Cylindrical algebraic decomposition II: an adjacency algorithm for the plane
SIAM Journal on Computing
Decreasing the nesting depth of expressions involving square roots
Journal of Symbolic Computation
Real quantifier elimination is doubly exponential
Journal of Symbolic Computation
A cluster-based cylindrical algebraic decomposition algorithm
Journal of Symbolic Computation
ACM SIGSAM Bulletin
“According to Abramowitz and Stegun” or arccoth needn't be uncouth
ACM SIGSAM Bulletin - Special issue of OpenMath
Reasoning about the Elementary Functions of Complex Analysis
Annals of Mathematics and Artificial Intelligence
An Assume Facility for CAS, with a Sample Implementation for Maple
DISCO '92 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
MKM from Book to Computer: A Case Study
MKM '03 Proceedings of the Second International Conference on Mathematical Knowledge Management
Better simplification of elementary functions through power series
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
ESF: an automatically generated encyclopedia of special functions
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
A poly-algorithmic approach to simplifying elementary functions
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Not seeing the roots for the branches: multivalued functions in computer algebra
ACM SIGSAM Bulletin
Adherence is better than adjacency: computing the Riemann index using CAD
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
A Comparison of Equality in Computer Algebra and Correctness in Mathematical Pedagogy
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
ACM Communications in Computer Algebra
Understanding branch cuts of expressions
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
Students' comparison of their trigonometric answers with the answers of a computer algebra system
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
Automated simplification of large symbolic expressions
Journal of Symbolic Computation
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We present an algorithm for simplifying a large class of elementary functions in the presence of branch cuts. This algorithm works by:(a) verifying that the proposed simplification is correct as a simplification of multi-valued functions;(b) decomposing C (or Cn in the case of multivariate simplifications) according to the branch cuts of the relevant functions;(c) checking that the proposed identity is valid on each component of that decomposition.This process can be interfaced to an assume facility, and, if required, can verify that simplifications are valid "almost everywhere".