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1.

図書

図書
Eduardo D. Sontag
出版情報: Berlin ; New York : Springer-Verlag, 1979  viii, 168 p. ; 25 cm
シリーズ名: Lecture notes in control and information sciences ; 13
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2.

図書

図書
Le Baron O. Ferguson
出版情報: Providence, R.I. : American Mathematical Society, 1980  xi, 160 p. ; 26 cm
シリーズ名: Mathematical surveys ; no. 17
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3.

図書

図書
David E. Handelman
出版情報: Berlin ; Tokyo : Springer-Verlag, c1987  x, 136 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1282
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4.

図書

図書
Theodore J. Rivlin, Edward B. Saff, editors
出版情報: New York : Springer, c2000  xliv, 682 p. ; 25 cm
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5.

図書

図書
Naum Z. Shor
出版情報: Boston : Kluwer, 1998  xvii, 394p ; 25cm
シリーズ名: Nonconvex optimization and its applications ; v. 24
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6.

図書

図書
Nikolay V. Kyurkchiev
出版情報: Berlin : Wiley-VCH, c1998  180 p. ; 24 cm
シリーズ名: Mathematical research ; v. 104
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7.

図書

図書
by Jacek Graczyk and Grzegorz Świa̦tek
出版情報: Princeton, N.J. : Princeton University Press, 1998  viii, 148 p. ; 24 cm
シリーズ名: Annals of mathematics studies ; no. 144
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目次情報: 続きを見る
Review of Concepts / 1:
Theory of Quadratic Polynomials / 1.1:
Dense Hyperbolicity / 1.2:
Steps of the Proof of Dense Hyperbolicity / 1.3:
Quasiconformal Gluing / 2:
Extendibility and Distortion / 2.1:
Saturated Maps / 2.2:
Gluing of Saturated Maps / 2.3:
Polynomial-Like Property / 3:
Domains in the Complex Plane / 3.1:
Cutting Times / 3.2:
Linear Growth of Moduli / 4:
Box Maps and Separation Symbols / 4.1:
Conformal Roughness / 4.2:
Growth of the Separation Index / 4.3:
Quasiconformal Techniques / 5:
Initial Inducing / 5.1:
Quasiconformal Pull-back / 5.2:
Gluing Quasiconformal Maps / 5.3:
Regularity of Saturated Maps / 5.4:
Straightening Theorem / 5.5:
Bibliography
Index
Review of Concepts / 1:
Theory of Quadratic Polynomials / 1.1:
Dense Hyperbolicity / 1.2:
8.

図書

図書
Claudio Procesi
出版情報: New York : M. Dekker, 1973  viii, 190 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 17
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9.

図書

図書
Władysław Narkiewicz
出版情報: Berlin ; New York : Springer-Verlag, c1995  130 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1600
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10.

図書

図書
George Pólya ; edited by R.P. Boas
出版情報: Cambridge, Mass. : MIT Press, c1974  x, 444 p. ; 26 cm
シリーズ名: Mathematicians of our time ; 8 . Collected papers / George Pólya ; v. 2
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11.

図書

図書
A.G. Khovanskiĭ
出版情報: Providence, R.I. : American Mathematical Society, c1991  viii, 139 p. ; 27 cm
シリーズ名: Translations of mathematical monographs ; v. 88
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目次情報: 続きを見る
An Analogue of the Bezout
Theorem for a System of Real Elementary
Equations Two Simple Versions of the Theory of Fewnomials
Analogues of the Theorems of Rolle and Bezout for Separating
Solutions of Pfaff Equations
Pfaff Manifolds Real-Analytic
Varieties with Finiteness
Properties and Complex
Abelian Integrals
An Analogue of the Bezout
Theorem for a System of Real Elementary
Equations Two Simple Versions of the Theory of Fewnomials
12.

図書

図書
B. Malgrange
出版情報: Boston : Birkhäuser, c1991  232 p. ; 25 cm
シリーズ名: Progress in mathematics ; v. 96
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13.

