## Can Your Computer Do Complex Analysis?

### BibTeX

@MISC{Aslaksen_canyour,

author = {Helmer Aslaksen},

title = {Can Your Computer Do Complex Analysis?},

year = {}

}

### OpenURL

### Abstract

### Citations

45 |
Theory of Complex Functions
- Remmert
- 1991
(Show Context)
Citation Context ...ds, we get 2 Log. z/ D 2 Log z, or Log. z/ D Log z. If (5) holds, we would have 1 D p 1 D p . 1/. 1/ D i i D 1: For (6), we consider a paradox due to the Danish mathematician Thomas Clausen ([Cla27], =-=[Rem91]-=-). It was published as an exercise in Crelle’s journal in 1827. Let n be an integer. Then e 1C2n i D e; and If we assume (6), we get .e 1C2n i / 1C2n i D e 1C2n i D e: .e 1C2n i / 1C2n i 1C4n i 4n2 2 ... |

14 |
and Misdemeanors in the Computer Algebra Trade
- Stoutemyer, Crimes
- 1991
(Show Context)
Citation Context ...ake the readers aware of some of the problems and their solutions, and to encourage the readers to sit down and experiment with their favorite programs. I hope the following eight tests (adapted from =-=[Sto91]-=-) will serve as a starting point for interesting explorations. Computer algebra systems are in general much better at reducing the difference between two equivalent expressions to 0, rather than simpl... |

12 |
Theory of Complex Functions, Graduate Texts
- Remmert
- 1991
(Show Context)
Citation Context ..., we get 2 Log(−z) = 2Logz, or Log(−z) = Logz. If (5) holds, we would have 1 = √ 1 = � (−1)(−1) =ii = −1. (7) For (6), we consider a paradox due to the Danish mathematician Thomas Clause=-=n ([Claus27], [Remme91]). It w-=-as published as an exercise in Crelle’s journal in 1827. Let n be an integer. Then e 1+2nπi =e, 2sand If we assume (6), we get and it follows that (e 1+2nπi ) 1+2nπi =e 1+2nπi =e. (e 1+2nπi ) 1... |

9 | Multiple-valued complex functions and computer algebra
- Aslaksen
- 1996
(Show Context)
Citation Context ...re Singapore 117543 Singapore aslaksen@math.nus.edu.sg www.math.nus.edu.sg/aslaksen/ The purpose of this paper is to elaborate on the results in my earlier paper on multiple-valued complex functions (=-=[Asl96]-=-) using the unwinding number notation introduced by Corless and Jeffrey ([CJ96]). 2 Basic problems of multiple-valued complex functions For z D x C iy, the complex exponential function is defined by e... |

6 |
A review of CAS mathematical capabilities. Computer Algebra Nederland Nieuwsbrief 13
- Wester
- 1994
(Show Context)
Citation Context ...ecome interesting. 5s3 Computer tests Many people have attempted to test the capabilities of different computer algebra systems. The most well known is probably the tests developed by Michael Wester (=-=[Weste94]-=-). While such tests definitely serve a purpose, I am sometimes troubled by their use in comparing different systems. It is not clear to me that the way a program performs on such problems truly reflec... |

5 | A Review of CAS Mathematical Capabilities
- Wester
- 1994
(Show Context)
Citation Context ... become interesting. 3 Computer tests Many people have attempted to test the capabilities of different computer algebra systems. The most well known is probably the tests developed by Michael Wester (=-=[Wes94]-=-). While such tests definitely serve a purpose, I am sometimes troubled by their use in comparing different systems. It is not clear to me that the way a program performs on such problems truly reflec... |

2 | Editor’s Corner: The Unwinding number
- Corless, Jeffrey
- 1996
(Show Context)
Citation Context ...sen/ The purpose of this paper is to elaborate on the results in my earlier paper on multiple-valued complex functions ([Asl96]) using the unwinding number notation introduced by Corless and Jeffrey (=-=[CJ96]-=-). 2 Basic problems of multiple-valued complex functions For z D x C iy, the complex exponential function is defined by e z D e x .cos y C i sin y/: We define the principal argument by z D jzje i Arg ... |

2 |
Aufgabe 53
- Clausen
(Show Context)
Citation Context ...t (4) holds, we get 2 Log(−z) = 2Logz, or Log(−z) = Logz. If (5) holds, we would have 1 = √ 1 = � (−1)(−1) =ii = −1. (7) For (6), we consider a paradox due to the Danish mathematician Th=-=omas Clausen ([Claus27], [Rem-=-me91]). It was published as an exercise in Crelle’s journal in 1827. Let n be an integer. Then e 1+2nπi =e, 2sand If we assume (6), we get and it follows that (e 1+2nπi ) 1+2nπi =e 1+2nπi =e. (e... |

1 |
1827) Aufgabe 53. Journal für die Reine und Angewandte Mathematik 2
- Clausen
(Show Context)
Citation Context ...t (4) holds, we get 2 Log. z/ D 2 Log z, or Log. z/ D Log z. If (5) holds, we would have 1 D p 1 D p . 1/. 1/ D i i D 1: For (6), we consider a paradox due to the Danish mathematician Thomas Clausen (=-=[Cla27]-=-, [Rem91]). It was published as an exercise in Crelle’s journal in 1827. Let n be an integer. Then e 1C2n i D e; and If we assume (6), we get .e 1C2n i / 1C2n i D e 1C2n i D e: .e 1C2n i / 1C2n i 1C4n... |