This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.
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Editorial Reviews
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"... Fazit: das Buch ist kein Lehrbuch im traditionellen Sinn. Sicherlich ist Teil I eine gelungene Einführung, wenn man schon die elementaren Grundlagen der Algebraischen oder Analytischen Geometrie kennt. In Teil II ist das Buch aber eher wie ein Tagungsband, in dem einzelne Spezialisten ihre Themen vorstellen. Hier kann man sich etwas aussuchen, denn die Artikel sind unabhängig voneinander. ... Ich habe beim Lesen viele interessante Stellen gefunden, die man beim flüchtigen Durchblättern übersehen kann. Man muss sich Zeit nehmen, dann wird der Band wirklich zum Gewinn für alle, die Interesse an Algebraischer Geometrie haben."
S.Müller-Stach, Jahresberichte der DMV 2002, Bd. 104, Heft 4
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Inside This Book
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First Sentence:
Our first example concerns geometric objects in (complex) affine 3-space. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
extra syzygies, prune homology, local cohomological dimension, transpose vars, flip graph, generic initial ideal, cohomology operators, graded complete intersection, monomial ideal, toric ideal, holonomic modules, bigraded module, cohomological degree, affine patch, local cohomology modules, minimal injective resolution, linear syzygies, standard monomials, minimal generators, schubert calculus, canonical curves, conic bundles, adjunction theory, enumerative problems, entries gens Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Bernd Sturmfels, David Eisenbud, Shape Lemma, David Cox, Donal O'Shea, John Little, Ezra Miller, Journal of Symbolic Computation, Algebraic Geom New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Our first example concerns geometric objects in (complex) affine 3-space. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
extra syzygies, prune homology, local cohomological dimension, transpose vars, flip graph, generic initial ideal, cohomology operators, graded complete intersection, monomial ideal, toric ideal, holonomic modules, bigraded module, cohomological degree, affine patch, local cohomology modules, minimal injective resolution, linear syzygies, standard monomials, minimal generators, schubert calculus, canonical curves, conic bundles, adjunction theory, enumerative problems, entries gens Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Bernd Sturmfels, David Eisenbud, Shape Lemma, David Cox, Donal O'Shea, John Little, Ezra Miller, Journal of Symbolic Computation, Algebraic Geom New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 16
books:
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- Computer Algebra and Differential Equations (London Mathematical Society Lecture Note Series) by Evelyne Tournier in Back Matter
- New York (Land of Liberty) by Ellen Sturm on page 214
- Principles of Algebraic Geometry by Phillip Griffiths in Back Matter
- Some Tapas of Computer Algebra (Algorithms and Computation in Mathematics) by Arjeh M. Cohen on page 128
- Lectures on Polytopes (Graduate Texts in Mathematics) by Gunter M. Ziegler on page 214
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