図書

図書
Gove W. Effinger and David R. Hayes
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, c1991  xvi, 157 p. ; 24 cm
シリーズ名: Oxford mathematical monographs
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目次情報: 続きを見る
The Polynomial Waring and Goldbach Problems / 1:
Local Singular Series / 2:
Local Gauss Sums and Local Derivatives / 3:
The Adele Ring over k / 4:
L-functions of Dirichlet Type / 5:
The Polynomial 3-Primes Generating Function / 6:
The Polynomial 3-Primes Problem: An Asymptotic Solution / 7:
The Polynomial Waring Problem / 8:
The Polynomial Waring and Goldbach Problems / 1:
Local Singular Series / 2:
Local Gauss Sums and Local Derivatives / 3:
14.

図書

図書
Hans Lausch and Wilfried Nöbauer
出版情報: Amsterdam : North-Holland Pub. Co , New York : American Elsevier, 1973  xi, 322 p. ; 23 cm
シリーズ名: North-Holland mathematical library ; v. 5
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15.

図書

図書
[by] Robert P. Feinerman [and] Donald J. Newman
出版情報: Baltimore : Williams & Wilkins, c1974  viii, 148 p. ; 24 cm
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16.

図書

図書
Jacques Chaillou ; translated from the French by J.W. Nienhuys
出版情報: Dordrecht, Holland ; Boston : D. Reidel Pub. Co., c1979  xv, 168 p. ; 23 cm
シリーズ名: Mathematics and its applications ; v. 3
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17.

図書

図書
[by] Marvin J. Greenberg
出版情報: New York : W. A. Benjamin, 1969  167 p ; 23 cm
シリーズ名: Mathematics lecture note series
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18.

図書

図書
Vladimír Kučera
出版情報: Chichester, [Eng.] : J. Wiley, c1979  206 p. ; 25 cm
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19.

図書

図書
E.J. Barbeau
出版情報: New York ; Tokyo : Springer-Verlag, c1989  xxii, 441 p. ; 25 cm
シリーズ名: Problem books in mathematics / edited by K. Bencsáth and P.R. Halmos
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20.

図書

図書
Dominique Foata, Marcel-P. Schützenberger
出版情報: Berlin ; New York : Springer-Verlag, 1970  v, 94 p ; 26 cm
シリーズ名: Lecture notes in mathematics ; 138
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21.

図書

図書
by Morris Marden
出版情報: Providence : American Mathematical Society, 1966  xi, 243 p. ; 27 cm
シリーズ名: Mathematical surveys ; no. 3
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22.

図書

図書
by W.E. Sewell
出版情報: Princeton : Princeton University Press , New York : Kraus Reprint Co., 1965, c1942  ix, 236 p. ; 23 cm
シリーズ名: Annals of mathematics studies ; no. 9
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23.

図書

図書
by Curtis T. McMullen
出版情報: Princeton, N.J. : Princeton University Press, 1994  vii, 214 p. ; 24 cm
シリーズ名: Annals of mathematics studies ; no. 135
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目次情報: 続きを見る
Background in conformal geometry
Dynamics of rational maps
Holomorphic motions and the Mandelbrot set Compactness in holomorphic dynamics
Polynomials and external rays
Renormalization Puzzles and infinite renormalization
Robustness Limits of renormalization
Real quadratic polynomials
Background in conformal geometry
Dynamics of rational maps
Holomorphic motions and the Mandelbrot set Compactness in holomorphic dynamics
24.

図書

図書
Vilmos Totik
出版情報: Berlin ; New York : Springer-Verlag, c1994  vi, 114 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1569
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25.

図書

図書
G.V. Milovanović, D.S. Mitrinović, Th.M. Rassias
出版情報: Singapore : World Scientific, c1994  xiii, 821 p. ; 23 cm
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26.

図書

図書
Steven Roman
出版情報: New York : Springer-Verlag, c1995  xii, 272 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 158
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27.

