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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Semidefinite programming, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Semialgebraic sets and related spaces, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation B. Bank, M. Giusti, J. Heintz, and L. M. Pardo, \textit{Generalized polar varieties and an efficient real elimination}, Kybernetika \textbf{40} (2004), no. 5, 519-550. Real algebraic sets, Singularities in algebraic geometry, Symbolic computation and algebraic computation, Analysis of algorithms and problem complexity
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Cremona, [Cremona 97] J. E., \textit{Algorithms for Modular Elliptic Curves}, (1997), Cambridge University Press, Cambridge Computational aspects of algebraic curves, Elliptic curves, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves over global fields, Number-theoretic algorithms; complexity, Analytic computations, Symbolic computation and algebraic computation, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Licciardi, S.; Mora, T.: Implicitization of hypersurfaces and curves by the primbasissatz and basis conversion. Proceedings of ISSAC'94, 191-196 (1994) Computational aspects of algebraic curves, Computational aspects of algebraic surfaces, 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 Luis M. Pardo, How lower and upper complexity bounds meet in elimination theory, Applied algebra, algebraic algorithms and error-correcting codes (Paris, 1995) Lecture Notes in Comput. Sci., vol. 948, Springer, Berlin, 1995, pp. 33 -- 69. Symbolic computation and algebraic computation, Analysis of algorithms and problem complexity, 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 Computable structure theory, computable model theory, Other Turing degree structures, Theory of numerations, effectively presented structures, 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 G. Blekherman, G. G. Smith, and M. Velasco, \textit{Sums of squares and varieties of minimal degree}, J. Amer. Math. Soc., 29 (2016), pp. 893--913. Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Semidefinite programming
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation D. Prill, On Approximations and Incidence in Cylindrical Algebraic Decompositions,SIAM J. Comput. 15 (1986), 972--993. Software, source code, etc. for problems pertaining to algebraic geometry, Real algebraic and real-analytic geometry, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation J. Cremona, Algorithms for modular elliptic curves. Cambridge: Cambridge University Press, 1992. Zbl0758.14042 MR1201151 Computational aspects of algebraic curves, Elliptic curves, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves over global fields, Number-theoretic algorithms; complexity, Analytic computations, Symbolic computation and algebraic computation, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Vector bundles on curves and their moduli, Effectivity, complexity and computational aspects of algebraic geometry, Divisors, linear systems, invertible sheaves
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Lairez, Pierre, Computing periods of rational integrals, Math. Comp., 85, 300, 1719-1752, (2016) Symbolic computation and algebraic computation, Analytic theory of abelian varieties; abelian integrals and differentials, de Rham cohomology and algebraic geometry, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Linear ordinary differential equations and systems in the complex domain
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Lasserre J.B.: Representation of nonnegative convex polynomials. Arch. Math. 91(2), 126--130 (2008) Semialgebraic sets and related spaces, Sums of squares and representations by other particular quadratic forms, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), 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 Oaku, T.; Takayama, N., An algorithm for de Rham cohomology groups of the complement of an affine variety via \(D\)-module computation, J. Pure Appl. Algebra, 139, 201-233, (1999) de Rham cohomology and algebraic geometry, Symbolic computation and algebraic computation, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Computational aspects of higher-dimensional varieties
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Effectivity, complexity and computational aspects of algebraic geometry, Numerical computation of solutions to systems of equations, 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, Effectivity, complexity and computational aspects of algebraic geometry, Eigenvalues, singular values, and eigenvectors
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Robson, R.: Constructing real prime divisors using Nash arcs. Rocky Mt. J. Math.14, 967-969 (1984) Real algebraic and real-analytic geometry, Real-analytic and Nash manifolds, 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 R. Bahloul, Global generic Bernstein-Sato polynomial on an irreducible affine scheme, Proc. Japan Acad. Ser. A Math. Sci. 79 (2003), no. 9, 146-149. Rings of differential operators (associative algebraic aspects), Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects), 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 Variant quantifier elimination, H. Hong; M. Safey El Din; , J. Symbolic Comput., 47 (2012), pp. 883--901 Software, source code, etc. for problems pertaining to algebraic geometry, Computational aspects of higher-dimensional varieties, Symbolic computation and algebraic computation, Real algebraic and real-analytic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Elliptic curves, Riemann surfaces; Weierstrass points; gap sequences, 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 Fibrations, degenerations in algebraic geometry, Effectivity, complexity and computational aspects of algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation M. Putinar, \textit{Positive polynomials on compact semi-algebraic sets}, Indiana Univ. Math. J., 42 (1993), pp. 969--984, . Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Moment problems, Semialgebraic sets and related spaces, Sums of squares and representations by other particular quadratic forms
