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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Eberhard Becker, On the real spectrum of a ring and its application to semialgebraic geometry, Bull. Amer. Math. Soc. (N.S.) 15 (1986), no. 1, 19-60. Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Varieties and morphisms, Other model constructions, Relevant commutative algebra
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Semialgebraic sets and related spaces, Computational real algebraic geometry, Global stability of solutions to ordinary differential equations, Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.), Low-dimensional dynamical systems
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Köck, B; Singerman, D, Real Belyi theory, Q. J. Math., 58, 463-478, (2007) Arithmetic ground fields for curves, Klein surfaces, Real algebraic sets, Riemann surfaces; Weierstrass points; gap sequences
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Group actions on varieties or schemes (quotients), Approximation by other special function classes, Finite transformation groups, Real algebraic sets, Lie groups, Rational and birational maps
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Kaveh, K.; Khovanskii, A. G., \textit{convex bodies and multiplicities of ideals}, Proc. Steklov Inst. Math., 286, 268-284, (2014) Valuations and their generalizations for commutative rings, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes, Toric varieties, Newton polyhedra, Okounkov bodies, Deformations and infinitesimal methods in commutative ring theory
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Marshall, M.: Separating families for semi-algebraic sets. Manuscripta math. 80, 73-79 (1993) Semialgebraic sets and related spaces, Real-analytic and semi-analytic sets, Ordered fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) R. Benedetti, F. Loeser, and J.-J. Risler, \textit{Bounding the number of connected components of a real algebraic set}, Discrete Comput. Geom., 6 (1991), pp. 191--209, . Real algebraic sets, Toric varieties, Newton polyhedra, Okounkov bodies
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Special surfaces, Real algebraic sets, Computational aspects of algebraic surfaces
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Equations in general fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Special surfaces, Determinants, permanents, traces, other special matrix functions, Linear transformations, semilinear transformations, Euclidean analytic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) DOI: 10.1007/s00209-002-0480-0 Real algebraic sets, Automorphisms of curves, Reflection and Coxeter groups (group-theoretic aspects), Klein surfaces
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Campillo, A., Lemahieu, A.: Poincaré series for filtrations defined by discrete valuations with arbitrary center. J. Algebra 377, 66-75 (2013) Valuations and their generalizations for commutative rings, Filtered associative rings; filtrational and graded techniques, Singularities in algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) DOI: 10.1353/ajm.0.0029 Elliptic surfaces, elliptic or Calabi-Yau fibrations, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Topology of real algebraic varieties, Harmonic functions on Riemann surfaces
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) E. Becker: ?Extended Artin-Schreier theory of fields?, Rocky Mountain J. of Math., vol. 14, \# 4, Fall 1984 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Model theory of fields, Research exposition (monographs, survey articles) pertaining to field theory, Normed fields, Real algebraic and real-analytic geometry, Forms of degree higher than two, Separable extensions, Galois theory, Decidability and field theory, Model-theoretic algebra
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Symbolic computation and algebraic computation, Real algebraic sets, Analysis of algorithms
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Sums of squares and representations by other particular quadratic forms, Real algebra, Rational points, Hypersurfaces and algebraic geometry, Forms of degree higher than two
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Semialgebraic sets and related spaces, Real algebraic sets, Decidability of theories and sets of sentences
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Van Hamel, J., Algebraic cycles and topology of real algebraic varieties, (2000), Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam Topology of real algebraic varieties, Algebraic cycles, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Real algebraic sets, Classical real and complex (co)homology in algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Semialgebraic sets and related spaces, Sums of squares and representations by other particular quadratic forms, Forms over real fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Convex programming
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebra, Semialgebraic sets and related spaces
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) J. Morgan, P. Shalen. Valuations, trees, and degenerations of hyperbolic structures. I, \textit{Ann. of Math. } 120 (1984), 401--476. General low-dimensional topology, Abelian varieties and schemes, Valuations and their generalizations for commutative rings, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Compactification of analytic spaces, Group rings of finite groups and their modules (group-theoretic aspects), Classification theory of Riemann surfaces
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) J. Pach and F. de Zeeuw: Distinct distances on algebraic curves in the plane, arXiv:1308.0177. Erdős problems and related topics of discrete geometry, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Alexander Prestel, On the axiomatization of PRC-fields, Methods in mathematical logic (Caracas, 1983) Lecture Notes in Math., vol. 1130, Springer, Berlin, 1985, pp. 351 -- 359. Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Rational points, Real algebraic and real-analytic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Noh S., Watanabe K., Adjacent integrally closed ideals in 2-dimensional regular local rings, J. Algebra, 2006, 302(1), 156--166 Regular local rings, Relevant commutative algebra, Valuations and their generalizations for commutative rings, Integral closure of commutative rings and ideals
