An improved projection operation for cylindrical algebraic decomposition of three-dimensional space
Journal of Symbolic Computation
Quantifier elimination: Optimal solution for two classical examples
Journal of Symbolic Computation
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
On projection in CAD-based quantifier elimination with equational constraint
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
A New Approach for Automatic Theorem Proving in Real Geometry
Journal of Automated Reasoning
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
QEPCAD B: a program for computing with semi-algebraic sets using CADs
ACM SIGSAM Bulletin
Efficient projection orders for CAD
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
On using bi-equational constraints in CAD construction
Proceedings of the 2005 international symposium on Symbolic and algebraic 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
MetiTarski: An Automatic Prover for the Elementary Functions
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Computing cylindrical algebraic decomposition via triangular decomposition
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
MetiTarski: An Automatic Theorem Prover for Real-Valued Special Functions
Journal of Automated Reasoning
Speeding up cylindrical algebraic decomposition by gröbner bases
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
Real algebraic strategies for metitarski proofs
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
ACM Communications in Computer Algebra
Cylindrical algebraic decompositions for boolean combinations
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Program Verification in the Presence of Complex Numbers, Functions with Branch Cuts etc
SYNASC '12 Proceedings of the 2012 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
| Hi-index | 0.00 |
Cylindrical algebraic decomposition (CAD) is an important tool for the study of real algebraic geometry with many applications both within mathematics and elsewhere. It is known to have doubly exponential complexity in the number of variables in the worst case, but the actual computation time can vary greatly. It is possible to offer different formulations for a given problem leading to great differences in tractability. In this paper we suggest a new measure for CAD complexity which takes into account the real geometry of the problem. This leads to new heuristics for choosing: the variable ordering for a CAD problem, a designated equational constraint, and formulations for truth-table invariant CADs (TTICADs). We then consider the possibility of using Gröbner bases to precondition TTICAD and when such formulations constitute the creation of a new problem.