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Wen-Tsun W. — Mathematics Mechanization
Wen-Tsun W. — Mathematics Mechanization

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Название: Mathematics Mechanization

Автор: Wen-Tsun W.

Аннотация:

This book is a collection of essays centred around the subject of mathematical mechanization. It tries to deal with mathematics in a constructive and algorithmic manner so that reasoning becomes mechanical, automated and less laborious.
The book is divided into three parts. Part I concerns historical developments of mathematics mechanization, especially in ancient China. Part II describes the underlying principles of polynomial equation-solving, with polynomial coefficients in fields restricted to the case of characteristic 0. Based on the general principle, some methods of solving such arbitrary polynomial systems may be found. This part also goes back to classical Chinese mathematics as well as treating modern works in this field. Finally, Part III contains applications and examples.
Audience: This volume will be of interest to research and applied mathematicians, computer scientists and historians in mathematics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 420

Добавлена в каталог: 20.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$Spec_{K}( )$      c3n1. 10 c3t2.
2 : 1 Principle      c2s2. 3
4-bar linkage      c8d1. 1
4-bar linkage design      c8s8. 3
6-Pole Theorem      c7e2. 5
6R-robot      c6d5. 1
8-triad configuration      c7e3. 1
8-Triad Theorem      c7e3 1 c7e4.
Affine algebraic variety      c3s3. 2
Affine space      c3s3. 1 c3nl.
Affine variety      c3s3. 2 c3d2.
Al-Khwarizmi, fl. ( + 842 — + 847)      c1s1. 3
Algebraic correspondence      c5s5. 2 c5d2.
Algebraic cycle      c5s5. 3
Algebraic equivalence class      c5s5. 3
Algebraic equivalence group      c5s5. 3
Algebraic line      c7s7. 1
Algebraic variety      c3s3. 2 c3d2.
Algebraic variety associated to an irreducible asc-set      c3d6. 5 c3d6.
Algebraically parallel      c7s7. 1
Algebriac equivalence      c5s5. 3
Algorithm Bas-Set      c3s3. 4
Algorithm Char-Set      c3s3. 4
Annotations, or Annotations to Nine Chapters      c1s1. 1 c1s1. c2s2.
Antonisz Value (of $\pi$)      c2s2. 3
Appolonius Problem      c6s6. 3 c6e3.
Approximate char-series      c6d2. 5
Approximate char-set      c6d2. 5
Approximate factorization      c6d2. 6
Arithmetic      c1s1. 1
Art of Mending (=Zhui Shu)      c1s1. 1 c2s2.
Asc-set      c3s3. 3 cÇaÇ. c6s6.
ascending order      c3s3. 3 c3d3. c3d3.
Ascending set      c3s3. 3 c3d3. c3d3. c6s6.
Autoreduced polset      c4d2. 7
Autoreduced set      c4d1. 9
Autoreduced tuple-set(s)      c4d1. 9
Auxiliary equations      c6s6. 1
Axiom of infinity      c7s7. 1
Bas-set      c3a3. 2
Bas-Set Algorithm      c3s3. 4
Basic field (= ground field)      c3s3. 1 c3n1.
Basic set      c3s3. 3 c3d3.
Basis of variety      c3s3. 2 c3d2.
Biao      c1s1. 1 c2s2.
Bifurcation hand-position (of robot)      c6d5. 10
Bifurcation position (of robot hand)      c6d5. 10
Bisector (of oriented angle)      c7d2. 4
Bokowski Theorem      c2s2.2 c2e2.
Bounded coordinates (of extended point)      c3s3. 1 c3d1.
Broken-Bamboo Problem      c2s2. 3
Buchberger Theorem      c4t2. 6
Burmester geometric theory      c8s8. 3
Burmester Theorems      c8pp3. 3 c8pp3.
CAGD (= Computer-Aided Geometry Design)      c8s8. 4
Canonical form      c4d5. 1 c4d5. c4n5.
Canonical representation (of extended point)      c3s3. 1
Canonical representation (of extended point) (of pol)      c4s3. 7
CaO      c1s1. 1
Cavalieri principle      c2s2. 3
Cavalieri, B. ( + 1598, +1647)      c2s2. 3
Center (of vortex configuration)      c6s6. 4
Center curve      c8d3 3
center point      c8d3.2
Central configuration      c6s6. 4 c6d4.