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Plane and space curves, Coverings in algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Ghomi, M; Howard, R, Tangent cones and regularity of hypersurfaces, J. Reine Angew. Math., 697, 221-247, (2014) Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Nash functions and manifolds, Representations of Lie and linear algebraic groups over real fields: analytic methods, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), Topological linear spaces of test functions, distributions and ultradistributions
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) J. Loftin. The compactification of the moduli space of convex \({{\mathbb{RP}}^2}\) surfaces. I. \textit{Journal of Differential Geometry}, (2)\textbf{68} (2004), 223-276. Families, moduli of curves (analytic), Real algebraic sets, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Differentials on Riemann surfaces
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Topology of real algebraic varieties
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Schwartz, Niels: Convex extensions of partially ordered rings. Géométrie algébrique et analytique réelle (2004) Real algebra, Ordered rings, algebras, modules, Ordered rings, Valuations and their generalizations for commutative rings, Real algebraic and real-analytic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Temkin, M., Tame distillation and desingularization by \textit{p}-alterations, Ann. of Math. (2), 186, 1, 97-126, (2017) Global theory and resolution of singularities (algebro-geometric aspects), Ramification problems in algebraic geometry, Group actions on varieties or schemes (quotients), Valued fields, Valuations and their generalizations for commutative rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Y. Matsui, K. Takeuchi, Projective duality and topological X-ray Radon transforms, in preparation Real algebraic sets, Topology of real algebraic varieties, Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs, Sheaves of differential operators and their modules, \(D\)-modules, Projective differential geometry, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) J. Borcea and B. Shapiro, Classifying real polynomial pencils, Int. Math. Res. Not. 69 (2004), 3689--3708. Real algebraic sets, Classical problems, Schubert calculus, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) --------, Affine schemes and topological closures in the Zariski-Riemann space of valuation rings, J. Pure Appl. Algebra 219 (2015), 1720--1741. Valuations and their generalizations for commutative rings, Integral closure of commutative rings and ideals, Dedekind, Prüfer, Krull and Mori rings and their generalizations, Schemes and morphisms
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Polynomials in real and complex fields: location of zeros (algebraic theorems)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Bergman, G.: Can one factor the classical adjoint of a generic matrix?, Transform. groups 11, No. 1, 7-15 (2006) Factorization of matrices, Valuations and their generalizations for commutative rings, Determinants, permanents, traces, other special matrix functions, Sphere bundles and vector bundles in algebraic topology
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Brugallé, E.; Mikhalkin, G., Floor decompositions of tropical curves: the planar case, (Proceedings of the 15th Gökova Geometry-Topology Conference, (2008)), 64-90 Enumerative problems (combinatorial problems) in algebraic geometry, Real algebraic sets, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Projective techniques in algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) DOI: 10.1080/00927878408823060 Valuations and their generalizations for commutative rings, Local deformation theory, Artin approximation, etc.
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Dwi Juniati & David Trotman, Determination of Lipschitz stratifications for the surfaces \(y^a = z^b x^c + x^d\), Singularités Franco-Japonaises, Séminaires et Congrès 10, Société Mathématique de France, 2005, p. 127-138 Singularities of surfaces or higher-dimensional varieties, Singularities in algebraic geometry, Real algebraic sets, Equisingularity (topological and analytic)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Domokos, M.: Invariant theoretic characterization of subdiscriminants of matrices, Linear multilinear algebra (2013) Polynomial rings and ideals; rings of integer-valued polynomials, Real algebraic sets, Vector and tensor algebra, theory of invariants, Actions of groups on commutative rings; invariant theory, Determinants, permanents, traces, other special matrix functions, Sums of squares and representations by other particular quadratic forms, Representation theory for linear algebraic groups
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Temkin, M., Tyomkin, I.: Prüfer algebraic spaces. Math. Z. 10.1007/s00209-016-1748-0 Generalizations (algebraic spaces, stacks), Rational and birational maps, Valuations and their generalizations for commutative rings, Dedekind, Prüfer, Krull and Mori rings and their generalizations, Valuation rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Toric varieties, Newton polyhedra, Okounkov bodies, Real algebraic sets, Real polynomials: analytic properties, etc., Polynomials and rational functions of several complex variables, Bundle convexity
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets
| 0
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Semialgebraic sets and related spaces, Real rational functions
