The complexity of linear problems in fields
Journal of Symbolic Computation
The complexity of almost linear diophantine problems
Journal of Symbolic Computation
Towards computing non algebraic cylindrical decompositions
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Wu's method and the Khovanskii finiteness theorem
Journal of Symbolic Computation
The elementary constant problem
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
Nonlinear control system design 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
Advances on the simplification of sine-cosine equations
Journal of Symbolic Computation
Algorithms for trigonometric curves (simplification, implicitization, parameterization)
Journal of Symbolic Computation
Mixed real-integer linear quantifier elimination
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Quantifier elimination for trigonometric polynomials by cylindrical trigonometric decomposition
Journal of Symbolic Computation
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Symbolic Reachability Computation for Families of Linear Vector Fields
Journal of Symbolic Computation
Deciding polynomial-exponential problems
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Interactions Between PVS and Maple in Symbolic Analysis of Control Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Deciding polynomial-transcendental problems
Journal of Symbolic Computation
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In this paper, we present a decision procedure for certain linear-trigonometric problems for the reals and integers formalized in a suitable first-order language. The inputs are restricted to formulas, where all but one of the quantified variables occur linearly and at most one occurs both linearly and in a specific trigonometric function. Moreover we may allow in addition the integer-part operation in formulas. Besides ordinary quantifiers, we allow also counting quantifiers. Furthermore we also determine the qualitative structure of the connected components of the satisfaction set of the mixed linear-trigonometric variable. We also consider the decision of these problems in subfields of the real algebraic numbers.