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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Cucker, F.; Lanneau, H.; Mishra, B.; Pedersen, P.; Roy, M. F.: NC algorithms for real algebraic numbers, applicable algebra in engineering. Comm. comput. 3, 79-98 (1992) Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), 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 Seiler, W.M., Effective genericity, \textit{ {\(\delta\)}}-regularity and strong Noether position, Commun. algebra, 40, 3933-3949, (2012) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Polynomial rings and ideals; rings of integer-valued polynomials, Effectivity, complexity and computational aspects of 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 Gamboa J.\ M. and Recio T., Ordered fields with the dense orbits property, J. Pure Appl. Algebra 30 (1983), 237-246. Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Algebraic field extensions, Transcendental field extensions, Ordered fields, Real algebraic and real-analytic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Lombardi, H.; Quitté, C.; Yengui, I., Hidden constructions in abstract algebra (6) the theorem of maroscia, brewer and costa, J. pure appl. algebra, 212, 1575-1582, (2008) Projective and free modules and ideals in commutative rings, Stability for projective modules, Effectivity, complexity and computational aspects of algebraic geometry, Other constructive mathematics
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Berr, R., On real holomorphy rings, (), 47-66 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, Valuation rings, 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 Wu, Wen-Tsün, Mechanical theorem proving in geometries, (1994), Springer-Verlag Mechanization of proofs and logical operations, Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations, Symbolic computation and algebraic computation, Research exposition (monographs, survey articles) pertaining to computer science, Computer graphics; computational geometry (digital and algorithmic aspects), 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 Effectivity, complexity and computational aspects of algebraic geometry, Real polynomials: location of zeros, Real algebraic sets, Real algebra, 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 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Solving polynomial systems; resultants, Symbolic computation and algebraic computation, Effectivity, complexity and computational aspects of algebraic geometry, Group actions on affine 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 Henselian rings, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Solving polynomial systems; resultants, Effectivity, complexity and computational aspects of algebraic geometry, Other constructive mathematics
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Vorobjov, N.: Complexity of computing the local dimension of semialgebraic set. J. symbol. Comput. 27, No. 6, 565-579 (1999) Semialgebraic sets and related spaces, Symbolic computation and algebraic computation, 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 Ludwig Bröcker, On the separation of basic semialgebraic sets by polynomials, Manuscripta Math. 60 (1988), no. 4, 497 -- 508. Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, Quadratic forms over general fields
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Oaku, T.; Takayama, N., Algorithms for \(D\)-modules--restriction, tensor product, localization, and local cohomology groups, J. Pure Appl. Algebra, 156, 267-308, (2001) Commutative rings of differential operators and their modules, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Effectivity, complexity and computational aspects of algebraic geometry, Sheaves of differential operators and their modules, \(D\)-modules, Local cohomology 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 D. Bayer & D. Mumford: \textit{What can be computed in algebraic geometry?}, Computational algebraic geometry and commutative algebra (Cortona, 1991), 1--48, Sympos. Math., XXXIV, Cambridge Univ. Press, Cambridge, 1993. Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, 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 Effectivity, complexity and computational aspects of 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 Chtcherba, A.D., Kapur, D., 2002a. Constructing Sylvester-type resultant matrices using Dixon formulation. Technical Report TR-CS-2002-16. Department of Computer Science, University of New Mexico, Albuquerque, New Mexico, USA Computational aspects and applications of commutative rings, Effectivity, complexity and computational aspects of algebraic geometry, Determinants, permanents, traces, other special matrix functions, 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. Barhoumi, H. Lombardi, I. Yengui, Projective modules over polynomial rings: A constructive approach, preprint, 2006 Projective and free modules and ideals in commutative rings, Stability for projective modules, Effectivity, complexity and computational aspects of algebraic geometry, Other constructive mathematics