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Combinatorial aspects of tropical varieties, Exact enumeration problems, generating functions, Recurrences, 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 Arnon, D. S.: A cluster-based cylindrical algebraic decomposition algorithm. Eurocal 85 204, 262-269 (1985) Symbolic computation and algebraic computation, Real algebraic and real-analytic geometry, Software, source code, etc. for problems pertaining to algebraic geometry, Graph theory
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Topological and ordered rings and modules, Real algebra, Semialgebraic sets and related spaces, Ordered rings, algebras, modules, 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 Symbolic computation and algebraic computation, Number-theoretic algorithms; complexity, Analytic computations, Algebraic number theory computations, Computer solution of Diophantine equations, 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 Fernando, J. F.; Gamboa, J. M.; Ueno, C., Polynomial, regular and Nash images of Euclidean spaces, (Ordered Algebraic Structures and Related Topics, Contemp. Math., vol. 697, (2017), Amer. Math. Soc. Providence, RI), 145-167 Semialgebraic sets and related spaces, Real-valued functions in general topology, 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; Pasechnik, DV; Roy, M-F, Bounding the Betti numbers and computing the Euler-Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials, J. Eur. Math. Soc. (JEMS), 12, 529-553, (2010) Semialgebraic sets and related spaces, Topology of real algebraic varieties, Effectivity, complexity and computational aspects of algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Arnon D.S. (1988). A cluster-based CAD algorithm. J. Symb. Comput. 5(1/2): 189--212 Symbolic computation and algebraic computation, Software, source code, etc. for problems pertaining to algebraic geometry, Software, source code, etc. for problems pertaining to field theory, 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 Francesca Acquistapace, Fabrizio Broglia, and José F. Fernando, On Hilbert's 17th problem and Pfister's multiplicative formulae for the ring of real analytic functions, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 13 (2014), no. 2, 333 -- 369. Sums of squares and representations by other particular quadratic forms, Real-analytic functions, Real-analytic sets, complex Nash functions, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), 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 Conformal mappings of special domains, Boundary value and inverse problems for harmonic functions in two dimensions, 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 Cutkosky S., Ein L., Lazarsfeld R.: Positivity and complexity of ideal sheaves. Math. Ann. 321(2), 213--234 (2001) Computational aspects in algebraic geometry, Symbolic computation and algebraic computation, Analysis of algorithms and problem complexity, Vanishing theorems 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 Graf v. Bothmer H.-C.: Cord Erdenberger, and Katharina Ludwig. A new family of rational surfaces in \({\mathbb{P}^{4}}\) . J. Symbolic Comput. 39(1), 51--60 (2005) Families, moduli, classification: algebraic theory, Rational and ruled surfaces, 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 Möller H.M., Computational aspects of reduction strategies to construct resolutions of monomial ideals 228 (1986) Ideals and multiplicative ideal theory in commutative rings, Software, source code, etc. for problems pertaining to commutative algebra, Software, source code, etc. for problems pertaining to algebraic geometry, Polynomial rings and ideals; rings of integer-valued polynomials, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Ma, Y., Zhi, L.: Computing real solutions of polynomial systems via low-rank moment matrix completion. In Proceedings of the 2012 international symposium on symbolic and algebraic computation, pp 249-256. ACM press, New York (2012) Symbolic computation and algebraic computation, Solving polynomial systems; resultants, 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 Symbolic computation and algebraic computation, Power series rings, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Real algebraic sets, Foundations: limits and generalizations, elementary topology of the line, Real rational functions
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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, Analysis of algorithms and problem complexity, Computational aspects of algebraic curves, 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 Effectivity, complexity and computational aspects of algebraic geometry, Real algebraic and real-analytic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation M. Infusino, \textit{Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions}, Trends in Mathematics, to appear, arXiv:1405.3573. Polynomials in real and complex fields: location of zeros (algebraic theorems), Semialgebraic sets and related spaces, Moment problems, 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 Computational real algebraic geometry, Real algebraic sets, Symbolic computation and algebraic computation, Semidefinite programming