Char-pols      c3a4 1
Char-series      c3s3. 5 c3d5.
Char-set      c3s3. 4 c3a4.
Char-Set Algorithm      c3s3. 4
Char-set Method      c3 c6s6.
Characteristic pols      c3d4. 1
Characteristic series      c3s3. 5 c3d5.
Characteristic set      c3s3. 4 c3d4.
Characteristic set modulo factors      c3s3 4 c3d4.
Chern character      c5d3 15
Chern classes      c5s5. 3 c5d3. c8s8.
Chern classes of partition $\pi$      c5s3. 10 c5d3.
Chern numbers      c5s5. 3 c5d3. c5n3.
Chern, S. S.      c5s5. 3
Chinese remainder theorem      c1s1. 1
Chou - Gao Theorem      c7t4. 1
Chou - Schelter - Yang Theorem      c4t4. 10
Chow basis      c3d6. 8 c5d2.
Chow coordinates      c5s5. 2 c5d2.
Chow form      c3t6. 8 c5d2. c5t2.
Chow ring      c5s5. 3 c5d3.
Chow, W. L.      c3s3. 6 c5s5. c5s5. c5t3.
City - Width Problem      c1s1. 2 c2s2.
Class (of polynomial)      c3d2. 1
Class set (of polset)      c3d5. 5
Close ratio (of $\pi$)      c2s2. 3
Coarse ratio (of $\pi$)      c2s2. 3
Codimension      c5s5. 3 c5d3. c5n3.
Collins - Li phenomenon      c3s3. 4 c6s6.
Collision Problem      c8e2. 7
Complete ascending set      c3d3. 19
Complete tuple-set(s)      c4d1. 13
Completed homogeneous coordinates      c3d1. 11
Completed pols      c4d4. 3 c4n3.
Completed polset      c4d3. 3
Completed projective space      c3d1. 11
Completion      c4d1. 12 c4n1. c4d3. c4n3.
Completion of tuple-set(s)      c4d1. 12 c4n1.
Complex algebraic variety      c5s5. 1
Complex variety      c5d1. 12 c5s5.
Complexification (of real variety)      c5d1. 16
Computer wise fashion (of geometry theorem-proving)      c2s2. 2
Computerwise stage (of geometry theorem-proving)      c2s2. 2
Conclusion (of theorem)      c7s7. 1 c7d1. c7d1. c7d1.
Condensed coefficients      c6s6. 1
Configuration class      c6d4. 3
Configuration space      c6d5. 3
Conjugate points      c3s3. 1 c3dl. c3e1. c3e1.
Contractible irreducible decomposition (of varieties)      c3d2. 15
Contraction      c4d1. 14 c4n1. c4d3. c4n3.
Contraction of complete tuple-set(s)      c4d1. 14 c4n1.
Control parameters (of robot)      c6d5. 2
Control space (of robot)      c6d5. 4
Coordinate at infinity      c3d1. 11
Coordinate sum of tuple(s)      c4d1. 1 c4n1.
Coordinates (of extended point)      c3d1. 3
Coordinates of tuple(s)      c4d1. 1 c4n1.
Counting board      c1s1. 1
Counting principle      c5s5. 2 c5t2.
Counting rod      c1s1 1
Coupler curve      c8d1. 1 c8e1.
Coupler plane      c8d1. 1
Coupler point      c8d1. 1
Coupler rod      c8d1. 1
Cover of tuple(s)      c4d1. 18
Cubic Syzygy Theorem      c7e2. 6
Cubic-Root Extraction Shu      c1s1. 1
Cycle (of algebraic variety)      c5s5. 3
Dead position (of robot hand)      c6d5. 11
Definig polynomial set (of extended point)      c3d1. 7 c3r1. c3r1.
Defining asc-set (of extended point)      c3d6. 4
Defining ascending set (of extended point)      c3d6. 4
Defining equations (of extended point)      c3d1. 7
Defining field      c3d1. 5
Defining polynomials (of extended point)      c3d1. 7 c3r1.
Degeneracy condition      c7s7. 1
Degeneracy position (of robot hand)      c6d5. 12
Degenerate      c7s7. 1
Degenerate sense      c7s7. 1
Degree (of algebraic variety)      c5d1. 5
Degree (of pol)      c3d3. 1 c3n3.
