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Complex Arithmetic

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From:
Edward Cherlin
Date:
May 19, 2005 02:06
Subject:
Complex Arithmetic
Message ID:
200505190210.46390.cherlin@pacbell.net
There was a discussion of the principal value of square root on 
this list some time back, making the point that for positive 
real numbers the positive square root is the value of the 
standard function. In the complex plane it is desirable to 
define the principal value at every point so as to produce a 
minimum of surprises, such as sudden jumps at discontinuities. 
However, there must necessarily be a line of discontinuity. 
Similarly for other complex-valued functions, particularly the 
trig and inverse trig functions, some of which are 
infinite-valued. 

It turns out that the domain and range and the location of the 
cut lines have to be worked out separately for different 
functions. Mathematical practice is not entirely consistent in 
making these decisions, but in programming, there seems to be 
widespread agreement that the shared definitions used in the 
APL, Common LISP, and Ada standards are the best available.

Do we want to get into all of this in Perl6?
-- 
Edward Cherlin
Generalist & activist--Linux, languages, literacy and more
"A knot! Oh, do let me help to undo it!"
--Alice in Wonderland
http://cherlin.blogspot.com

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