Branch cuts in computer algebra
ISSAC '94 Proceedings of the 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
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
A poly-algorithmic approach to simplifying elementary functions
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Testing elementary function identities using CAD
Applicable Algebra in Engineering, Communication and Computing
What Might "Understand a Function" Mean?
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
A Review of Mathematical Knowledge Management
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
NIST Handbook of Mathematical Functions
NIST Handbook of Mathematical Functions
The challenges of multivalued "Functions"
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
ACM Communications in Computer Algebra
Cylindrical algebraic decompositions for boolean combinations
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Program Verification in the Presence of Complex Numbers, Functions with Branch Cuts etc
SYNASC '12 Proceedings of the 2012 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
Hi-index | 0.00 |
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse trigonometric functions. Understanding these cuts is essential for working with the single-valued counterparts, the common approach to encoding multi-valued functions in computer algebra systems. While the defining choices are usually simple (typically portions of either the real or imaginary axes) the cuts induced by the expression may be surprisingly complicated. We have made explicit and implemented techniques for calculating the cuts in the computer algebra programme Maple. We discuss the issues raised, classifying the different cuts produced. The techniques have been gathered in the BranchCuts package, along with tools for visualising the cuts. The package is included in Maple 17 as part of the FunctionAdvisor tool.