図書

図書
David Masser
出版情報: Cambridge : Cambridge University Press, 2016  xviii, 348 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 207
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28.

図書

図書
T. Sheil-Small
出版情報: Cambridge : Cambridge University Press, 2002  xix, 428 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 75
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目次情報: 続きを見る
Preface
List of notation
The algebra of polynomials / 1:
The degree principle and the fundamental theorem of algebra / 2:
The Jacobian problem / 3:
Analytic and harmonic functions in the unit disc / 4:
Circular regions and Grace's theorem / 5:
The Ilieff-Sendov conjecture / 6:
Self-inversive polynomials / 7:
Duality and an extension of Grace's theorem to rational functions / 8:
Real polynomials / 9:
Level curves / 10:
Miscellaneous topics / 11:
References
Index
Preface
List of notation
The algebra of polynomials / 1:
29.

図書

図書
Teo Mora
出版情報: Cambridge, U.K. : Cambridge University Press, 2003  xiii, 423 p. ; 24 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 88
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目次情報:
The Kronecker-Duval philosophy
Factorization
The Kronecker-Duval philosophy
Factorization
30.

図書

図書
Alexander Prestel, Charles N. Delzell
出版情報: Berlin : Springer, c2001  viii, 267 p. ; 24 cm
シリーズ名: Springer monographs in mathematics
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目次情報: 続きを見る
Introduction
Real Fields / 1:
Ordered Fields / 1.1:
Extensions of Orderings / 1.2:
The Real Closure / 1.3:
Exercises / 1.4:
Bibliographical and Historical Comments / 1.5:
Semialgebraic Sets / 2:
Ultraproducts / 2.1:
Elimination of Quanti ers / 2.3:
The "Finiteness Theorem" / 2.4:
Quadratic Forms over Real Fields / 2.5:
Witt Decomposition / 3.1:
The Witt Ring of a Field / 3.2:
Signatures / 3.3:
Quadratic Forms Over Real Function Fields / 3.4:
Generalization of HilbertÆs 17th Problem / 3.5:
Real Rings / 3.6:
The Real Spectrum of a Commutative Ring / 4.1:
The Positivstellensatz / 4.2:
öContinuousö Representation of Polynomials / 4.3:
-Fields / 4.4:
The Real Spectrum of R[X1;: : : ;Xn / 4.5:
Archimedean Rings / 4.6:
Quadratic Modules and Semiorderings / 5.1:
Rings with Archimedean Preorderings / 5.2:
Rings with Archimedean Quadratic Modules / 5.3:
Rings with Archimedean Preprimes / 5.4:
Positive Polynomials on Semialgebraic Sets / 5.5:
Semiorderings and Weak Isotropy / 6.1:
Archimedean Quadratic Modules on R[X1;: : : ;Xn / 6.2:
Distinguished Representations of Positive Polynomials / 6.3:
Applications to the Moment Problem / 6.4:
Sums of 2mth Powers / 6.5:
Preorderings and Semiorderings of Level 2m / 7.1:
Semiorderings of Level 2m on Fields / 7.2:
Archimedean Modules of Level 2m / 7.3:
Bounds / 7.4:
Length of Sums of Squares / 8.1:
Existence of Degree Bounds / 8.2:
Positive Polynomials over Non-Archimedean Fields / 8.3:
Distinguished Representations in the Non-Archimedean Case / 8.4:
Exercise / 8.5:
Appendix: Valued Fields / 8.6:
Valuations / A.1:
Algebraic Extensions / A.2:
Henselian Fields / A.3:
Complete Fields / A.4:
Dependence and Composition of Valuations / A.5:
Transcendental Extensions / A.6:
Bibliographical Comments / A.7:
References
Glossary of Notations
Index
Introduction
Real Fields / 1:
Ordered Fields / 1.1:
31.

