regale
发表于 2025-3-25 06:07:17
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Deadpan
发表于 2025-3-25 11:10:04
Real Spectrum,ebraic properties of the real spectrum of the ring of polynomial functions on .. In Section 3, we define the value of a semi-algebraic function at a point of the real spectrum; we also show that the continuous semi-algebraic functions are the sections of a sheaf on the real spectrum. Section 4 deals
飞行员
发表于 2025-3-25 15:02:21
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阐释
发表于 2025-3-25 16:09:25
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VALID
发表于 2025-3-25 21:49:22
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Vital-Signs
发表于 2025-3-26 01:59:36
Polynomial or Regular Mappings with Values in Spheres,rnionic projective lines. The theory of algebraic vector bundles developed in the previous chapter plays a crucial role. For example, from the fact that every topological (ℝ, ℂ or ℍ) line bundle over .. is isomorphic to an algebraic one, we deduce that ℛ(....) is dense in ....... for . = 1,2,4. In S
烦人
发表于 2025-3-26 07:47:25
Introduction,ry is the study of real algebraic sets i.e. subsets of .. defined by polynomial equations. By means of a simple example one can see some features which point up the difference between real and complex algebraic geometry. Let us consider the intersection of the straight line . = ., depending on the p
有偏见
发表于 2025-3-26 11:15:34
Semi-algebraic Sets,d inequalities. This class of sets has a remarkable property: stability under projection. Several applications of this basic property are investigated. The study of semi-algebraic sets is based mainly on the ∜slicingℝ technique, which makes it possible to decompose them into a finite number of subse
intertwine
发表于 2025-3-26 16:29:29
Real Algebraic Varieties,ic varieties. In fact, we shall be concerned almost exclusively with affine real algebraic varieties, i.e. real algebraic sets ∜up to a biregular isomorphism∝ The third section concerns the notion of nonsingularity. In addition to recalling some properties of varieties valid over an arbitrary field
外向者
发表于 2025-3-26 18:51:57
Real Algebra,tellensatz, which characterizes the ideals of polynomials vanishing on an algebraic set, when the ground field is real closed. The next two sections develop an ℜArtin-Schreier theoryℝ for rings, which is an extension of the theory presented in Chap. 1 for fields. The notion of a prime cone of a ring