Computational geometry: an introduction
Computational geometry: an introduction
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
Basic principles of mechanical theorem proving in elementary geometrics
Journal of Automated Reasoning
Mechanical geometry theorem proving
Mechanical geometry theorem proving
The complexity of linear problems in fields
Journal of Symbolic Computation
A bibliography of quantifier elimination for real closed fields
Journal of Symbolic Computation
Applications of Gro¨bner bases in non-linear computational geometry
Trends in computer algebra
Communications of the ACM
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Well … it isn't quite that simple
ACM SIGSAM Bulletin
An elimination method for polynomial systems
Journal of Symbolic Computation
Quantifier elimination for real algebra—the cubic case
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Guarded expressions in practice
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
Testing stability by quantifier elimination
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
Simulation and optimization by quantifier elimination
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
Simplification of quantifier-free formulae over ordered fields
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
A Geometrical Decision Algorithm Based on the Gröbner Bases Algorithm
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Mechanically Proving Geometry Theorems Using a Combination of Wu's Method and Collins' Method
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Approaches to parallel quantifier elimination
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Mixed real-integer linear quantifier elimination
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Solving Geometric Problems with Real Quantifier Elimination
ADG '98 Proceedings of the Second International Workshop on Automated Deduction in Geometry
Algebraic and Semialgebraic Proofs: Methods and Paradoxes
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
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
A generic projection operator for partial cylindrical algebraic decomposition
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Computer algebra handbook
Multiple object semilinear motion planning
Journal of Symbolic Computation
Implementing the cylindrical algebraic decomposition within the Coq system
Mathematical Structures in Computer Science
The complexity of quantifier elimination and cylindrical algebraic decomposition
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Investigating Generic Methods to Solve Hopf Bifurcation Problems in Algebraic Biology
AB '08 Proceedings of the 3rd international conference on Algebraic Biology
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
ACM Transactions on Programming Languages and Systems (TOPLAS)
Connecting the 3D DGS Calques3D with the CAS Maple
Mathematics and Computers in Simulation
Automatic discovery of geometry theorems using minimal canonical comprehensive Gröbner systems
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Verification and synthesis using real quantifier elimination
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Automatic verification of the adequacy of models for families of geometric objects
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
An introduction to java geometry expert
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
Towards solving the dynamic geometry bottleneck via a symbolic approach
ADG'04 Proceedings of the 5th international conference on Automated Deduction in Geometry
New domains for applied quantifier elimination
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
Solving dynamic geometric constraints involving inequalities
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
Proceedings of the 27th Annual ACM Symposium on Applied Computing
Optimising problem formulation for cylindrical algebraic decomposition
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
Note: On the complexity of quantified linear systems
Theoretical Computer Science
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We present a new method for proving geometric theorems in the real planeor higher dimension. The method is derived from elimination set ideas forquantifier elimination in linear and quadratic formulas over the reals. Incontrast to other approaches, our method can also prove theorems whosecomplex analogues fail. Moreover, the problem formulation may involve orderinequalities. After specification of independent variables, nondegeneracyconditions are generated automatically. Moreover, when trying to proveconjectures that – apart from nondegeneracy conditions – do nothold in the claimed generality, missing premises are found automatically. Wedemonstrate the applicability of our method to nontrivial examples.