Eisenbud D. — Computations in Algebraic Geometry with Macaulay 2 :: Электронная библиотека попечительского совета мехмата МГУ

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Eisenbud D. — Computations in Algebraic Geometry with Macaulay 2

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Название: Computations in Algebraic Geometry with Macaulay 2

Автор: Eisenbud D.

Аннотация:

This book presents algorithmic tools for algebraic geometry and experimental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems.

Язык:

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 345

Добавлена в каталог: 12.03.2005

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Предметный указатель

Monomial ideal      73 74
Monomial order on       287
Monomial support      75
monomialCurveIdeal      18
MonomialIdeal      74
Multiplicity      61 69
Nilpotent orbits      56
Normaliz      203
Normalization      203
Normally ordered expression      287
NP-complete      81
nullhomotopy      134
Number field      277
One-parameter family      68
Oo      48
Pfaffan complex      268
Pluecker coordinate      115 121 122 127
Pluecker embedding      115
Pluecker ideal      115
Poincare series      162
polarCone.m2      207
Polarization      92
Polyhedral subdivision      190
Polynomial equations      101 103
Polynomial equations, deficient      101
Polynomial equations, overdetermined      117
Positions      34
Prepend      44
Presentation      21
Presentation minimal      25
Primary decomposition      30 77 81 84
print      46
Printing to a file      48
PRODUCT      44
Product rule      289 291
Projective space      17
Prune      25
Quadratic form      113 121
Random curves      253
Random nodal curve      254
Random points      253
Rank 1 linear syzygy      272
Rational normal curve      118
Rational normal scroll      34
Rational parameterization      56
Rational quartic curve      63 93
Reduced Ext module      149
Reduced form      19
Reduced ring of cohomology operators      149
Rees algebra      64
res      21
Resolution      150
Resolution, free      21
RETURN      45
Riemann — Roch theorem, geometric      34
Ring of cohomology operators      147
Ring, making one      47
saturate      29
Saturation      29 55 62 103 123
SCAN      45 167
Scheme over a number field      60
Scheme, affne      55 64
Scheme, arithmetic      55
Scheme, irreducible      56
Scheme, non-reduced      62 69
Scheme, reduced      62
Schreyer’s algorithm for free resolutions      22
Schubert calculus      114 115 117 118 120
Scroll, rational normal      34
Secondary polytope      191
Segre embedding      66
Sequences      42

Serre correspondence      18
Serre’s intersection formula      26
Set      50
Shape lemma      104 120
Shapiros’s Conjecture      118
Sheaf      26
Sheaf cohomology      26 222 224 225
Sheaf, representation of      18
Simplicial complex      75
Simplicial complex, f -vector      75
Singular locus      58 65
Singular locus of a scheme      30
Solving polynomial equations      103 251
Solving polynomial equations via eigenvectors      106
Solving polynomial equations via elimination      104
Solving polynomial equations via numerical homotopy      110
Solving polynomial equations, real solutions      107
Source      22
Sphere      113 122 127
Splitting theorem of Grothendieck      227
Splitting theorem of Horrocks      227
Stable equivalence      228
Standard pair      83–86
standardPairs      85
Stanley — Reisner ideal      75 191
stdio      46
Stickelberger’s theorem      106
strings      42
Sturm sequence      107
SUM      44
Support variety      167 175
Symbol      287
Symbolic computation      102
symbols      41
Symmetric algebra      139
Syzygies of canonical curves      263
Table of Betti numbers      252
tally      50
TARGET      22
Tate resolution      215 222
Tautological subbundle      227
Term order on       288
Time      30
toExternalString      48
Top dimensional part of an ideal      30
Topology of a projective variety      29
Tor      28
Toric Hilbert scheme      179
Toric ideal      87 179
toString      48
Trace form      108
Triangulation      190
Triangulation, regular      191
Trigonal curve      32
TRIM      33
Twisted cubic      18
Unirationality      251 258
Value      48
Values of a hash table      49
variables, local      44
Vector bundle      226
Veronese surface      34
Vertex cover      81
Vertex ideal      98
Visible lists      42
Wall ideal      186
Weight      287
Weight vector      295
Weight vector for       287
Weight vectors, equivalent      199
Weyl algebra      286
while      45 183

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