Degree set (of polset)      c3d5. 6
Degree-tuple      c4d2. 2
Degree-tuple-set      c4d2. 6 c4n2. c4d4.
Denavit — Hartenberg coordinate system      c6d5. 13
Denavit — Hartenberg frame      c6n5. 1
Desargues Axiom      c7s7. 1 c7d1.
Desargues theorem      c2s2. 1 c2e1. c2e1. c3e6. c3e6. c7s7. c7e3.1
Desargues, G., ( + 1593, + 1662)      c2s2. 1
Desarguesian axiomatic system      c7d7. 1
Desarguesian geometry      c7s7. 1
Descartes, R., ( + 1596, + 1650)      c1s1. 3 c2s2.
Descartesian fashion (of geometry theorem-proving)      c2s2. 1
Descartesian program      c1s1. 3 c6s6.
Descartesian stage (of geometry theorem-proving)      c2s2. 1
Differential geometry      c7s7. 1
DIMENSION      c3s3. 1 c3d1. c3s3. c3d2.
Ding-fa      c1s1. 2
Discriminant      c6d5. 18
Discriminant system      c8e1. 8 c8r1. c8s8.
Divisor of tuple(s)      c4d1. 3
Dominant class      c3s3. 5 c3d5.
Dominant component      c8d4. 1
Dominant degree      c3s3. 5 c3d5.
Dual (of Schbert cycle)      c5d3. 4 c5n3.
Dual Grassmannian coordinates      c5d2. 8
Dual of fundamental Schubert Cycle      c5d3. 4 c5n3.
E-point      c5a5. 1
E-value      c5a5. 1
E-zero      c5a5. 1
Earth element      c1s1. 2 c2s2.
Ehresmann class      c5d3. 7 c5d3.
Ehresmann symbol      c5d3. 2
Ehresmann, Ch., ( + 1905, +1979)      c5s5. 3
Elementary geometry      c7s7. 1
Eliminant      c3s3 5 c3d5.
Elimination      c1s1. 2
Ellipse Problem      c8e2. 5
End-effector      c6d5. 1
Enumerative geometry      c6s6 3
Equality domain      c7d1. 11
Equi - Bisector Theorem      c7e4. 5 c7e4.
Erd$\ddot{o}$s Problem      c8s8. 5
Essential part      c6e2. 2
Euclid, fl. 300B.C.      c2s2. 1
Euclidean fashion (of geometry theorem-proving)      c2s2. 1
Euclidean geometry      c7d1. 8
Euclidean stage (of geometry theorem-proving)      c2s2. 1
Euler inequality      c7s7. 4 c7e4.
Euler ratio      c7s7. 4 c7e4.
Euler, L., ( + 1707, +1783)      c7s7. 4
Evolution PDE      c8s8. 5
Exact representation      c6d2. 1 c6d2.
Explicitly constructible      c7d2. 1
Explicitly constructible type      c7d2. 1
EXPONENT      c3s3. 5 c3d5.
Extended point      c3s3. 1 c3d1.
Extension field      c3s3. 1 c3d1.
Extremal point      c5d5. 1
Extremal Problem E      c5s5. 5
Extremal value      c5d5. 2
Extremal zero      c5d5. 1
FA      c1s1.2
Fang - Cheng      c1s1. 2
Fang - Cheng Shu      c1s1. 2
Fermat last theorem      c3e2. 3
Feuerbach theorem      c7r1. 2 c8e1.
Finite geometry      c7rl. 8 c8s8.
Finite kernel set      c5d5. 8 c5t5. c5n5.
Finite Kernel Theorem      c5t5. 2 c5t5.
Fixed configuration      c6d4. 5 c6r4.
Formula of Pieri - Giambelli      c5s5. 4
Free coordinates (of extended point)      c3s3. 1 c3d1.
Fundamental Schubert Cycle      c5d3. 3
Gamkrelidze - Todd classes      c5d3. 8
Gauss - Line Theorem      c1s1. 2 c2e1.
Gauss Pentagon Theorem      c8e1. 3
Gauss, C.F., ( + 1777, + 1856)      c1s1. 3 c2s2.
Gaussian elimination      c1s1. 3 c6s6.
Generic hand-position (of robot)      c6d5. 8
Generic line, etc.      c3r2. 6
Generic point      c3s3. 2 c3d2.