図書

図書
J.S. Lomont, John Brillhart
出版情報: Boca Raton : Chapman & Hall/CRC, c2001  xxiii, 289 p. ; 25 cm
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目次情報: 続きを見る
Contents
Tables
Preface
Introduction
Binomial Sequences of Polynomials / 1.:
The functions F / (a):
The functions F[subscript 0]--The sequences {G[subscript m](z)} and {H[subscript m](z)} / (b):
The Binomial Sequences Generated from f[superscript -1], f [set membership] F[superscript 0] / 2.:
The Functions F[subscript 1]--Elliptic Polynomials of the First Kind / 3.:
The Moment Polynomials--P[subscript n](x,y), Q[subscript n](x,y), and R[subscript n](x,y) / 4.:
The Functions F[superscript -1 subscript 1]--Elliptic Polynomials of Second Kind / 5.:
Inner Products, Integrals, and Moments--Favard's Theorem / 6.:
The Functions F[subscript 2]--Orthogonal Sequences {G[subscript m](z)}, {H[subscript m](z)} / 7.:
The Functions in Classes I and II / 8.:
Class I Functions--The elliptic functions sn (t,k)
Class II Functions--The polynomials f*(t,k)
The Tangent Numbers / 9.:
Class III Functions--The [delta subscript n](x) Polynomials / 10.:
Coefficients of the [delta subscript n](x) Polynomials / 11.:
The [lambda subscript n](x) Polynomials / 12.:
The Orthogonal Sequences {A[subscript m](z)} and {B[subscript m](z)} / 13.:
The Weight Functions for {A[subscript m](z)} and {B[subscript m](z)} / 14.:
Miscellaneous Results / 15.:
Uniqueness and Completion Results / 16.:
Polynomial Inequalities / 17.:
Some Concluding Questions / 18.:
References
Name Index
Subject Index
Symbol Index
Contents
Tables
Preface
32.

図書

図書
Mihai Tibăr
出版情報: Cambridge, UK : Cambridge University Press, 2007  xii, 253 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 170
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33.

図書

図書
Andrew J. Sommese, Charles W. Wampler,II
出版情報: New Jersey : World Scientific, c2005  xxii, 401 p. ; 26 cm
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34.

図書

図書
Martin Dietzfelbinger
出版情報: Berlin : Springer, 2004  x, 147 p. ; 29 cm.
シリーズ名: Lecture notes in computer science ; 3000
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35.

図書

図書
Hans Blomberg and Raimo Ylinen
出版情報: London ; New York : Academic Press, 1983  xx, 360 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 166
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36.

図書

図書
Stephen Barnett
出版情報: New York : M. Dekker, c1983  xi, 452 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 77
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37.

電子ブック

EB
Teo Mora
出版情報:   1 online resource (xiii, 423 p.)
シリーズ名: Encyclopedia of mathematics and its applications ; 88
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目次情報: 続きを見る
Preface
The Kronecker-Duval Philosophy / Part I:
Euclid / 1:
Intermezzo: Chinese remainder theorems / 2:
Cardano / 3:
Intermezzo: multiplicity of roots / 4:
Kronecker I: Kronecker's philosophy / 5:
Intermezzo: Sylvester / 6:
Galois I: finite fields / 7:
Kronecker II: Kronecker's model / 8:
Steinitz / 9:
Lagrange / 10:
Duval / 11:
Gauss / 12:
Sturm / 13:
Galois II / 14:
Factorization / Part II:
Ouverture / 15:
Kronecker III: factorization / 16:
Berlekamp / 17:
Zassenhaus / 18:
Fermeture / 19:
Bibliography
Index
Preface
The Kronecker-Duval Philosophy / Part I:
Euclid / 1:
38.

電子ブック

EB
Teo Mora
出版情報: Cambridge Core  1 online resource (xviii, 275 p.)
シリーズ名: Encyclopedia of mathematics and its applications ; volume 157
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39.

電子ブック

EB
Jean Bernard Lasserre, LAAS-CNRS and Institut de Mathématiques, Toulouse, France
出版情報:   1 online resource (xiv, 339 p.)
シリーズ名: Cambridge texts in applied mathematics ; 52
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40.

