Contents
Preface
Chapter 1. Polynomial s i n On e Variabl e
1.1.
1.2.
1.3.
1.4.
1.5.
1.6.
The Fundamenta l Theore m o f Algebr a
Numerical Roo t Findin g
Real Root s
Puiseux Serie s
Hypergeometric Serie s
Exercises
Chapter 2 . Grobne r Base s o f Zero-Dimensiona l Ideal s
2.1.
2.2.
2.3.
2.4.
2.5.
2.6.
Computing Standar d Monomial s an d th e Radica l
Localizing an d Removin g Know n Zero s
Companion Matrice s
The Trac e For m
Solving Polynomia l Equation s i n Singula r
Exercises
Chapter 3 . Bernstein' s Theore m an d Fewnomial s
3.1.
3.2.
3.3.
3.4.
3.5.
3.6.
From Bezout' s Theore m t o Bernstein' s Theore m
Zero-dimensional Binomia l System s
Introducing a Toric Deformatio n
Mixed Subdivision s o f Newton Polytope s
Khovanskii's Theore m o n Fewnomial s
Exercises
Chapter 4 . Resultant s
4.1.
4.2.
4.3.
4.4.
4.5.
4.6.
The Univariat e Resultan t
The Classica l Multivariat e Resultan t
The Spars e Resultan t
The Unmixe d Spars e Resultan t
The Resultan t o f Four Trilinea r Equation s
Exercises
Chapter 5 . Primar y Decompositio n
5.1.
5.2.
5.3.
5.4.
5.5.
Prime Ideals , Radica l Ideal s an d Primar y Ideal s
How to Decompos e a Polynomia l Syste m
Adjacent Minor s
Permanental Ideal s
Exercises
vii
1
1
3
5
6
8
11
13
13
15
17
20
23
26
29
29
32
33
35
38
41
43
43
46
49
52
55
57
59
59
61
63
67
69
V
Previous Page Next Page