Generically true      c2s2. 2
Geng Shouchang, fl. ( - 57, - 54)      c1s1. 1
Geometric - Loci Problem      c5s5. 4 c5r4.
Geometric constraints      c6d5. 2
Geometrical line      c7s7. 1
Geometrically parallel      c7s7. 1
Geometry-problem solving      c2s2. 3
Geometry-theorem proving      c2
Gou      c2s2. 3
Gou - Gu Form      c1s1. 1 c2s2.
Gou - gu rational triple      c2s2. 3 c3e2.
Gou - Gu Theorem      c2s2. 3
Grassmannian variety      c5n2. 5 c5t2.
Grassmannian variety of composite elements      c5n2. 5 c5t2. c5s5. c5d3.
Greatest common multiple of tuple(s)      c4dl. 6 c4n1.
Groebner basis      c4d2. 15
Groebner basis of an ideal      c4d2. 16
Gu      c2s2. 3
Guo Shoujing, ( + 1213 — +1316)      c2s2. 3
Hand (of robot)      c6d5. 1
Hand-position (of robot)      c6d5. 7
Healthy approximation      c6s6. 1
Healthy exact representation      c6d2. 7
Heaven’s - Element Shu      c1s1. 1 c1s1. c2s2.
Heaven’s element      c1s1. 1 c1s1. c2s2.
Hensel construction      c6s6. 2 c6t2.
Heron - Qin Formula      c2s2. 3
Heron formula      c2s2. 1 c2el.
Heron, fl. + 62(?)      c2s2. 1
Higher ordering      c3d3. 5 c3d3.12 c3d5.10 c3d5. c4d1. c4n1. c4d2. c4n2. c4d2. c4n2. c4d2. c4n2.
Hilbert class (of theorems)      c2s2. 1
Hilbert Finite-Basis Theorem      c3pf2. 9 c5pf1.
Hilbert mechanization theorem      c2s2. 2 c7t2.
Hilbert, D., ( + 1862 — + 943)      c2s2. 1 c2s2. c7s7. c7s7.
Hilbertian domain      c7d1. 10
Hilbertian fashion (of geometry theorem-proving)      c2s2. 1
Hilbertian stage (of geometry theorem-proving)      c2s2. 1
Hilbertian type      c7d2. 1
Homogeneous point      c3dl. 11
Homogeneous polset      c3d2. 18 c3n2.
Homogeneous polynomial      c3d1. 12
Homogeneous zero      c3d2. 18 c3n2.
Hu - Wang Method (of factorization)      c4s4. 5
Hybrid method (of polynomial equations-solving)      c6s6. 2
Hypothesis      c7s7. 1 c7d1. c7d1. c7d1.
Ideal (associated to an irreducible asc-set)      c3d6. 7
Ideal (of point set)      c5d1. 14 c5n1.
Ideal( )      c3r6. 5 c4n2.
Ideal[ ]      c3n6. 3
Image-variety (of irreducible algebraic correspondence)      c5d2. 6 c5n2.
Implicit equations      c5r4. 2
Implicitizaion Problem      c5s5. 4
Implicitization      c5d4. 2
In- and Es-Center Theorem      c7t3. 3
Incomparable ordering      c3d5. 11 c3n5. c4d2. c4n2. c4d2.10 c4n2. c4d2.11 c4n2.
Incomplete ascending set      c3d3. 19
Index-set (of pol)      c3d3. 1
Inertial coordinate system      c6d4. 2
Initial (of pol)      c3s3. 3 c3d3.
Initial-product      c3s3. 3 c3d3.
Initial-separant-product      c3s3. 3 c3d3.
Integer tuple(s)      c4d1. 1
Intersection morphism      c5d3. 12
Intersection ring      c5s5. 3 c5d3.
Inverse kinematic equations      c6s6. 5 c6d5.
Inverse tangential morphism      c5d3. 11
Irreducible algebraic correspondence      c5d2. 2
Irreducible ascending set      c3d6. 2 c3d6.
Irreducible component      c3d2. 16
Irreducible decomposition (of varieties)      c3s3. 2 c3d2. c3t2.
Irreducible variety      c3d2. 12
Jacobi, Carl G. J., ( + 1804, +1851)      c5s5. 5 c8s8.
Jacobian condition      c8s8. 5
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