Integration of rational functions: Rational computation of the logarithmic part
Journal of Symbolic Computation
A note on subresultants and the Lazard/Rioboo/Trager formula in rational function integration
Journal of Symbolic Computation
“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
Equality in computer algebra and beyond
Journal of Symbolic Computation - Integrated reasoning and algebra systems
Adherence is better than adjacency: computing the Riemann index using CAD
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Testing elementary function identities using CAD
Applicable Algebra in Engineering, Communication and Computing
Computing the real solutions of polynomial systems with the RegularChains library in Maple
ACM Communications in Computer Algebra
Understanding branch cuts of expressions
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
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Although, formally, mathematics is clear that a function is a single-valued object, mathematical practice is looser, particularly with n-th roots and various inverse functions. In this paper, we point out some of the looseness, and ask what the implications are, both for Artificial Intelligence and Symbolic Computation, of these practices. In doing so, we look at the steps necessary to convert existing texts into (a) rigorous statements (b) rigorously proved statements. In particular we ask whether there might be a constant "de Bruijn factor" [18] as we make these texts more formal, and conclude that the answer depends greatly on the interpretation being placed on the symbols.