Lagrange multipliers and optimality
SIAM Review
A Skeptic’s Approach to Combining HOL and Maple
Journal of Automated Reasoning
Formal Verification of Floating Point Trigonometric Functions
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
Verifying the Accuracy of Polynomial Approximations in HOL
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
An effective decision method for semidefinite polynomials
Journal of Symbolic Computation
A proof-producing decision procedure for real arithmetic
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
An algebraic approach for the unsatisfiability of nonlinear constraints
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Parametric Linear Arithmetic over Ordered Fields in Isabelle/HOL
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Proving Bounds on Real-Valued Functions with Computations
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
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
Automated deduction for verification
ACM Computing Surveys (CSUR)
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Efficient and accurate computation of upper bounds of approximation errors
Theoretical Computer Science
Proof certificates for algebra and their application to automatic geometry theorem proving
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
On the generation of positivstellensatz witnesses in degenerate cases
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
Differential dynamic logics: automated theorem proving for hybrid systems
Differential dynamic logics: automated theorem proving for hybrid systems
A functional framework for result checking
FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
Abstract partial cylindrical algebraic decomposition i: the lifting phase
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Formalization of Bernstein Polynomials and Applications to Global Optimization
Journal of Automated Reasoning
Certification of bounds of non-linear functions: the templates method
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
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Techniques based on sums of squares appear promising as a general approach to the universal theory of reals with addition and multiplication, i.e. verifying Boolean combinations of equations and inequalities. A particularly attractive feature is that suitable 'sum of squares' certificates can be found by sophisticated numerical methods such as semidefinite programming, yet the actual verification of the resulting proof is straightforward even in a highly foundational theorem prover. We will describe our experience with an implementation in HOL Light, noting some successes as well as difficulties. We also describe a new approach to the univariate case that can handle some otherwise difficult examples.