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation A. Gabrielov & N. Vorobjov (2015). On topological lower bounds for algebraic computation trees. \textit{Found. Comput. Math}., 10.1007/s10208-015-9283-7. Effectivity, complexity and computational aspects of algebraic geometry, Semialgebraic sets and related spaces, Topology of real algebraic varieties, 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 Computer graphics; computational geometry (digital and algorithmic aspects), Computational aspects and applications of commutative rings, Computational aspects of higher-dimensional varieties, Geometric constructions in real or complex geometry, Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry), Numerical aspects of computer graphics, image analysis, and computational geometry, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Computational aspects of higher-dimensional varieties, Effectivity, complexity and computational aspects of algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Difference algebra, Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Effectivity, complexity and computational aspects of algebraic geometry, Quantifier elimination, model completeness, and related topics, 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 Gamboa, JM, Compact Klein surfaces with boundary viewed as real compact smooth algebraic curves, Mem. Real Acad. Cienc. Exact. Fís. Nat. Madr., 27, iv+96, (1991) Arithmetic ground fields for curves, Klein surfaces, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to functions of a complex variable, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), 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 Saito, M., Sturmfels, B., Takayama, N.: Gröbner Deformations of Hypergeometric Differential Equations, Vol.~6 of Algorithms and Computation in Mathematics. Springer, Berlin (2000) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, Research exposition (monographs, survey articles) pertaining to commutative algebra, Research exposition (monographs, survey articles) pertaining to computer science, Basic hypergeometric integrals and functions defined by them, Commutative rings of differential operators and their modules, Toric varieties, Newton polyhedra, Okounkov bodies, Rings of differential operators (associative algebraic aspects), Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Automorphisms of curves, Computational aspects of algebraic curves, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Finite ground fields in algebraic geometry, Special algebraic curves and curves of low genus, 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 Vector spaces, linear dependence, rank, lineability, Multilinear algebra, tensor calculus, 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
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Symbolic computation and algebraic computation, Real algebraic sets, Computational aspects related to convexity, Semidefinite programming
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Dickenstein, A; Sturmfels, B, Elimination theory in codimension 2, J. Symb. Comput., 34, 119-135, (2002) Toric varieties, Newton polyhedra, Okounkov bodies, Parametrization (Chow and Hilbert schemes), Low codimension problems in algebraic geometry, Computational aspects of higher-dimensional varieties, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Saliba, C.: Le théorème des zéros centraux de la géométrie algébrique réelle. CR acad. Sci. Paris sér. I math. 298, 337-340 (1984) Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), 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 Computational aspects of algebraic curves, Symbolic computation and algebraic computation, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Families, moduli of curves (algebraic), Minimal model program (Mori theory, extremal rays), Geometric invariant theory, Effectivity, complexity and computational aspects of algebraic geometry, \(n\)-dimensional polytopes
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation K. Shiihara and T. Sasaki, Analytic continuation and Riemann surface determination of algebraic functions by computer. Japan J. Indust. Appl. Math.,13 (1996), 107--116. Numerical computation of solutions to single equations, Symbolic computation and algebraic computation, Algebraic functions and function fields in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Computational real algebraic geometry, Numerical approximation and computational geometry (primarily 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 Number-theoretic algorithms; complexity, Effectivity, complexity and computational aspects of algebraic geometry, Computational aspects of algebraic curves, Theta functions and curves; Schottky problem, Theta functions and abelian varieties, Relationships between algebraic curves and physics, Software, source code, etc. for problems pertaining to number theory
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Syzygies, resolutions, complexes and commutative rings, Effectivity, complexity and computational aspects of algebraic geometry, Research exposition (monographs, survey articles) pertaining to commutative algebra
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Cryptography, Applications to coding theory and cryptography of arithmetic geometry, Algebraic coding theory; cryptography (number-theoretic aspects), 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 U. Walther, Algorithmic computation of de Rham cohomology of complements of complex affine varieties, J. Symb. Comput. 29(4--5), 795--839 (2000). de Rham cohomology and algebraic geometry, Symbolic computation and algebraic computation, Computational aspects of higher-dimensional varieties
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Bernstein, D., Chen, H., Cheng, C., Lange, T., Niederhagen, R., Schwabe, P., Yang, B.: ECC2K-130 on NVIDIA GPUs. In: Progress in Cryptology-INDOCRYPT 2010. Springer LNCS 6498, pp. 328-344 (2010) Cryptography, Number-theoretic algorithms; complexity, Applications to coding theory and cryptography of arithmetic geometry, Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation 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 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 F. Rossi and W. Spangher, Some effective methods in the openness of loci for Cohen-Macaulay and Gorenstein properties, inEffective Methods in Algebraic Geometry, Proc. Intern. Conf. MEGA 90, Castiglioncello 1990, T. Mora and C. Traverso, eds., Progress in Mathematics94, Birkhäuser (1990), 441-455. Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Effectivity, complexity and computational aspects of algebraic geometry, Linkage, complete intersections and determinantal ideals, Cohen-Macaulay modules
