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======= At 2005-06-03, 00:25:02 bear wrote: ======= > >In particular, be careful not to assume that all complex numbers >are internally represented in the same way; several implementations, >I believe, use both polar and cartesian representations internally. Agree. And I think internal polar representations is more prefered than cartesian in some cases. > >Finally, from a mathematical point of view, a number is either >inexact or exact; this includes complex numbers. A few >implementations allow differing exactness in the real and >imaginary parts of a complex number. This is a fact, but the >fact lies at some intermediate position between being a mere >artifact of the representation and a mathematical error. >Consult a number theorist to understand more fully the nature >of this error; it is beyond my feeble ability to explicate. > What if we know (exactly) a number is an imaginary number, but only know ineaxtly it's magnitude? "0+1.0i" seems nature. And for polar representations, a number with exact angle but inexact magnitude also seems nature. - Chongkai Zhu