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Effectivity, complexity and computational aspects of algebraic geometry, 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 Kudo, M., Analysis of an algorithm to compute the cohomology groups of coherent sheaves and its applications, MI preprints 2016-1, 2016, available at Effectivity, complexity and computational aspects of algebraic geometry, (Co)homology theory in algebraic geometry, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, Applications of commutative algebra (e.g., to statistics, control theory, optimization, 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 Ordered fields, Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered 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 Real-analytic and semi-analytic sets, Quantifier elimination, model completeness, and related topics, Effectivity, complexity and computational aspects of algebraic geometry, Real-analytic functions, Semi-analytic sets, subanalytic sets, and generalizations, 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, The real holomorphy ring and sums of 2\?th powers, Real algebraic geometry and quadratic forms (Rennes, 1981) Lecture Notes in Math., vol. 959, Springer, Berlin-New York, 1982, pp. 139 -- 181. Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, Valuations and their generalizations for commutative rings, General valuation theory for fields, Real algebraic and real-analytic geometry, Waring's problem and variants, 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 Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation, Semidefinite programming, 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 Giusti, M; Yakoubsohn, JC, Multipliity hunting and approximating multiple roots of polynomials systems, Contemp. Math., 604, 105c-128, (2013) Solving polynomial systems; resultants, Effectivity, complexity and computational aspects of algebraic geometry, Numerical computation of solutions to systems of equations, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Joos Heintz, Bart Kuijpers, and Andrés Rojas Paredes, Software engineering and complexity in effective algebraic geometry, J. Complexity 29 (2013), no. 1, 92 -- 138. Analysis of algorithms, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Symbolic computation and algebraic computation, 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 Hauenstein, J.D.; Mourrain, B.; Szanto, A.; On deflation and multiplicity structure; J. Symb. Comput.: 2017; Volume 83 ,228-253. Solving polynomial systems; resultants, Symbolic computation and algebraic computation, Effectivity, complexity and computational aspects of algebraic geometry, 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 Toeplitz, Cauchy, and related matrices, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation, Toeplitz operators, Hankel operators, Wiener-Hopf operators
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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, Real algebraic sets, 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 Multilinear algebra, tensor calculus, Vector spaces, linear dependence, rank, lineability, Effectivity, complexity and computational aspects of 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 Zhao S Z, Fu H G. An extended fast algorithm for constructing the Dixon resultant matrix. Sci China Ser A-Math, 48(1): 131--143 (2005) Effectivity, complexity and computational aspects of 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 Topology of real algebraic varieties, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), 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 Massarenti, A.; Raviolo, E., The rank of \(n \times n\) matrix multiplication is at least \(3 n^2 - 2 \sqrt{2} n^{\frac{3}{2}} - 3 n\), Linear Algebra Appl., 438, 11, 4500-4509, (2013) Analysis of algorithms and problem complexity, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Effectivity, complexity and computational aspects of algebraic geometry, Computational aspects and applications of commutative rings, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Becker E., Gondard D., Notes on the space of real places of a formally real field, In: Real Analytic and Algebraic Geometry, Trento, September 21--25, 1992, de Gruyter, Berlin, 1995, 21--46 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, Real algebraic and real-analytic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Scheiblechner, P., Castelnuovo-Mumford regularity and computing the de Rham cohomology of smooth projective varieties, Found. Comput. Math., 12, 541-571, (2012) Effectivity, complexity and computational aspects of algebraic geometry, Analysis of algorithms and problem complexity, de Rham cohomology 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 Mishra, B.: Computational real algebraic geometry. In: Handbook of discrete and computational geometry. CRC Press Ser. Discret. Math. Appl., 537-556 (1997). CRC, Boca Raton Symbolic computation and algebraic computation, Semialgebraic sets and related spaces, Computational aspects in algebraic geometry, Decidability of theories and sets of sentences, Applications of computability and recursion theory, Mechanization of proofs and logical operations
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Coste, M.: Sous-ensemble algébriques réels de codimension 1. C. R. Acad. sci. 300, No. 1, 661-664 (1985) Real algebraic and real-analytic geometry, Low codimension problems in algebraic geometry, Singular homology and cohomology theory, Ordered fields, 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 Actions of groups on commutative rings; invariant theory, Polynomial rings and ideals; rings of integer-valued polynomials, Commutative rings defined by binomial ideals, toric rings, etc., Group actions on varieties or schemes (quotients), Other algebraic groups (geometric aspects), Toric varieties, Newton polyhedra, Okounkov bodies, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation, Fibrations, degenerations 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 Effectivity, complexity and computational aspects of algebraic geometry, Computational methods for problems pertaining to field theory, Polynomials, factorization in commutative rings, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation J.M. Landsberg and J. Morton, Computational complexity and geometry, book in preparation. Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Effectivity, complexity and computational aspects of algebraic geometry, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), 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 Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation, Rationally connected varieties, Derivations and 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 Symbolic computation and algebraic computation, 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 González-Vega, Laureano; Lombardi, Henri, A real Nullstellensatz and Positivstellensatz for the semipolynomials over an ordered field, J. Pure Appl. Algebra, 90, 2, 167-188, (1993) Ordered fields, Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Basu, S., Roy, M.F., Safey El Din, M., Schost, É.: A baby step-giant step roadmap algorithm for general algebraic sets. Found. Comput. Math. 14(6), 1117--1172 (2014) Effectivity, complexity and computational aspects of algebraic geometry, Real algebraic sets, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Chou S C, \textit{Mechanical Geometry Theorem Proving}, D. Reidel, Dordrecht, 1988. Projective techniques in algebraic geometry, Software, source code, etc. for problems pertaining to algebraic geometry, Questions of classical algebraic geometry, Mechanization of proofs and logical operations, 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 DOI: 10.1007/BF03322485 Field extensions, Model theory of fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Relevant commutative algebra, Decidability of theories and sets of sentences, Model-theoretic algebra, Ordered fields, Quantifier elimination, model completeness, and related topics, Algebraic number theory: local fields, Dedekind, Prüfer, Krull and Mori rings and their generalizations
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Wilson, D., Bradford, R., Davenport, J.H., England, M.: Cylindrical algebraic sub-decompositions. Math. Comput. Sci. 8, 263--288 (2014) Symbolic computation and algebraic computation, Semialgebraic sets and related spaces, 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 Valued fields, 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.), 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 Massarenti, Alex; Raviolo, Emanuele: On the rank of \(n{\times}\)n matrix multiplication Analysis of algorithms and problem complexity, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Effectivity, complexity and computational aspects of algebraic geometry, Computational aspects and applications of commutative rings, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation D. Henrion, S. Naldi, and M. Safey El Din, \textit{Exact algorithms for linear matrix inequalities}, SIAM J. Optim., 26 (2016), pp. 2512--2539. Semidefinite programming, Symbolic computation and algebraic computation, 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 Li, N; Zhi, L, Computing the multiplicity structure of an isolated singular solution: case of breadth one, J. Symb. Comput., 47, 700-710, (2012) Solving polynomial systems; resultants, Symbolic computation and algebraic computation, Complexity and performance of numerical algorithms, 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 D. Grigoriev and D. V. Pasechnik, \textit{Polynomial-time computing over quadratic maps I. Sampling in real algebraic sets}, Comput. Complexity, 14 (2005), pp. 20--52. 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), 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 Dratman E, Matera G, Waissbein A (2009) Robust algorithms for generalized Pham systems. Comput Complex 18(1): 105--154 Computational aspects of algebraic curves, Symbolic computation and algebraic computation, Formal power series rings, Effectivity, complexity and computational aspects of algebraic geometry, 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 A. Greuet and M. Safey El Din, \textit{Probabilistic algorithm for the global optimization of a polynomial over a real algebraic set}, SIAM J. Optim., 24 (2014), pp. 1313--1343. Nonconvex programming, global optimization, Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Effectivity, complexity and computational aspects of 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 J. Canny, D. Yu. Grigor\(^{\prime}\)ev, and N. N. Vorobjov Jr., Finding connected components of a semialgebraic set in subexponential time, Appl. Algebra Engrg. Comm. Comput. 2 (1992), no. 4, 217 -- 238. Semialgebraic sets and related spaces, Analysis of algorithms and problem complexity, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Symbolic computation and algebraic computation, Quantifier elimination, model completeness, and related topics
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Burr, M.A., Continuous amortization and extensions: with applications to bisection-based root isolation, J. symb. comput., 77, 78-126, (2016) Symbolic computation and algebraic computation, Effectivity, complexity and computational aspects of algebraic geometry, Analysis of algorithms and problem complexity
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Bernd Sturmfels, Ngô Viêt Trung, and Wolfgang Vogel, Bounds on degrees of projective schemes, Math. Ann. 302 (1995), no. 3, 417 -- 432. Effectivity, complexity and computational aspects of algebraic geometry, Schemes and morphisms, 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 Analysis of algorithms and problem complexity, Polynomials over finite fields, Effectivity, complexity and computational aspects of 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 Symbolic computation and algebraic computation, Solving polynomial systems; resultants, Effectivity, complexity and computational aspects of algebraic geometry, Analysis of algorithms and problem complexity
