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Branch Cuts in Computer Algebra (1994)
| Content Provider | CiteSeerX |
|---|---|
| Author | Dingle, Adam Fateman, Richard |
| Description | Many standard functions, such as the logarithm and square root functions, cannot be defined continuously on the complex plane. Mistaken assumptions about the properties of these functions lead computer algebra systems into various conundrums. We discuss how they can manipulate such functions in a useful fashion. 1 Introduction Many standard functions, such as the logarithm and square root functions, cannot be defined continuously on the complex plane. When working with such functions, arbitrary lines of discontinuity, or branch cuts, must be chosen. For example, the conventional branch cut for the complex logarithm function lies along the negative real axis, so that log(\Gamma1) = ßi but when ffl 1 is small, real, and positive, we require log(\Gamma1 \Gamma ffl 1 i) = \Gammaßi + ffl 2 for some small, complex ffl 2 . Most computer algebra systems provide little assistance in working with expressions involving functions with complex branch cuts. Worse, by their ignorance of the existen... |
| File Format | |
| Language | English |
| Publisher | ACM Press |
| Publisher Date | 1994-01-01 |
| Publisher Institution | In ISSAC '94 Proc. Internat. Symp. Symbolic Algebraic Comput |
| Access Restriction | Open |
| Subject Keyword | Complex Ffl Branch Cut Useful Fashion Complex Plane Little Assistance Various Conundrum Negative Real Axis Complex Logarithm Function Computer Algebra System Square Root Function Mistaken Assumption Many Standard Function Arbitrary Line Introduction Many Standard Function Conventional Branch Cut Computer Algebra Gamma1 Gamma Complex Branch Cut |
| Content Type | Text |
| Resource Type | Article |
