Computational algebraic geometry of projective configurations

Authors:
Bernd Sturmfels
Affiliations:
Department of Mathematics, Cornell University, Ithaca, NY 14858, U.S.A.
Venue:
Journal of Symbolic Computation
Year:
1991

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Abstract

This article deals with algorithmic and structural aspects related to the computer-aided study of incidence configurations in plane projective geometry. We describe invariant-theoretic algorithms and complexity results for computing the realization space and deciding the coordinatizability of configurations. A practical procedure for automated theorem proving in projective geometry is obtained as a special case. We use the final polynomial technique of Bokowski and Whiteley for encoding the resulting proofs, and we apply Buch-berger's Grobner basis method for computing minimum degree final polynomials and final syzygies, thus attaining the bounds in the recent effective versions of Hubert's Nullstellen-satz.