Read e-book online Automated Deduction in Geometry: 4th International Workshop, PDF

By Gábor Bodnár (auth.), Franz Winkler (eds.)

This e-book constitutes the completely refereed post-proceedings of the 4th overseas Workshop on computerized Deduction in Geometry, ADG 2002, held at Hagenberg citadel, Austria in September 2002.

The thirteen revised complete papers offered have been rigorously chosen in the course of rounds of reviewing and development. one of the matters addressed are theoretical and methodological themes, similar to the answer of singularities, algebraic geometry and laptop algebra; quite a few geometric theorem proving structures are explored; and functions of computerized deduction in geometry are proven in fields like computer-aided layout and robotics.

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Extra info for Automated Deduction in Geometry: 4th International Workshop, ADG 2002, Hagenberg Castle, Austria, September 4-6, 2002. Revised Papers

Example text

It is straight forward to convert a statement in predicate form to algebraic form. The following is the algebraic form of Simson’s theorem in predicate form given above. geom([[y5,x5,y4,x4,y3,x3,y2,x2,y1,x1,v2,u1,v1],[], [2*v1*y1-v1^2,2*v2*y1+2*u2*x1-v2^2-u2^2, y2^2-2*y1*y2+x2^2-2*x1*x2,-v1*x3, -v1*y3+v1*y2,u2*y4-v2*x4+v1*x4-u2*v1, -v2*y4+v1*y4-u2*x4+v2*y2-v1*y2+u2*x2,u2*y5-v2*x5, -v2*y5-u2*x5+v2*y2+u2*x2], [v1^2,v2^2-2*v1*v2+v1^2+u2^2,v2^2+u2^2], [x4*y5-x3*y5-y4*x5+y3*x5+x3*y4-y3*x4]]); MMP/Geometer – A Software Package for Automated Geometric Reasoning 49 Natrual Language Form Constructive Form AGDG Predicate Form Algebraic Form Fig.

After a statement is inputted, it may be described in four forms: the natural language form, the constructive form, the predicate form, and the algebraic form. The purpose of using different input forms is that each input form has its merit. For instance, the natural language input may be the favorable choice for high school students. The constructive form is the input form for several proving methods, like the area method[8]. The predicate form is the most general way of describing a statement.

5 Partition’s Cells Computation A way to represent such cells is now to compute a Cylindrical Algebraic Decomposition (CAD - see [3]) of R3 adapted to this set of polynomials. But it may give us a result very huge and difficult to analyse in practice, and with lots of cells we are not interested in. In order to obtain a decomposition easier to manipulate, we use the fact that we are just interested in the “generic” solutions, so in the cells of maximal dimension in our partition of the space of parameters.

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