Computations in Algebraic Geometry with Macaulay 2

ISBN: 978-3-642-07592-6 (Print) 978-3-662-04851-1 (Online)

Table of contents (11 chapters)

  1. Front Matter

    Pages i-xv

  2. Introducing Macaulay 2

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-15

      Ideals, Varieties and Macaulay 2

    3. No Access

      Book Chapter

      Pages 17-40

      Projective Geometry and Homological Algebra

    4. No Access

      Book Chapter

      Pages 41-53

      Data Types, Functions, and Programming

    5. No Access

      Book Chapter

      Pages 55-70

      Teaching the Geometry of Schemes

  3. Mathematical Computations

    1. Front Matter

      Pages 71-71

    2. No Access

      Book Chapter

      Pages 73-100

      Monomial Ideals

    3. No Access

      Book Chapter

      Pages 101-129

      From Enumerative Geometry to Solving Systems of Polynomial Equations

    4. No Access

      Book Chapter

      Pages 131-178

      Resolutions and Cohomology over Complete Intersections

    5. No Access

      Book Chapter

      Pages 179-214

      Algorithms for the Toric Hilbert Scheme

    6. No Access

      Book Chapter

      Pages 215-249

      Sheaf Algorithms Using the Exterior Algebra

    7. No Access

      Book Chapter

      Pages 251-279

      Needles in a Haystack: Special Varieties via Small Fields

    8. No Access

      Book Chapter

      Pages 281-323

      D-modules and Cohomology of Varieties

  4. Back Matter

    Pages 325-329