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Campillo, A., Delgado, F., Gusein-Zade, S.: On Poincaré series of filtrations. Azerbaijan J. Math. 5(2), 125-139 (2015) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Valuations and their generalizations for commutative rings, Arcs and motivic integration, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) 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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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Cossart, V., Galindo, C., Piltant, O.: Un exemple effectif de gradué non noetherien associé à une valuation divisorielle. Ann. Inst. Fourier 50, 105-112 (2000) Valuations and their generalizations for commutative rings, Valuation rings, Singularities in algebraic geometry, Chain conditions, finiteness conditions in commutative ring theory, Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Critical points and critical submanifolds in differential topology, Topological properties in algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) 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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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Garrity, T.; Warren, J.: Geometric continuity. Cagd 8, 51-65 (1991) Computer-aided design (modeling of curves and surfaces), Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Polynomial optimization, Semialgebraic sets and related spaces, Semidefinite programming, Nonconvex programming, global optimization, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Skew fields, division rings, Brauer groups of schemes, Brauer groups (algebraic aspects)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Semialgebraic sets and related spaces, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Kucharz, W.; Maciejewski, Ł, Complexification and homotopy, Homol. Homotopy Appl., 16, 159-165, (2014) Real algebraic sets, Topology of real algebraic varieties
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Computational aspects of algebraic curves, Real algebraic sets, Solving polynomial systems; resultants, Symbolic computation and algebraic computation
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Garcia, R., and Sotomayor, J. (1996). Lines of curvature on algebraic surfaces. Bull. des Sci. Math. 120, 367-395. Surfaces in Euclidean and related spaces, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) V. A. Krasnov, ''The topological type of the Fano surface of a real cubic M-threefold,'' Izv. Ross. Akad. Nauk Ser. Mat. 69(6), 61--94 (2005) [Russian Acad. Sci. Izv.Math. 69 (6), 1137--1167 (2005)]. Fano varieties, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) S. Iliman and T. De Wolff, \textit{Lower bounds for polynomials with simplex Newton polytopes based on geometric programming}, SIAM J. Optim., 26 (2016), pp. 1128--1146. Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic and real-analytic geometry, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Convex programming
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [S1] J. Schmid,On totally positive units of real holomorphy rings Israel J. Math.85 (1994), 339--350 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic and real-analytic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) 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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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Rump, W; Yang, YC, Jaffard-ohm correspondence and hochster duality, Bull. Lond. Math. Soc., 40, 263-273, (2008) Divisibility and factorizations in commutative rings, Integral domains, Ordered abelian groups, Riesz groups, ordered linear spaces, Valuations and their generalizations for commutative rings, Relevant commutative algebra
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Marshall M.: The Pierce--Birkhoff conjecture for curves. Can. J. Math. 44, 1262--1271 (1992) Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Semialgebraic sets and related spaces, Polynomials in real and complex fields: location of zeros (algebraic theorems), Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Polynomial optimization, Nonconvex programming, global optimization
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Geometric invariant theory, Real algebraic sets, Applications of linear algebraic groups to the sciences, Point estimation, Probabilistic graphical models, Algebraic statistics
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Ghezzi, L; Kashcheyeva, O, Toroidalization of generating sequences in dimension two function fields of positive characteristic, J. Pure Appl. Algebra, 209, 631-649, (2007) Local structure of morphisms in algebraic geometry: étale, flat, etc., Ramification problems in algebraic geometry, Valuations and their generalizations for commutative rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Enumerative problems (combinatorial problems) in algebraic geometry, Rational and ruled surfaces, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Jesús M. Ruiz, Cônes locaux et complétions, C. R. Acad. Sci. Paris Sér. I Math. 302 (1986), no. 2, 67 -- 69 (French, with English summary). Complete rings, completion, Valuations and their generalizations for commutative rings, Real algebraic and real-analytic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Alonso, M.E.; Raimondo, M., The computation of the topology of a planar semi-algebraic set, (1989), Rend. Sem. Mat. Univ. Politecnico Torino Algebraic topology on manifolds and differential topology, Real algebraic sets, Semialgebraic sets and related spaces, Complexity classes (hierarchies, relations among complexity classes, etc.), Parallel algorithms in computer science
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Systems biology, networks, Polynomials in real and complex fields: location of zeros (algebraic theorems), Real algebraic sets, Stability of solutions to ordinary differential equations, Numerical computation of roots of polynomial equations, Chemical kinetics in thermodynamics and heat transfer
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Jean-Philippe Monnier, Anneaux d'holomorphie et Positivstellensatz archimédien, Manuscripta Math. 97 (1998), no. 3, 269 -- 302 (French, with English summary). Relevant commutative algebra, Real algebraic and real-analytic geometry, Algebraic theory of quadratic forms; Witt groups and rings, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Arithmetic rings and other special commutative rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Wasserman, A. G.: Extending algebraic action. Revista Mathematica computense 12, No. 2, 463-474 (1999) Real-analytic and Nash manifolds, Group actions on varieties or schemes (quotients), Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Scheiderer, C., A positivstellensatz for projective real varieties, \textit{Manuscripta Mathematica},, \textit{138}, 1, 73-88, (2012) Real algebraic sets, Divisors, linear systems, invertible sheaves, Projective techniques in algebraic geometry, Real algebra, Sums of squares and representations by other particular quadratic forms
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Generalizations (algebraic spaces, stacks), Valuations and their generalizations for commutative rings, Schemes and morphisms, Rational and birational maps
