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We thank the National Science Foundation for generous funding since 1993 for this project, Gert-Martin Greuel and Ruediger Stobbe for the incorporation of their library Singular-Factory, and David Eisenbud, Wolfram Decker and Sorin Popescu for early support, encouragement and suggestions. We also acknowledge an intellectual debt to Dave Bayer, who, with Michael Stillman, wrote Macaulay, a specialized computer algebra system for algebraic geometry and the predecessor of this program.

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