پایه‌های گربنر و چندوجهی‌های محدب (سری سخنرانی‌های دانشگاهی، شماره ۸)

This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Gr?¶bner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry. image172......Page 0 image002......Page 1 image003......Page 2 image004......Page 3 image005......Page 4 image006......Page 5 image007......Page 6 image008......Page 7 image009......Page 8 image010......Page 9 image011......Page 10 image012......Page 11 image013......Page 12 image014......Page 13 image015......Page 14 image016......Page 15 image018......Page 17 image019......Page 18 image020......Page 19 image021......Page 20 image022......Page 21 image023......Page 22 image024......Page 23 image025......Page 24 image026......Page 25 image027......Page 26 image028......Page 27 image029......Page 28 image030......Page 29 image031......Page 30 image032......Page 31 image033......Page 32 image034......Page 33 image035......Page 34 image036......Page 35 image037......Page 36 image038......Page 37 image039......Page 38 image040......Page 39 image041......Page 40 image042......Page 41 image043......Page 42 image044......Page 43 image045......Page 44 image046......Page 45 image047......Page 46 image048......Page 47 image049......Page 48 image050......Page 49 image051......Page 50 image052......Page 51 image053......Page 52 image054......Page 53 image055......Page 54 image056......Page 55 image057......Page 56 image058......Page 57 image059......Page 58 image060......Page 59 image061......Page 60 image062......Page 61 image063......Page 62 image064......Page 63 image065......Page 64 image066......Page 65 image067......Page 66 image068......Page 67 image069......Page 68 image070......Page 69 image071......Page 70 image072......Page 71 image073......Page 72 image074......Page 73 image075......Page 74 image076......Page 75 image077......Page 76 image078......Page 77 image079......Page 78 image080......Page 79 image081......Page 80 image082......Page 81 image083......Page 82 image084......Page 83 image085......Page 84 image086......Page 85 image087......Page 86 image088......Page 87 image089......Page 88 image090......Page 89 image091......Page 90 image092......Page 91 image093......Page 92 image094......Page 93 image095......Page 94 image096......Page 95 image097......Page 96 image098......Page 97 image099......Page 98 image100......Page 99 image101......Page 100 image102......Page 101 image103......Page 102 image104......Page 103 image105......Page 104 image106......Page 105 image107......Page 106 image108......Page 107 image109......Page 108 image110......Page 109 image111......Page 110 image112......Page 111 image113......Page 112 image114......Page 113 image115......Page 114 image116......Page 115 image117......Page 116 image118......Page 117 image119......Page 118 image120......Page 119 image121......Page 120 image122......Page 121 image123......Page 122 image124......Page 123 image125......Page 124 image126......Page 125 image127......Page 126 image128......Page 127 image129......Page 128 image130......Page 129 image131......Page 130 image132......Page 131 image133......Page 132 image134......Page 133 image135......Page 134 image136......Page 135 image137......Page 136 image138......Page 137 image139......Page 138 image140......Page 139 image141......Page 140 image142......Page 141 image143......Page 142 image144......Page 143 image145......Page 144 image146......Page 145 image147......Page 146 image148......Page 147 image149......Page 148 image150......Page 149 image151......Page 150 image152......Page 151 image153......Page 152 image154......Page 153 image155......Page 154 image156......Page 155 image157......Page 156 image158......Page 157 image159......Page 158 image160......Page 159 image161......Page 160 image162......Page 161 image163......Page 162 image164......Page 163 image165......Page 164 image166......Page 165 image167......Page 166 image168......Page 167 image169......Page 168 image170......Page 169 image171......Page 170 This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Gröbner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry. This Book Is About The Interplay Of Computational Commutative Algebra And The Theory Of Convex Polytopes. It Centers Around A Special Class Of Ideals In A Polynomial Ring: The Class Of Toric Ideals. They Are Characterized As Those Prime Ideals That Are Generated By Monomial Differences Or As The Defining Ideals Of Toric Varieties (not Necessarily Normal). The Interdisciplinary Nature Of The Study Of Grobner Bases Is Reflected By The Specific Applications Appearing In This Book. These Applications Lie In The Domains Of Integer Programming And Computational Statistics. The Mathematical Tools Presented In The Volume Are Drawn From Commutative Algebra, Combinatorics, And Polyhedral Geometry.