计数几何演算法 (The Calculus of Enumerative Geometry)（英文版）

Hermann Schubert, Translated by Wolfgang Globke

198.00元
ISBN：
978-7-04-058053-2

310.000千字

16开

2022-06-29

• 前辅文
• Part I The symbolism of conditions
• S1 The number of constants of a structure
• S2 The description of the conditions
• S3 The dimension of a condition and the level of a system
• S4 The principle of conservation of numbers
• S5 The representation of the numbers of con\discretionary- ditions by the symbols of conditions, and computations with these symbols
• S6 The equations between the elementary conditions of each of the three principal elements
• Part II The incidence formulae
• S7 The incidence formulae for points and lines
• S8 Applications of incidence formulae (I), (II) and (III) to the incidence of a tangent with its point of contact
• S9 Further examples for the incidence formulae (I), (II), (III)
• S10 The remaining incidence formulae
• S11 Examples for the incidence formulae (IV) to (XIV)
• S12 Application of the incidence formulae to systems of principal elements incident with principal elements
• Part III The coincidence formulae
• S13 The coincidence formulae of a pair of points and Bezout's theorems
• S14 Application of the coincidence formulae of \S13 to determine the numbers concerning contacts of planar curves and surfaces
• S15 The pair of lines and its coincidence conditions
• S16 Application of the coincidence formulae for pairs of lines to the two ruled families lying on a surface of degree two [23]
• S17 The pairs of distinct principal elements and the coincidence conditions
• S18 Derivation of the Cayley-Brill correspondence formula from the general coincidence formulae for pairs of points
• Part IV The computations of numbers via degeneracies
• S19 Numbers for structures consisting of finitely many principal elements
• S20 Numbers for conic sections [30]
• S21 The reduction of Chasles and Zeuthen [32]
• S22 Numbers for surfaces of degree two [33]
• S23 Numbers for cubic planar curves with cusp [34]
• S24 Numbers for cubic planar curves with double point [34]
• S25 Numbers for cubic space curves [35]
• S26 Numbers for planar curves of order four in a fixed plane
• S27 Numbers for the linear congruence [40]
• S28 Numbers for structures consisting of two lines whose points and planes are projective [41]
• S29 Numbers for structures consisting of a pencil of planes and a pencil of lines projective to it [41]
• S30 Numbers for the structure consisting of two projective pencils of lines [41]
• S31 Numbers for structure consisting of two collinear bundles [42]
• S32 Numbers for structures consisting of two correlative bundles [42]
• Part V The multiple coincidences
• S33 Coincidence of intersection points of a line and a surface [43]
• S34 The coincidence of multiple points on a line [48]
• S35 The coincidence of multiple lines of a pencil of lines [48]
• S36 Singularities of the generic line complex [49]
• Part VI The theory of characteristics
• S37 The problem of characteristics for an arbitrary structure Gamma
• S38 The problem of characteristics for the conic section [51]
• S39 Derivation and application of the characteristic formulae for the structure consisting of a line and a point on it [52]
• S40 Derivation and application of the characteristic formula for the pencil of lines [52]
• S41 Derivation and application of the characteristic formula for the structure consisting of a line, a point on that line, and a plane through that line [52]
• S42 The theory of characteristics of the structure consisting of a line and n points on it [53]
• S43 Computation of the numbers for multiple secants of the intersection curve of two surfaces
• S44 Theory of characteristics of the structure consisting of a pencil of lines and n lines in it. Application to congruences common to two complexes
• Remarks on the literature
• Index
• Author index