link to my thesis

Contents
Contents
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1 Introduction 3
1.1 Motivation ................................. 3
1.2 Approach .................................. 4
1.3 Research questions ............................. 5
1.4 Thesis outline ................................ 6
I General introduction and background 9
2 Algebraic Background 11
2.1 Rings and Ideals .............................. 11
2.2 Varieties ................................... 13
2.3 Monomial orderings ............................ 14
2.4 Gröbner Basis Theory ........................... 16
2.5 The Buchberger Algorithm ........................ 19
3 Solving polynomial systems of equations 25
3.1 Solving polynomial equations in one variable .............. 26
3.2 Methods for solving polynomial systems of equations .......... 28
3.2.1 Resultant methods ......................... 28
3.2.2 Homotopy methods ........................ 29
3.2.3 Subdivision methods ........................ 32
3.2.4 Algebraic methods ......................... 32
3.3 The Stetter-Möller matrix method .................... 35
3.4 Counting real solutions . . . ........................ 36
3.5 Example ................................... 37
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