On the application of Buchberger's algorithm to automated geometry theorem proving
Journal of Symbolic Computation
Using Gröbner bases to reason about geometry problems
Journal of Symbolic Computation
Mechanical geometry theorem proving
Mechanical geometry theorem proving
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Implementation of a geometry theorem proving package in SCRATCHPAD II
EUROCAL '87 Proceedings of the European Conference on Computer Algebra
Automated reasoning in geometries using the characteristic set method and Gröbner basis method
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Connecting the 3D DGS Calques3D with the CAS Maple
Mathematics and Computers in Simulation
| Hi-index | 0.00 |
Modern application areas like computer-aided design and robotics have revived interest in geometry. The algorithmic techniques of computer algebra are important tools for solving large classes of nonlinear geometric problems. However, their application requires a translation of geometric problems into algebraic form. So far, this algebraization process has not gained special attention, since it was considered “obvious”.In the context of automated geometry theorem proving, the use of algebraic deduction techniques lead to very promising results, but it seemed to change the nature of proof problems from deciding the validity of a theorem to finding nondegeneracy conditions under which the theorem holds.A careful analysis shows, that this is mainly due to the “careless” translation method. A careful translation technique is presented that resolves this defect. The usefulness of the new algebraization method is demonstrated on concrete examples, a practical comparison with the former “careless” translation is done.Keywords: computational analytical geometry, automated geometry theorem proving.