in algebraic geometry, Divisors, linear systems, invertible sheaves, Algebraic field extensions
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Proceedings of conferences of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Proceedings, conferences, collections, etc. pertaining to field theory, Proceedings, conferences, collections, etc. pertaining to numerical analysis, Proceedings, conferences, collections, etc. pertaining to computer science, Effectivity, complexity and computational aspects of algebraic geometry, Numerical computation of solutions to systems of equations, Algorithms in computer science
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Effectivity, complexity and computational aspects of algebraic geometry, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Polynomial rings and ideals; rings of integer-valued 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 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics, Symbolic computation and algebraic computation, Toric varieties, Newton polyhedra, Okounkov bodies, Global theory and resolution of singularities (algebro-geometric aspects), Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes, 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 Fitchas, N.; Galligo, A., Nullstellensatz effectif et conjecture de Serre (théorème de Quillen-Suslin) pour le calcul formel, Math. nachr., 149, 231-253, (1990) Relevant commutative algebra, Projective and free modules and ideals 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 Eriksen, E.; Gustavsen, T. S.: Computing obstructions for existence of connections on modules, J. symbolic comput. 42, No. 3, 313-323 (2007) (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.), Cohen-Macaulay modules, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Singularities 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 Effectivity, complexity and computational aspects of algebraic geometry, \(\zeta (s)\) and \(L(s, \chi)\), 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 Computational aspects of algebraic curves, Real algebraic sets, Solving polynomial systems; resultants, 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. Iliman and T. De Wolff, \textit{Lower bounds for polynomials with simplex Newton polytopes based on geometric programming}, SIAM J. Optim., 26 (2016), pp. 1128--1146. Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic and real-analytic geometry, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Convex 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 [S1] J. Schmid,On totally positive units of real holomorphy rings Israel J. Math.85 (1994), 339--350 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 Analysis of algorithms and problem complexity, Computational aspects in algebraic geometry, Complexity classes (hierarchies, relations among complexity classes, 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 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebra, 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 Marshall M.: The Pierce--Birkhoff conjecture for curves. Can. J. Math. 44, 1262--1271 (1992) 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 Real algebra, Semialgebraic sets and related spaces, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Analysis of algorithms, 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 Semialgebraic sets and related spaces, Polynomials in real and complex fields: location of zeros (algebraic theorems), Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Polynomial optimization, Nonconvex programming, global optimization
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Real algebraic and real-analytic geometry, Noncommutative algebraic geometry, Algebras of unbounded operators; partial algebras of operators, Ordered rings, Ordered fields, Rings with involution; Lie, Jordan and other nonassociative 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 Relativistic gravitational theories other than Einstein's, including asymmetric field theories, Effectivity, complexity and computational aspects of algebraic geometry, Macroscopic interaction of the gravitational field with matter (hydrodynamics, 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 Ruiz, J. M.: Pythagorean real curve germs. J. algebra 94, 126-144 (1985) 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.), Valued fields
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Intersection theory, characteristic classes, intersection multiplicities 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 1. M. Andersson and E. Wulcan, Variants of the effective Nullstellensatz and residue calculus, in Notions of Positivity and the Geometry of Polynomials, Vol. 1731, Trends Mathematics (Birkhäuser/Springer Basel AG, Basel, 2011). genRefLink(16, 'S0129167X16500427BIB001', '10.1007%252F978-3-0348-0142-3_2'); Effectivity, complexity and computational aspects of algebraic geometry, Residues for several complex variables, Local 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 Geometric aspects of numerical algebraic geometry, Artificial neural networks and deep learning, 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 Dokken T, Thomassen JB (2003) Overview of approximate implicitization. Topics in algebraic geometry and geometric modeling. AMS Cont Math 334:169--184 Computer-aided design (modeling of curves and 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 Jean-Philippe Monnier, Anneaux d'holomorphie et Positivstellensatz archimédien, Manuscripta Math. 97 (1998), no. 3, 269 -- 302 (French, with English summary). Relevant commutative algebra, Real algebraic and real-analytic geometry, Algebraic theory of quadratic forms; Witt groups and rings, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Arithmetic rings and other special 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 Z. She, B. Xue, Z. Zheng, Algebraic analysis on asymptotic stability of continuous dynamical systems, in: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation, 2011, pp. 313-320. Symbolic computation and algebraic computation, Semialgebraic sets and related spaces, Stability of solutions to 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 Classical problems, Schubert calculus, Computational aspects of higher-dimensional varieties, Effectivity, complexity and computational aspects of algebraic geometry, Software, source code, etc. for problems pertaining to algebraic geometry, Intersection theory, characteristic classes, intersection multiplicities 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 Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Effectivity, complexity and computational aspects of algebraic geometry, Randomized 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 Y. Ren, Computing tropical varieties over fields with valuation using classical standard basis techniques. ACM Commun. Comput. Algebra 49(4), 127-129 (2015) 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 Effectivity, complexity and computational aspects of algebraic geometry, Eigenvalues, singular values, and eigenvectors, Matrix pencils, Random matrices (algebraic aspects), Numerical computation of eigenvalues and eigenvectors of matrices