電子ブック

EB
Teo Mora
出版情報:   1 online resource (xxii, 759 p.)
シリーズ名: Encyclopedia of mathematics and its applications ; 99
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目次情報: 続きを見る
Preface
Setting
Gauss, Euclid, Buchberger: Elementary Grobner Bases / Part 3:
Hilbert / 20:
Affine Algebraic Varieties and Ideals / 20.1:
Linear Change of Coordinates / 20.2:
Hilbert's Nullstellensatz / 20.3:
*Kronecker Solver / 20.4:
Projective Varieties and Homogeneous Ideals / 20.5:
*Syzygies and Hilbert Function / 20.6:
*More on the Hilbert Function / 20.7:
Hilbert's and Gordan's Basissatze / 20.8:
Gauss II / 21:
Some Heretical Notation / 21.1:
Gaussian Reduction / 21.2:
Gaussian Reduction and Euclidean Algorithm Revisited / 21.3:
Buchberger / 22:
From Gauss to Grobner / 22.1:
Grobner Basis / 22.2:
Toward Buchberger's Algorithm / 22.3:
Buchberger's Algorithm (1) / 22.4:
Buchberger's Criteria / 22.5:
Buchberger's Algorithm (2) / 22.6:
Macaulay I / 23:
Homogenization and Affinization / 23.1:
H-bases / 23.2:
Macaulay's Lemma / 23.3:
Resolution and Hilbert Function for Monomial Ideals / 23.4:
Hilbert Function Computation: the 'Divide-and-Conquer' Algorithms / 23.5:
H-bases and Grobner Bases for Modules / 23.6:
Lifting Theorem / 23.7:
Computing Resolutions / 23.8:
Macaulay's Nullstellensatz Bound / 23.9:
*Bounds for the Degree in the Nullstellensatz / 23.10:
Grobner I / 24:
Rewriting Rules / 24.1:
Grobner Bases and Rewriting Rules / 24.2:
Grobner Bases for Modules / 24.3:
Grobner Bases in Graded Rings / 24.4:
Standard Bases and the Lifting Theorem / 24.5:
Hironaka's Standard Bases and Valuations / 24.6:
*Standard Bases and Quotients Rings / 24.7:
*Characterization of Standard Bases in Valuation Rings / 24.8:
Term Ordering: Classification and Representation / 24.9:
*Grobner Bases and the State Polytope / 24.10:
Gebauer and Traverso / 25:
Gebauer-Moller and Useless Pairs / 25.1:
Buchberger's Algorithm (3) / 25.2:
Traverso's Choice / 25.3:
Gebauer-Moller's Staggered Linear Bases and Faugere's F[subscript 5] / 25.4:
Spear / 26:
Zacharias Rings / 26.1:
Lexicographical Term Ordering and Elimination Ideals / 26.2:
Ideal Theoretical Operation / 26.3:
*Multivariate Chinese Remainder Algorithm / 26.4:
Tag-Variable Technique and Its Application to Subalgebras / 26.5:
Caboara-Traverso Module Representation / 26.6:
*Caboara Algorithm for Homogeneous Minimal Resolutions / 26.7:
Duality / Part 4:
Noether / 27:
Noetherian Rings / 27.1:
Prime, Primary, Radical, Maximal Ideals / 27.2:
Lasker-Noether Decomposition: Existence / 27.3:
Lasker-Noether Decomposition: Uniqueness / 27.4:
Contraction and Extension / 27.5:
Decomposition of Homogeneous Ideals / 27.6:
The Closure of an Ideal at the Origin / 27.7:
Generic System of Coordinates / 27.8:
Ideals in Noether Position / 27.9:
Chains of Prime Ideals / 27.10:
Dimension / 27.11:
Zero-dimensional Ideals and Multiplicity / 27.12:
Unmixed Ideals / 27.13:
Moller I / 28:
Moller Algorithm / 28.1:
Lazard / 29:
The FGLM Problem / 29.1:
