Galois' theory of algebraic equations
Galois' theory of algebraic equations
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Branch cuts in computer algebra
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Multiple-valued complex functions and computer algebra
ACM SIGSAM Bulletin
A representation of branch-cut information
ACM SIGSAM Bulletin
Function evaluation on branch cuts
ACM SIGSAM Bulletin
ACM SIGSAM Bulletin
Rectifying transformations for the integration of rational trigonometric functions
Journal of Symbolic Computation
Simplication of symbolic-numerical interval expressions
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
“According to Abramowitz and Stegun” or arccoth needn't be uncouth
ACM SIGSAM Bulletin - Special issue of OpenMath
Computer algebra: the end of mathematics?
ACM SIGSAM Bulletin
Reasoning about the Elementary Functions of Complex Analysis
Annals of Mathematics and Artificial Intelligence
Towards better simplification of elementary functions
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Better simplification of elementary functions through power series
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Algebra: An elementary text-book.--
Algebra: An elementary text-book.--
Adherence is better than adjacency: computing the Riemann index using CAD
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Useful computations need useful numbers
ACM Communications in Computer Algebra
CTP-based programming languages?: considerations about an experimental design
ACM Communications in Computer Algebra
Ten commandments for good default expression simplification
Journal of Symbolic Computation
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We discuss the multiple definitions of multivalued functions and their suitability for computer algebra systems. We focus the discussion by taking one specific problem and considering how it is solved using different definitions. Our example problem is the classical one of calculating the roots of a cubic polynomial from the Cardano formulae, which contain fractional powers. We show that some definitions of these functions result in formulae that are correct only in the sense that they give candidates for solutions; these candidates must then be tested. Formulae that are based on single-valued functions, in contrast, are efficient and direct.