Ken, Your 1/2 example is hyperbole. As I said earlier, 0.5 and 1/2 are far more related (rationals being dense in the reals and all that) than are 1/2 and 0.5+0.0i. Complex numbers are inherently different from the magnitudes that we normally use, and I think you will come to agree if you think about the various coercions that would naturally follow from what you propose. A well-rounded package for complex numbers would be greatly appreciated, but I fear we would regret fully wiring it into the magnitude hierarchy. There are times when taking the square root of a negative number means the algorithm has gone wrong and an error is appropriate; other times getting a complex answer is business as usual. Demanding that the programmer use #asComplex to enter a closed system of complex numbers and associated operators solves the problem of deciding between the two worlds. Trying to do their thining for them will backfire. Bill -----Original Message----- From: pharo-project-bounces@lists.gforge.inria.fr [mailto:pharo-project-bounces@lists.gforge.inria.fr] On Behalf Of Ken.Dickey Sent: Wednesday, August 12, 2009 10:11 AM To: Pharo-project@lists.gforge.inria.fr Subject: Re: [Pharo-project] Complex neurotic KenD> > Currently:

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-1 asComplex isNumber --> true ?1 asComplex isNumber -> true -1 asComplex < 1 asComplex --> error

-4 sqrt --> error

Igor Stasenko <siguctua@gmail.com>>

and it should. Not many people using a complex numbers. And -4 is an integer number, not complex number (i hope this non-objectionable?). And sqrt function is not defined for real/integer numbers < 0 ,and should lead to error, period. If you change this behavior, some of code will fail to work correctly , definitely. But you are free to use something like: -4 asComplex sqrt

So you prefer (1 asFraction / 2) -> 1/2 , where (1/2) gives an error because 1 and 2 are not fractions? (-1 sqrt) is the definition of 1i . Other dynamic languages I use [Scheme, Lisp] which define complex numbers all give square roots of negative numbers. I am trying to approach the Principle of Least Surprise here. Computers are very bad at math, but we have learned painfully to work around this. I would like pre-computer high school math to "just work". IEEE Floats only guarantee the wrong answer fast, IMHO. I would like square roots of negative numbers to work like they did before I got a computer! 8^) 8^O 8^{ Cheers, -KenD _______________________________________________ Pharo-project mailing list Pharo-project@lists.gforge.inria.fr http://lists.gforge.inria.fr/cgi-bin/mailman/listinfo/pharo-project