The complexity of linear problems in fields
Journal of Symbolic Computation
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
Simplification of quantifier-free formulae over ordered fields
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
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
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications
Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications
Combined Decision Techniques for the Existential Theory of the Reals
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
GiNaCRA: a C++ library for real algebraic computations
NFM'11 Proceedings of the Third international conference on NASA Formal methods
Virtual substitution for SMT-solving
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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We present $\texttt{SMT-RAT}$, a $\texttt{C++}$ toolbox offering theory solver modules for the development of SMT solvers for nonlinear real arithmetic (NRA). NRA is an important but hard-to-solve theory and only fragments of it can be handled by some of the currently available SMT solvers. Our toolbox contains modules implementing the virtual substitution method, the cylindrical algebraic decomposition method, a Gröbner bases simplifier and a general simplifier. These modules can be combined according to a user-defined strategy in order to exploit their advantages.