The FGLM Algorithm / 29.2:
Border Bases and Grobner Representation / 29.3:
Improving Moller's Algorithm / 29.4:
Hilbert Driven and Grobner Walk / 29.5:
The Structure of the Canonical Module / 29.6:
Macaulay II / 30:
The Linear Structure of an Ideal / 30.1:
Inverse System / 30.2:
Representing and Computing the Linear Structure of an Ideal / 30.3:
Noetherian Equations / 30.4:
Dialytic Arrays of M[superscript (r)] and Perfect Ideals / 30.5:
Multiplicity of Primary Ideals / 30.6:
The Structure of Primary Ideals at the Origin / 30.7:
Grobner II / 31:
Stability / 31.1:
Grobner Duality / 31.3:
Leibniz Formula / 31.4:
Differential Inverse Functions at the Origin / 31.5:
Taylor Formula and Grobner Duality / 31.6:
Grobner III / 32:
Macaulay Bases / 32.1:
Macaulay Basis and Grobner Representation / 32.2:
Macaulay Basis and Decomposition of Primary Ideals / 32.3:
Horner Representation of Macaulay Bases / 32.4:
Polynomial Evaluation at Macaulay Bases / 32.5:
Continuations / 32.6:
Computing a Macaulay Basis / 32.7:
Moller II / 33:
Macaulay's Trick / 33.1:
The Cerlienco-Mureddu Correspondence / 33.2:
Lazard Structural Theorem / 33.3:
Some Factorization Results / 33.4:
Some Examples / 33.5:
An Algorithmic Proof / 33.6:
Beyond Dimension Zero / Part 5:
Grobner IV / 34:
Nulldimensionalen Basissatze / 34.1:
Primitive Elements and Allgemeine Basissatz / 34.2:
Higher-Dimensional Primbasissatz / 34.3:
Ideals in Allgemeine Positions / 34.4:
Solving / 34.5:
Gianni-Kalkbrener Theorem / 34.6:
Gianni-Trager-Zacharias / 35:
Decomposition Algorithms / 35.1:
Zero-dimensional Decomposition Algorithms / 35.2:
The GTZ Scheme / 35.3:
Higher-dimensional Decomposition Algorithms / 35.4:
Decomposition Algorithms for Allgemeine Ideals / 35.5:
Zero-dimensional Allgemeine Ideals / 35.5.1:
Higher-dimensional Allgemeine Ideals / 35.5.2:
Sparse Change of Coordinates / 35.6:
Gianni's Local Change of Coordinates / 35.6.1:
Giusti-Heintz Coordinates / 35.6.2:
Linear Algebra and Change of Coordinates / 35.7:
Direct Methods for Radical Computation / 35.8:
Caboara-Conti-Traverso Decomposition Algorithm / 35.9:
Squarefree Decomposition of a Zero-dimensional Ideal / 35.10:
Macaulay III / 36:
Hilbert Function and Complete Intersections / 36.1:
The Coefficients of the Hilbert Function / 36.2:
Perfectness / 36.3:
Galligo / 37:
Galligo Theorem (1): Existence of Generic Escalier / 37.1:
Borel Relation / 37.2:
Galligo Theorem (2): the Generic Initial Ideal is Borel Invariant / 37.3:
Galligo Theorem (3): the Structure of the Generic Escalier / 37.4:
Eliahou-Kervaire Resolution / 37.5:
Giusti / 38:
The Complexity of an Ideal / 38.1:
Toward Giusti's Bound / 38.2:
Giusti's Bound / 38.3:
Mayr and Meyer's Example / 38.4:
Optimality of Revlex / 38.5:
Bibliography
Index
Preface
Setting
Gauss, Euclid, Buchberger: Elementary Grobner Bases / Part 3:
41.

電子ブック

EB
Teo Mora
出版情報:   1 online resource (xi, 820 p.)
シリーズ名: Encyclopedia of mathematics and its applications ; volume 158
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