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Riccardo Benedetti and Alexis Marin, Déchirures de variétés de dimension trois et la conjecture de Nash de rationalité en dimension trois, Comment. Math. Helv. 67 (1992), no. 4, 514 -- 545 (French). Real algebraic sets, Nash functions and manifolds
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) A. Seigal and B. Sturmfels, \textit{Real rank two geometry}, J. Algebra, 484 (2017), pp. 310--333, . Semialgebraic sets and related spaces, Projective techniques in algebraic geometry, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) 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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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Valuations and their generalizations for commutative rings, Valued fields, Global theory and resolution of singularities (algebro-geometric aspects)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Homotopy theory, Cohomotopy groups, Real algebraic sets, Topology of real algebraic varieties, Composition algebras
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) DOI: 10.1007/BF02570760 Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Becker, E.; Jacob, B.: Rational points on algebraic varieties over a generalized real closed field: A model theoretic approach. J. reine angew. Math. 357, 73-95 (1982) Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Model-theoretic algebra
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Recio, T., Sendra, J.R.: A really elementary proof of real Lüroth's theorem. Rev. Mat. Univ. Complut. Madrid, \textbf{10}(Special Issue, suppl.), 283-290 (1997) Transcendental field extensions, Real and complex fields, Algebraic functions and function fields in algebraic geometry, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Topological rings and modules, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Relevant commutative algebra, Polynomial rings and ideals; rings of integer-valued polynomials
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Rational points, Inseparable field extensions, Transcendental field extensions, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Francisco Javier Cirre, Birational classification of hyperelliptic real algebraic curves, The geometry of Riemann surfaces and abelian varieties, Contemp. Math., vol. 397, Amer. Math. Soc., Providence, RI, 2006, pp. 15 -- 25. Real algebraic sets, Klein surfaces, Algebraic functions and function fields in algebraic geometry, Rational and birational maps
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Group actions on varieties or schemes (quotients)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) O. Zariski and P. Samuel, \textit{Commutative Algebra}, Vol. 2, University Series in Higher Mathematics, Van Nostrand, Princeton, NJ-Toronto, ON-London-New York, 1960. Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Valuations and their generalizations for commutative rings, Polynomial rings and ideals; rings of integer-valued polynomials, Formal power series rings, Local rings and semilocal rings, Power series rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Nash functions and manifolds, Sums of squares and representations by other particular quadratic forms, Real rational functions
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) 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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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Semidefinite programming, Families, moduli of curves (algebraic), Geometric group theory, Convex programming
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Ducros, Antoine, Parties semi-algébriques d'une variété algébrique \(p\)-adique, Manuscripta Math., 111, 4, 513-528, (2003) Real algebraic sets, Local ground fields in algebraic geometry, Real-analytic and semi-analytic sets, \(p\)-adic differential equations
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Arithmetic rings and other special commutative rings, Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Mahé, L.: Sommes de carrés et anneaux de Witt réduits. C. R. Acad. sci. 300, 5-7 (1985) Real algebraic and real-analytic geometry, Forms over real fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) F. Mangolte, Real algebraic morphisms on 2-dimensional conic bundles, Adv. Geom., to appear. Zbl1097.14045 MR2243296 Real algebraic sets, Topology of real algebraic varieties, Rational and ruled surfaces
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Numerical computation of solutions to systems of equations, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Real algebraic sets, Symbolic computation and algebraic computation
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) C. Scheiderer, \textit{Sums of squares of regular functions on real algebraic varieties}, Trans. Amer. Math. Soc., 352 (1999), pp. 1039--1069. Real-analytic and semi-analytic sets, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Regular local rings, Sums of squares and representations by other particular quadratic forms, Real algebra, Other nonalgebraically closed ground fields in algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Multilinear algebra, tensor calculus, Eigenvalues, singular values, and eigenvectors, Homogeneous spaces and generalizations, Real algebraic sets, Differential geometric aspects in vector and tensor analysis
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) J. Bochnak and W. Kucharz, Line bundles, regular mappings and the underlying real algebraic structure of complex algebraic varieties, Math. Ann. 316 (2000), 793-817. Zbl0986.14041 MR1758454 Topology of real algebraic varieties, Étale and other Grothendieck topologies and (co)homologies, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Birational automorphisms, Cremona group and generalizations, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Singularities of surfaces or higher-dimensional varieties, Local complex singularities, Topology and geometry of orbifolds, Symmetries, equivariance on manifolds, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Valuations and their generalizations for commutative rings, Regular local rings, Global theory and resolution of singularities (algebro-geometric aspects)
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