عنوان

Mechanical theorem proving in geometries :

370916639X

9783709166390

b587227

Mechanical theorem proving in geometries :

[Book]

basic principles

by Wen-tsün Wu.

Vienna

Springer Vienna

1994

(xiv, 288 pages) : illustrations

Texts and Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes-Kepler-University, Linz, Austria.

Author's note to the English-language edition --; 1 Desarguesian geometry and the Desarguesian number system --; 1.1 Hilbert's axiom system of ordinary geometry --; 1.2 The axiom of infinity and Desargues' axioms --; 1.3 Rational points in a Desarguesian plane --; 1.4 The Desarguesian number system and rational number subsystem --; 1.5 The Desarguesian number system on a line --; 1.6 The Desarguesian number system associated with a Desarguesian plane --; 1.7 The coordinate system of Desarguesian plane geometry --; 2 Orthogonal geometry, metric geometry and ordinary geometry --; 2.1 The Pascalian axiom and commutative axiom of multiplication --; (unordered) Pascalian geometry --; 2.2 Orthogonal axioms and (unordered) orthogonal geometry --; 2.3 The orthogonal coordinate system of (unordered) orthogonal geometry --; 2.4 (Unordered) metric geometry --; 2.5 The axioms of order and ordered metric geometry --; 2.6 Ordinary geometry and its subordinate geometries --; 3 Mechanization of theorem proving in geometry and Hilbert's mechanization theorem --; 3.1 Comments on Euclidean proof method --; 3.2 The standardization of coordinate representation of geometric concepts --; 3.3 The mechanization of theorem proving and Hilbert's mechanization theorem about pure point of intersection theorems in Pascalian geometry --; 3.4 Examples for Hilbert's mechanical method --; 3.5 Proof of Hilbert's mechanization theorem --; 4 The mechanization theorem of (ordinary) unordered geometry --; 4.1 Introduction --; 4.2 Factorization of polynomials --; 4.3 Well-ordering of polynomial sets --; 4.4 A constructive theory of algebraic varieties --; irreducible ascending sets and irreducible algebraic varieties --; 4.5 A constructive theory of algebraic varieties --; irreducible decomposition of algebraic varieties --; 4.6 A constructive theory of algebraic varieties --; the notion of dimension and the dimension theorem --; 4.7 Proof of the mechanization theorem of unordered geometry --; 4.8 Examples for the mechanical method of unordered geometry --; 5 Mechanization theorems of (ordinary) ordered geometries --; 5.1 Introduction --; 5.2 Tarski's theorem and Seidenberg's method --; 5.3 Examples for the mechanical method of ordered geometries --; 6 Mechanization theorems of various geometries --; 6.1 Introduction --; 6.2 The mechanization of theorem proving in projective geometry --; 6.3 The mechanization of theorem proving in Bolyai-Lobachevsky's hyperbolic non-Euclidean geometry --; 6.4 The mechanization of theorem proving in Riemann's elliptic non-Euclidean geometry --; 6.5 The mechanization of theorem proving in two circle geometries --; 6.6 The mechanization of formula proving with transcendental functions --; References.

This book is a translation of Professor Wu's seminal Chinese book of 1984 on Automated Geometric Theorem Proving. The translation was done by his former student Dongming Wang jointly with Xiaofan Jin so that authenticity is guaranteed. Meanwhile, automated geometric theorem proving based on Wu's method of characteristic sets has become one of the fundamental, practically successful, methods in this area that has drastically enhanced the scope of what is computationally tractable in automated theorem proving. This book is a source book for students and researchers who want to study both the intuitive first ideas behind the method and the formal details together with many examples.

Automatic theorem proving.

Geometry -- Data processing.

Mathematics.

by Wen-tsün Wu.

Wen-tsün Wu

[Book]

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