Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
Cylindrical algebraic decomposition II: an adjacency algorithm for the plane
SIAM Journal on Computing
Mechanical geometry theorem proving
Mechanical geometry theorem proving
Algebraic methods for geometric reasoning
Annual review of computer science: vol. 3, 1988
Geometric reasoning with logic and algebra
Artificial Intelligence - Special issue on geometric reasoning
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Applications of Gro¨bner bases in non-linear computational geometry
Geometric reasoning
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Mechanical theorem proving in geometries
Mechanical theorem proving in geometries
Polynomial Algorithms in Computer Algebra
Polynomial Algorithms in Computer Algebra
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Automated Production of Readable Proofs for Theorems in Non-Euclidian Geometries
Selected Papers from the International Workshop on Automated Deduction in Geometry
Automated Geometric Reasoning: Dixon Resultants, Gröbner Bases, and Characteristic Sets
Selected Papers from the International Workshop on Automated Deduction in Geometry
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
A Practical Program of Automated Proving for a Class of Geometric Inequalities
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
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Automated discovering and proving for geometric inequalities have been considered a difficult topic in the area of automated reasoning for manyy ears. Some well-known algorithms are complete theoretically but inefficient in practice, and cannot verify non-trivial propositions in batches. In this paper, we present an efficient algorithm to discover and prove a class of inequality-type theorems automatically by combining discriminant sequence for polynomials with Wu's elimination and a partial cylindrical algebraic decomposition. Also this algorithm is applied to the classification of the real physical solutions of geometric constraint problems. Manygeom etric inequalities have been discovered by our program, DISCOVERER, which implements the algorithm in Maple.