| 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 Projective and free modules and ideals in commutative rings, Stability for projective modules, Effectivity, complexity and computational aspects of algebraic geometry, Other constructive mathematics
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Actions of groups on commutative rings; invariant theory, Geometric invariant theory, Symbolic computation and algebraic computation, 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 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, Valued fields, Valuations and their generalizations for commutative rings, 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 Dubois, D. W.; Recio, T.: Order extensions and real algebraic geometry. Contemporary math. 8 (1981) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, Real algebraic and real-analytic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation I. Yengui, Stably free modules over \(R[x]\) of rank \(> \dim(R)\) are free, Math. Comp. 80 (2011), 1093--1098. Projective and free modules and ideals in commutative rings, Stability for projective modules, Other constructive mathematics, Stability for linear groups, 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 Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, Topological properties in algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Mok, H. -N.; To, W. -K.: Effective Pólya semi-positivity for non-negative polynomials on the simplex, Journal of complexity 24, No. 4, 524-544 (2008) Effectivity, complexity and computational aspects of 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 Foundations of tropical geometry and relations with algebra, Symbolic computation and algebraic computation, Combinatorics in computer science, Analysis of algorithms and problem complexity, 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 Effectivity, complexity and computational aspects of 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 Beltrán, Carlos; Leykin, Anton, Robust certified numerical homotopy tracking, Found. Comput. Math., 13, 253-295, (2013) Effectivity, complexity and computational aspects of algebraic geometry, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Symbolic computation and algebraic computation
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Zeng, G. X., Homogeneous Stellensätze in semialgebraic geometry,Pacific J. Math., 1989, 136(1): 103. Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic and real-analytic geometry, Relevant commutative algebra, Ordered fields, 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 S. Basarab, A Nullstellensatz over ordered fields, Revue Roumaine Math., XXVIII (1983), No 7, 553--566. Relevant commutative algebra, Real algebraic and real-analytic geometry, Ordered 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 D. Eisenbud, 1993, Commutative algebra with a view to algebraic geometry, Parts 3 and 4 Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation, Problem books
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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, Ordered fields, Arithmetic ground fields for curves, Special algebraic curves and curves of low genus, Rational and unirational varieties, 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 Semialgebraic sets and related spaces, Quantifier elimination, model completeness, and related topics, Effectivity, complexity and computational aspects of algebraic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Bank, B.; Giusti, M.; Heintz, J.; Lecerf, G.; Matera, G.; Solernó, P.: Degeneracy loci and polynomial equation solving, Found. comput. Math. (2013) Complete intersections, Determinantal varieties, Effectivity, complexity and computational aspects of algebraic geometry, Real algebraic sets, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Amidou, M.; Yengui, I.: An algorithm for unimodular completion over Laurent polynomial rings, Linear algebra appl. 429, 1687-1698 (2008) Projective and free modules and ideals in commutative rings, Stability for projective modules, Effectivity, complexity and computational aspects of algebraic geometry, Other constructive mathematics
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Real algebra, Semialgebraic sets and related spaces, Effectivity, complexity and computational aspects of algebraic geometry, Other constructive mathematics
| 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, Topology of real algebraic varieties, Symmetric functions and generalizations, Effectivity, complexity and computational aspects of 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 R. Berr, The algebraic structure sheaf of the real spectrum Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, Model theory of fields, 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 Manfred Knebusch and Claus Scheiderer. Einf''uhrung in die reelle Algebra. Vieweg-Verlag, 1989. Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, Non-Archimedean valued fields, Topology of real algebraic varieties