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Averkov, G., Bröcker, L.: Minimal polynomial descriptions of polyhedra and special semialgebraic sets (2010, preprint), arXiv:1002.0921v1 Semialgebraic sets and related spaces, \(n\)-dimensional polytopes, 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 Mittmann, Johannes; Saxena, Nitin; Scheiblechner, Peter, Algebraic independence in positive characteristic: A \(p\)-adic calculus, Transactions of the American Mathematical Society, 366, 3425-3450, (2014) Polynomial rings and ideals; rings of integer-valued polynomials, Witt vectors and related rings, \(p\)-adic cohomology, crystalline cohomology, de Rham cohomology and algebraic geometry, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, 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 16.Roma``czuk U., Ustimenko V.: On the key exchange with matrices of large order and graph based nonlinear maps, Proceedings of the conference ''Applications of Computer Algebra'', Vlora, Special Issue, 4(4) (2010): 203-211. Cryptography, Applications of graph theory, Birational automorphisms, Cremona group and generalizations, 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 Benedetti R., Real Algebraic and Semi-Algebraic Sets (1991) Semialgebraic sets and related spaces, Effectivity, complexity and computational aspects of algebraic geometry, Triangulation and topological properties of semi-analytic and subanalytic sets, and related questions
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation T. Berry, On Coates' algorithm, SIGSAM Bull. 17 (1983), 12-17. Singularities of curves, local rings, Algorithms in computer science, Software, source code, etc. for problems pertaining to algebraic geometry, 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 Geometric aspects of numerical algebraic geometry, Computational aspects of algebraic curves, 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 Computational aspects of higher-dimensional varieties, Parametrization (Chow and Hilbert schemes), Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation DOI: 10.1007/s00229-004-0535-0 Forms over real fields, Sums of squares and representations by other particular quadratic forms, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Elliptic curves
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Cheng, J.-S.; Jin, K.; Lazard, D., Certified rational parametric approximation of real algebraic space curves with local generic position method, J. symb. comput., 58, 18-40, (2013) Computational aspects of algebraic curves, Real algebraic sets, Approximation by rational functions, Computer-aided design (modeling of curves and surfaces), Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Eisenbud, D., Grayson, D. R., Stillman, M., \& Sturmfels, B. (Eds.) (2002). Algorithms and computation in mathematics: Vol. 8. Computations in algebraic geometry with Macaulay 2. Berlin: Springer. Collections of articles of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to commutative algebra, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Proceedings, conferences, collections, etc. pertaining to computer science, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, Computational aspects in algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Dedekind, Prüfer, Krull and Mori rings and their generalizations, Divisors, linear systems, invertible sheaves, Ordered groups, 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 Phillipson, K., Rojas, J.M.: Fewnomial systems with many roots, and an adelic tau conjecture. In: Proceedings of Bellairs workshop on tropical and non-Archimedean geometry (May 6-13, 2011, Barbados). Contemporary Mathematics, vol. 605, pp. 45-71. AMS Press (2013) Solving polynomial systems; resultants, Effectivity, complexity and computational aspects of algebraic geometry, \(p\)-adic and power series fields, Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, 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, 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 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, Computational aspects of higher-dimensional varieties, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Initial value problems, existence, uniqueness, continuous dependence and continuation 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 A. Scaramuzza, Smooth complete toric varieties: an algorithmic approach, Ph. D. Thesis, Università degli Studi di ``Roma Tre'', 2007. Computational aspects in algebraic geometry, Toric varieties, Newton polyhedra, Okounkov bodies, Symbolic computation and algebraic computation, Semigroups
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Kaiser, R.: Das sphärische Spektrum eines graduierten Ringes. Regensbg. Math. Schr. 27 (1998) Relevant commutative algebra, Topology of real algebraic varieties, Ideals and multiplicative ideal theory in commutative rings, Graded rings, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Krone, Robert; Leykin, Anton: Eliminating dual spaces. J. symb. Comput. 79P3, 609-622 (2017) Computational aspects of algebraic curves, Symbolic computation and algebraic computation, Computational aspects in algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Gonzalez-Vega, Laureano; Lombardi, Henri; Mahé, Louis, Virtual roots of real polynomials, J. Pure Appl. Algebra, 124, 1-3, 147-166, (1998) Polynomials in real and complex fields: factorization, Semialgebraic sets and related spaces, Spline approximation, 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 Polynomial rings and ideals; rings of integer-valued polynomials, Relevant commutative algebra, Software, source code, etc. for problems pertaining to commutative algebra, Symbolic computation and algebraic computation, 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 L. D. Garcia, M. Stillman, and B. Sturmfels, \textit{Algebraic geometry of Bayesian networks}, J. Symbolic Comput., 39 (2005), pp. 331--355, . Symbolic computation and algebraic computation, Learning and adaptive systems in artificial intelligence, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), 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 A. L. Chistov, ''Polynomial complexity algorithm for factoring polynomials and constructing components of a variety in subexponential time'', Zap. Nauchn. Semin. POMI, 137, 124--188 (1984). Factorization, Polynomials over finite fields, Symbolic computation and algebraic computation, Varieties and morphisms
