Automated Deduction in Geometry: 5th International Workshop, by Laura I. Meikle, Jacques D. Fleuriot (auth.), Hoon Hong,

By Laura I. Meikle, Jacques D. Fleuriot (auth.), Hoon Hong, Dongming Wang (eds.)

This publication constitutes the completely refereed post-proceedings of the fifth foreign Workshop on automatic Deduction in Geometry, ADG 2004, held at Gainesville, FL, united states in September 2004.

The 12 revised complete papers provided have been conscientiously chosen from the papers accredited for the workshop after cautious reviewing. All present concerns within the zone are addressed - theoretical and methodological issues in addition to purposes thereof - specifically computerized geometry theorem proving, automatic geometry challenge fixing, difficulties of dynamic geometry, and an object-oriented language for geometric objects.

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Extra resources for Automated Deduction in Geometry: 5th International Workshop, ADG 2004, Gainesville, FL, USA, September 16-18, 2004. Revised Papers

Example text

Then g is in the radical of the ideal obner basis of (F, gy − 1). IF if and only if {1} is the reduced Gr¨ Proof. See [1, 5]. Proving Geometric Theorems by Partitioned-Parametric Gr¨ obner Bases 41 We can extend the above theorem to the case of polynomial ideals involving parameters to establish the following theorem, which can solve the parametric radical ideal membership problem. Theorem 5 (Parametric Radical Ideal Membership). Let h1 , . . , hr , g be polynomials in K[u, x], G={(C1 , G1 ), .

As are in K[u, x]. f is a linear combination with coefficients in K(u), of monomials, none of which is divisible by any of lm(f1 ), . . , lm(fs ). For example, F = {vxy + ux2 + x, uy 2 + x2 } and f = vy 2 + ux3 y + y, assuming a lexicographic order on terms defined by the variable order y > x. Then vuy − v 2 x2 − u3 x4 − u2 x3 f¯F = . uv Let f be a polynomial in K(u)[x]. We use num(f ) to denote the numerator of f ; num(f ) is in K[u, x]. Theorem 2. The parametric partition {(C1 , G1 ), . .

The axiom set provides the basis of computational origami. Namely, by implementing the axiom set by a computer, we can construct sophisticated origami works. Although the notion of completeness is unclear as we do not yet identify a class of origami constructible geometrical objects, by the subsequent works of several mathematicians, we know that origami is more powerful than classical Euclidean construction by a ruler and a compass. Huzita’s 6th axiom plainly states that we can make a fold that brings two points on two lines.

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