Em 30/08/2009 13:36, Schwab,Wilhelm K < bschwab@anest.ufl.edu > escreveu:
Ken,
On #cosH vs. #cosh, etc.,I do not like what you have done, but it's hardly cause to start a war. I would be more inclined to agree with your no-typo argument if you spelled out hyperbolic. We write cos and cosh; I see no advantage to typing cosH, which could just as easily be errant as cosh.
#angle vs. #argument. The terminology of modulus and argument is heavily drilled into engineers and physisists, so I would go with that inertia vs. anything from Scheme or Lisp.
============= "If Complex does not interoperate, at least to some extent, with Floats how would it be useful for anything? Smalltalk without polymorphism ???"
That's not it at all. Sig and I hav been very clear on using polymorphism to get he expected behavior in each world, and how it can extend to (for example) exponentials of matrices. I don't know how to make it more clear that we have done. We object to implicit coercion which works against anyone interested only in real results. =============
Let me see if I understand your point then: it is OK in your view that we can do: 1i squared. retuning "-1 + 0i" so a Complex, but (1i squared) sqrt. raises an error? Or should we follow your logic and even when the imaginary part of a Complex is zero it should not be automatically converted in a real number? Please not that once the programmer wrote: 1i whatever he already made her/his choice to use Complex numbers, right?
=============== >Complex>>angle looks like it will answer zero for a value of >zero?? >Complex>>AFAIK, there should be no direction for a zero > vector. In a way, it is splitting hairs because exact > comparisons of floats are dubious, but it probably should > raise an error for zero.
I am following ANSI X3J13 (they had a formal vote which declared the angle of zero to be zero). Let me know of a better refrerence. [The problem with standards is that there are so many to chose from ;^]. ===============
ANSI is the same group that put an end to time as we know it in 2037 (maybe 2038); if you thought y2k was a mess, just wait until time_t wraps. Zero vectors (and complex numbers act as vectors in this case) have no direction, and ANSI's vote does not change that. Many times you have shown a desire to make things more mathematically correct; ANSI is just plain wrong here. The only argument in their favor is that the distinction might be slightly vacant because computing a truly zero result is very unlikely in a floating point world.
Oh well, interesting way of looking at things: a non sequitur comment on size of time_t and a dismissal of an agreed upon Standard. You'll have a lot of problem using complex numbers as you want if you don't follow IEEE and ANSI stipulations on the angle of certain operations when voltage is squared to calculate power or the angle of it (which follows the angle of the load) as there is more than a single mathematical correct answer. Back to mathematical purity, then we have a conundrum: as Ken wrote several times Complex is considered a superset of Real numbers in mathematics is Smalltalk class hierarchy that "decided" to consider Number as a subclass of Magnitude that has to respond to #<, but this is not necessary in mathematics in general, no reference about number theory you find such necessary condition.