Now that I find myself in the position of wanting to offer a few excerpts from my book, I decided that it would not made sense to leave it under that other thread. ("Favorite short RPL program")

At the same time, my other thought is whether it is appropriate at all to do this here. Even if the moderators have no problem with it, I don't feel entirely comfortable doing this here, so I will limit it to two or three posts under this thread, and unless others have questions, I'll try not to wear out my welcome. If it goes beyond the bounds of what is appropriate, I assume that the moderators will let me know, and at that point it will come to an abrupt conclusion.

The first excerpt that I will give (I keep misspelling “excerpt” as “except”) is from the explanation of the effect of the CAS modes Numeric and Approx. Every one of the explanations of the actual effect of these modes that I was able to find in the various printed and PDF manuals provided by HP, were grossly incomplete and inadequate. They are all what I would characterize as allusions (I spelled that word correctly). I was never ever to escape the feeling that whoever wrote those explanations didn’t really understand the exact effect of those modes on the behavior of the calculator. And nowhere did I find any hint of the fact that they do not behave the same in RPN mode as they do in Algebraic mode. Not only do they behave differently in the two operating modes, the related behavior when neither of those modes is set, whereby the user is prompted to set the Approx mode, is different in the two operating modes. Try this on for size:

“When neither Numeric nor Approx is selected, the calculator avoids carrying out operations that will introduce real numbers in the results. ... If there is a simpler way to represent the result of an operation without introducing any real numbers, then that simplification will often be performed. ... In Algebraic mode, if you try to perform a binary operation that combines a real number with a symbolic constant, or with the pending result of a unary operation that can’t be performed because to do so would introduce a real number, the calculator will prompt you to set the Approx mode. One effect of setting the Approx mode in either operating mode is that integers will be converted to real upon input, automatically. In Algebraic mode, Approx has the additional effect of causing all operations to be carried out, excepting only operations that involve undefined variables. In RPN mode, however, symbolic constants will not be replaced with real numbers unless Numeric is set, so if only Approx is set, operations that involve symbolic constants will still not be performed. In either operating mode, Numeric has the effect that Approx has in Algebraic mode, but undefined variables will cause an error in lieu of a result if Numeric is set, whereas if only Approx is set, undefined variable names will silently carry through to the result. … There are situations in RPN mode where the calculator will prompt you to set Approx, but these are mostly limited to when you use EVAL to evaluate an algebraic expression, or when an integrand expression combines integer and real. If you use EVAL to evaluate an algebraic expression in RPN mode, the effect of Approx will be the same as it is in Algebraic mode.”

Whenever I write something of this sort, I take it for granted that I have overlooked something and that it is not 100% correct. Nevertheless, I am confident that this is substantially more complete than any of the laughably incomplete explanations that I was able to find in any of the manuals that come from HP.

Tom