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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 of conferences of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to numerical analysis, Computational aspects of algebraic curves, Proceedings, conferences, collections, etc. pertaining to computer science
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Nonlinear programming, Symbolic computation and algebraic computation, Separable extensions, Galois theory, 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 Solving polynomial systems; resultants, Software, source code, etc. for problems pertaining to commutative algebra, Numerical algebraic geometry, Geometric aspects of numerical algebraic geometry, Symbolic computation and algebraic computation, 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 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Power series rings, Effectivity, complexity and computational aspects of algebraic geometry, Valuations, completions, formal power series and related constructions (associative rings and algebras), Algebras of analytic functions of one complex variable, Power series, series of functions of several complex variables, Algebras of 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 DOI: 10.1007/BF02570760 Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Strzeboński, A.: Computation with semialgebraic sets represented by cylindrical algebraic formulas. Proceedings of the international symposium on symbolic and algebraic computation, 61-68 (2010) Symbolic computation and algebraic computation, Quantifier elimination, model completeness, and related topics, Semialgebraic sets and related spaces
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Becker, E.; Jacob, B.: Rational points on algebraic varieties over a generalized real closed field: A model theoretic approach. J. reine angew. Math. 357, 73-95 (1982) Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Model-theoretic 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 Geometric aspects of numerical algebraic geometry, Numerical algebraic geometry, Symbolic computation and algebraic computation, Foundations of tropical geometry and relations with 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 Topological rings and modules, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Relevant commutative algebra, Polynomial rings and ideals; rings of integer-valued 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 Rational points, Inseparable field extensions, Transcendental field extensions, 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 van Hoeij, M., Rational parametrizations of algebraic curves using a canonical divisor, \textit{Journal of Symbolic Computation}, 23, 2-3, 209-227, (1997) Symbolic computation and algebraic computation, Divisors, linear systems, invertible sheaves, Computational aspects of algebraic curves
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Bronstein, M., Salvy, B.: Full partial fraction decomposition of rational functions. In: ISSAC '93: Proceedings of the 1993 International Symposium on Symbolic and Algebraic Computation, pp. 157--160. ACM, New York, NY, USA (1993) Symbolic computation and algebraic computation, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function 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 Mehlhorn, K.; Sagraloff, M.; Wang, P., From approximate factorization to root isolation with application to cylindrical algebraic decomposition, J. Symb. Comput., 66, 0, 34-69, (2015) 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 Gallo, G.; Mishra, B.: Wu--ritt characteristic sets and their complexity. Discrete and computational geometry: papers from the DIMACS special year, 111-136 (1991) Symbolic computation and algebraic computation, Analysis of algorithms and problem complexity, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Varieties and morphisms, Ideals and multiplicative ideal theory in commutative rings
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation DOI: 10.1016/j.jco.2004.09.007 Polynomials, factorization in commutative rings, Computational aspects in algebraic geometry, Numerical computation of solutions to systems of equations, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Joos Heintz, Marie-Françoise Roy, and Pablo Solernó, Single exponential path finding in semi-algebraic sets. II. The general case, Algebraic geometry and its applications (West Lafayette, IN, 1990) Springer, New York, 1994, pp. 449 -- 465. Semialgebraic sets and related spaces, Analysis of algorithms and problem complexity, 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 Software, source code, etc. for problems pertaining to algebraic geometry, Symbolic computation and algebraic computation, Relevant commutative algebra, 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 Computational aspects of algebraic curves, 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 F. Sottile, R. Vakil, and J. Verschelde, \textit{Solving Schubert problems with Littlewood-Richardson homotopies}, Proc. ISSAC 2010 (Stephen M. Watt, ed.), ACM, 2010, pp. 179-186. Symbolic computation and algebraic computation, Grassmannians, Schubert varieties, flag manifolds, Classical problems, Schubert calculus