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Valued fields, Topology of real algebraic varieties, 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 D. V. Grigoriev and N. N. Vorobjov, \textit{Solving systems of polynomial inequalities in subexponential time}, J. Symbolic Comput., 5 (1988), pp. 37--64. Software, source code, etc. for problems pertaining to field theory, Analysis of algorithms and problem complexity, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic and real-analytic geometry, Polynomials (irreducibility, etc.), 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 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Stability for projective modules, Effectivity, complexity and computational aspects of algebraic geometry, Other constructive mathematics, Chain conditions on annihilators and summands: Goldie-type conditions
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic and real-analytic geometry, Ordered fields
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation E. Becker, D. Gondard, On rings admitting orderings and 2-primary chains of orderings of higher level, Manuscr. Math. 65 (1989), 62--63. Ordered fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered rings, Real algebraic and real-analytic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation [H]B. Heinemann: On finite intersections of ''henselian valued'' fields. Manus. Math. 52 (1985), 37--61 Valued fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, Limits, profinite groups, 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 Ikenmeyer, Christian; Landsberg, J.M., On the complexity of the permanent in various computational models, (2016) Symbolic computation and algebraic computation, Effectivity, complexity and computational aspects of algebraic geometry, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, 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 Mechanization of proofs and logical operations, Quantifier elimination, model completeness, and related topics, Real algebraic sets, Symbolic computation and algebraic computation, Cell biology, Classical flows, reactions, etc. in chemistry
| 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.), Varieties and morphisms, Ordered 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 Yengui, I., The Gröbner ring conjecture in the lexicographic order case, Math. Z., 276, 261-265, (2014) Projective and free modules and ideals in commutative rings, Stability for projective modules, Effectivity, complexity and computational aspects of algebraic geometry, Other constructive mathematics
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Computer graphics; computational geometry (digital and algorithmic aspects), Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation, 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 Symbolic computation and algebraic computation, Polynomials in general fields (irreducibility, etc.), Polynomial rings and ideals; rings of integer-valued polynomials, Solving polynomial systems; resultants, Effectivity, complexity and computational aspects of algebraic geometry, Analysis of algorithms and problem complexity, Randomized algorithms, 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 G. Moroz, ''Complexity of the resolution of parametric systems of equations and inequations,'' in: ISSAC 2006 (Genova), ACM, New York (2006), pp. 246--253. Real algebraic and real-analytic geometry, Effectivity, complexity and computational aspects of algebraic geometry, Analysis of algorithms and problem complexity, Symbolic computation and algebraic computation
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Jeronimo, G.; Matera, G.; Solernó, P.; Waissbein, A., Deformation techniques for sparse systems, Found. comput. math., 9, 1, 1-50, (2009) Computational aspects of algebraic curves, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Symbolic computation and algebraic computation, Formal power series rings, Effectivity, complexity and computational aspects of 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 Convex sets in \(n\) dimensions (including convex hypersurfaces), Effectivity, complexity and computational aspects of algebraic geometry, Real algebraic sets, Symbolic computation and algebraic computation, Semidefinite programming
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Solving polynomial systems; resultants, History of commutative algebra, History of mathematics in the 20th century, History of mathematics in the 21st century, Computational methods for problems pertaining to field theory, Effectivity, complexity and computational aspects of 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 Solving polynomial systems; resultants, Effectivity, complexity and computational aspects of algebraic geometry, Computational real 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 Effectivity, complexity and computational aspects of algebraic geometry, Other constructive mathematics
| 0
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Numerical computation of solutions to single equations, Real algebraic sets, Effectivity, complexity and computational aspects of 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 Plesken W., Robertz D.: Elimination for coefficients of special characteristic polynomials. Experiment. Math. 17(4), 499--510 (2008) 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), 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 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Model theory of fields, Ordered fields, Model-theoretic 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 Software, source code, etc. for problems pertaining to algebraic geometry, Effectivity, complexity and computational aspects of algebraic geometry, Singularities in algebraic geometry, Symbolic computation and algebraic computation
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