Deciding polynomial-transcendental problems

DOI10.1016/j.jsc.2011.08.009zbMath1243.03015OpenAlexW2015314684MaRDI QIDQ654031

Scott McCallum, Volker Weispfenning

Publication date: 21 December 2011

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2011.08.009

zbMATH Keywords

exponential polynomialdecision proceduretranscendental function

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Decidability of theories and sets of sentences (03B25)

Related Items (12)

Positive root isolation for poly-powers by exclusion and differentiation ⋮ Isolating all the real roots of a mixed trigonometric-polynomial ⋮ Deciding first-order formulas involving univariate mixed trigonometric-polynomials ⋮ Automated proof of mixed trigonometric-polynomial inequalities ⋮ On the zeros of univariate E-polynomials ⋮ Decision problem for a class of univariate Pfaffian functions ⋮ On the set of reduced states of translation invariant, infinite quantum systems ⋮ Quantifier elimination for a class of exponential polynomial formulas ⋮ Zero counting for a class of univariate Pfaffian functions ⋮ A conflict-driven solving procedure for poly-power constraints ⋮ NIL: learning nonlinear interpolants ⋮ Exact solutions in log-concave maximum likelihood estimation

Uses Software

• REDUCE
• REDLOG

Cites Work

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• Quantifier elimination and cylindrical algebraic decomposition. Proceedings of a symposium, Linz, Austria, October 6--8, 1993
• Nonlinear control system design by quantifier elimination
• Robust multi-objective feedback design by quantifier elimination
• Testing stability by quantifier elimination
• Virtual roots of real polynomials
• Computing in the field of complex algebraic numbers
• On the Lambert \(w\) function
• Generalized Budan--Fourier theorem and virtual roots
• Cylindrical algebraic decomposition using validated numerics
• Real root isolation for tame elementary functions
• Deciding polynomial-exponential problems

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