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Strzeboński, A, Cylindrical algebraic decomposition using local projections, J. Symb. Comput., 76, 36-64, (2016) Semialgebraic sets and related spaces, Symbolic computation and algebraic computation, Quantifier elimination, model completeness, and related topics, Computational aspects in algebraic geometry, Computational aspects and applications of commutative rings
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Poteaux, A; Rybowicz, M, Complexity bounds for the rational Newton-Puiseux algorithm over finite fields, Appl. Algebra Eng. Commun. Comput., 22, 187-217, (2011) Symbolic computation and algebraic computation, Polynomials, factorization in commutative rings, Computational aspects of algebraic curves, 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 S. Fitchett, Generators of Fat Point Ideals on the Projective Plane, Doctoral dissertation, University of Nebraska--Lincoln, 1997. Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Projective techniques 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 Schemes and morphisms, Real algebraic and real-analytic geometry, Other constructive mathematics, Henselian 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 Huang M D. Local duality and the discrete logarithm problem. In: Lecture Notes in Computer Science, vol. 6639. Berlin: Springer, 2011, 213-222 Number-theoretic algorithms; complexity, Algebraic coding theory; cryptography (number-theoretic aspects), Effectivity, complexity and computational aspects of algebraic geometry, Cryptography
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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 curves, Numerical aspects of computer graphics, image analysis, and computational geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation J.F. Fernando, J.M. Gamboa: On the Krull dimension of rings of semialgebraic functions. Preprint RAAG (2010). http://www.mat.ucm.es/\( \sim \)josefer/pdfs/preprint/dim.pdf Semialgebraic sets and related spaces, Real-valued functions in general topology, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Chain conditions, finiteness conditions in commutative ring theory
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation von zur Gathen, J.; Shparlinski, I.; Sinclair, A., Finding points on curves over finite fields, SIAM J. comput., 32, 6, 1436-1448, (2003) Symbolic computation and algebraic computation, Computational aspects of algebraic curves, Algebraic number theory computations
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, 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, Ordered fields, Algebraic functions and function fields in algebraic geometry, 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 De La Rosa-Navarro, B.L., Frías-Medina, J.B., Lahyane, M.: Rational surfaces with finitely generated Cox rings and very high Picard numbers. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM. 111(2), 297-306 (2017) Divisors, linear systems, invertible sheaves, Picard groups, Rational and ruled surfaces, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Minimal model program (Mori theory, extremal rays), Effectivity, complexity and computational aspects of algebraic geometry
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Computational aspects of algebraic surfaces, Rational and ruled 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 Derivations and commutative rings, Group actions on affine varieties, 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 Helminck A. G., J. Symbolic Comput. 30 pp 521-- (2000) Linear algebraic groups over arbitrary fields, Homogeneous spaces and generalizations, Group actions on varieties or schemes (quotients), Symbolic computation and algebraic computation
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Mora, F.; Möller, H. M., The computation of the Hilbert function, (Computer Algebra, London, 1983, Lect. Notes Comput. Sci., vol. 162, (1983), Springer Berlin), 157-167 Homological methods in commutative ring theory, Software, source code, etc. for problems pertaining to commutative algebra, Multiplicity theory and related topics, Graded rings and modules (associative rings and algebras), 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 Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Effectivity, complexity and computational aspects of algebraic geometry, General nonlinear regression
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Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Other constructive mathematics, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mechanization of proofs and logical operations, Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation 9. Helmer, M.: A direct algorithm to compute the topological Euler characteristic and Chern-Schwartz-Macpherson class of projective complete intersection varieties. Submitted to a Special Issue of the Journal of Theoretical Computer Science for SNC-2014. Available on the, Computational aspects of higher-dimensional varieties, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Software, source code, etc. for problems pertaining to algebraic geometry, Complete intersections, 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 algebraic geometry, Computational aspects of higher-dimensional varieties, Kinematics of mechanisms and robots, Numerical computation of solutions to systems of equations, Symbolic computation and algebraic computation
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