Bibliography for Grobner Basis Minicourse, March 2005

• An Introduction to Grobner Bases by W. Adams and P. Loustaunau published by the American Mathematical Society (Graduate Studies in Mathematics, Vol 3).
• An Introduction to Grobner Bases by R. Froberg published by Wiley-Interscience Series.
• Ideals, Varieties, and Algorithms by D. Cox, J. Little, and D. O'Shea, published by Springer Verlag.
• Using Algebraic Geometry by D. Cox, J. Little, and D. O'Shea, published by Springer Verlag.
• Computational Commutative Algebra 1 by M. Kreuzer and L. Robbiano, published by Springer Verlag.
• A Singular Introduction to Commutative Algebra by Gert-Martin Greuel and Gerhard Pfister, published by Springer Verlag.
• Computations in Algebraic Geometry with Macaulay 2 by David Eisenbud, Daniel R. Grayson, Michael Stillman, Bernd Sturmfels (Eds.), published by Springer Verlag.
• Computational Methods in Commutative Algebra and Algebraic Geometry by Wolmer V. Vasconcelos, published by Springer Verlag.
• Computational Algebraic Geometry by Hal Schenck, published by Cambridge University Press.
• G.-M. Greuel, Computer Algebra and Algebraic Geometry- Achievements and Perspectives, Journal of Symbolic Computation, 30 (2000) 253-290.
• D. Bayer and D. Mumford, What can be computed in algebraic geometry?, Computational algebraic geometry and commutative algebra (Cortona, 1991), 1--48, Sympos. Math., XXXIV, Cambridge Univ. Press, Cambridge, 1993.

Computer Algebra Packages

• CoCoA: "Computations in Commutative Algebra" (See the book by Kreuzer and Robbiano.)
  Available free on the internet at http://cocoa.dima.unige.it.
• Macaulay 2: (See the book by Eisenbud, Grayson, Stillman, Sturmfels.)
  Available free on the internet at http://www.math.uiuc.edu/Macaulay2.
• Singular: (See the book by Greuel and Pfister)
  Available free on the internet at http://www.singular.uni-kl.de.
• Magma: This is available on the department machines by typing in the command "magma"
• Mathematica: This program has a good Grobner Basis package although it does not have the direct commands for computations in commutative algebra that the other four do. But it does have the only implementation of Grobner Bases over the integers that I am aware of that is readily available. It is on the department machines. Maple has a similar package.