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Nabeshima, K.; Tajima, S.: Computing logarithmic vector fields associated with parametric semi-quasihomogeneous hypersurface isolated singularities. International symposium on symbolic and algebraic computation, 291-298 (2015) Symbolic computation and algebraic computation, Singularities in algebraic geometry, Complex surface and hypersurface 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 Nicolás Botbol, The implicit equation of a multigraded hypersurface, J. Algebra 348 (2011), 381 -- 401. Toric varieties, Newton polyhedra, Okounkov bodies, 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 Arithmetic rings and other special commutative rings, Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Mahé, L.: Sommes de carrés et anneaux de Witt réduits. C. R. Acad. sci. 300, 5-7 (1985) Real algebraic and real-analytic geometry, Forms over real fields, 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 E.M. Jabbouri : Sur un critère pour l'indépendance algébrique de P. Philippon , in: P. Philippon (ed.) Approximations Diophantiennes et Nombres Transcendants . W. de Gruyter, Berlin (1992) pp. 195-202. Algebraic independence; Gel'fond's method, Measures of irrationality and of transcendence, 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 Effectivity, complexity and computational aspects of algebraic geometry, Complexity classes (hierarchies, relations among complexity classes, etc.), Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), General geometric structures on low-dimensional 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 M. Kudo; S. Harashita, Superspecial curves of genus 4 in small characteristic, Finite Fields Appl., 45, 131, (2017) Curves over finite and local fields, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Rational points, Jacobians, Prym varieties, 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 Schicho, J., Inversion of birational maps with Gröbner bases, (Buchberger, B.; Winkler, F., Gröbner Bases and Applications, London Mathematical Society Lecture Note Series, vol. 251, (1998), Cambridge University Press), 495-503 Rational and birational maps, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Effectivity, complexity and computational aspects of algebraic geometry, Software, source code, etc. for problems pertaining to algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Semialgebraic sets and related spaces, PL-topology, Topological manifolds, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Numerical computation of solutions to systems of equations, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Real algebraic sets, 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 Dupont, L., Lazard, D., Lazard, S., Petitjean, S.: Near-optimal parameterization of the intersection of quadrics: I. The generic algorithm. J. Symb. Comput. 43(3), 168--191 (2008) Computational aspects of algebraic curves, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation C. Scheiderer, \textit{Sums of squares of regular functions on real algebraic varieties}, Trans. Amer. Math. Soc., 352 (1999), pp. 1039--1069. Real-analytic and semi-analytic sets, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Regular local rings, Sums of squares and representations by other particular quadratic forms, Real algebra, Other nonalgebraically closed 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 Artal Bartolo, E; Carmona Ruber, J; Cogolludo Agustín, JI, Effective invariants of braid monodromy, Trans. Amer. Math. Soc., 359, 165-183, (2007) Structure of families (Picard-Lefschetz, monodromy, etc.), Coverings of curves, fundamental group, Plane and space curves, Symbolic computation and algebraic computation, Braid groups; Artin groups, Singularities of curves, local rings
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Corless, R.M.; Diaz-Toca, G.M.; Fioravanti, M.; Gonzalez-Vega, L.; Rua, I.F.; Shakoori, A., Computing the topology of a real algebraic plane curve whose defining equations are available only ``by values'', Comput. aided geom. des., 30, 7, 675-706, (2013) Topology of real algebraic varieties, Computer-aided design (modeling of curves and surfaces), 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 Gao, X S; Chou, S C, On the theory of resolvents and its applications, Syst Sci Math Sci, 12, 17-30, (1999) Polynomial rings and ideals; rings of integer-valued polynomials, Polynomials over commutative rings, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, Relevant commutative algebra
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation R. Benedetti and J.-J. Risler, \textit{Real Algebraic and Semi-algebraic Sets}, Actualités Mathématiques, Hermann, Paris, 1990. Real algebraic and real-analytic geometry, Relevant commutative algebra, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Introductory exposition (textbooks, tutorial papers, 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 Solving polynomial systems; resultants, Computational aspects of higher-dimensional varieties, 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 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebra, Real algebraic and real-analytic geometry, Finite-dimensional division rings
| 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 Giusti, M.; Lecerf, G.; Salvy, B., A Gröbner free alternative for polynomial system solving, J. Complexity, 17, 1, 154-211, (2001) Symbolic computation and algebraic computation, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Computational aspects in algebraic geometry, 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 Agnes Szanto, Multivariate subresultants using Jouanolou's resultant matrices, J. Pure Appl. Algebra, in press Solving polynomial systems; resultants, Symbolic computation and algebraic computation, Relevant commutative algebra
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Effectivity, complexity and computational aspects of algebraic geometry, Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
| 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 CR manifolds, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), 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 Topology of real algebraic varieties, 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 Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Sums of squares and representations by other particular quadratic forms, History of algebraic geometry, Semialgebraic sets and related spaces, Real-analytic and semi-analytic sets, History of mathematics in the 20th century
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Berberich E., Kerber M., Sagraloff M.: An efficient algorithm for the stratification and triangulation of an algebraic surface. Comput. Geom. Theory Appl. (CGTA) 43(3), 257--278 (2009) Numerical aspects of computer graphics, image analysis, and computational geometry, Computer-aided design (modeling of curves and surfaces), Symbolic computation and algebraic computation, Computational aspects of algebraic surfaces, Semialgebraic sets and related spaces
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