|Re: RPN vs AOS vs ALGEBRAIC ENTRY|
Message #4 Posted by rsenzer on 13 June 2006, 1:50 a.m.,
in response to message #3 by Palmer O. Hanson, Jr.
I think there are two valid ways of looking at "-3^2" and getting the result "-9". Note that in a textbook there is no difference between the "-" in "-3^2" and the "-" in "5 - 2".
The first way treats the leading "-" as a unary minus. On the EOS calculators, the unary minus operator has a separate key vs. the minus key. [Of course, this is true on most every scientific calculator, but its the way they are used on an EOS calculator that is pertinent here.]. So, "[(-)]3^2" is executed as (-1)*3^2 as stated above.
Another way to think about the textbook representation is that the "-" in "5 - 2" as well as "-3^2" is a minus. In the textbook representation, any expression or subexpression beginning with a
"-" implies a subtraction from zero. That is, "-3^2", in a textbook, using this interpretation, is equivalent to "0 - 3^2". This would then be "0 - 9" or "-9".
In this interpretation, "(-3)^2" would, of course, be equivalent to
"(0 - 3) * (0 - 3)" and, of course, "(0 - 3)" is equivalent to
Either interpretation will produce the same values as the end result. I prefer the latter methodology.
From a computer perspective, think about the statements,
ii := -3^2;
In a computer language that incorporates a "^" as an exponentiation operator. Conceptually, if the assignment statement was the first time ii was given a value, it might well have a zero in the corresponding register preceding the assignment and following the assignment, 9 would be subtracted from ii. [Needless to say this is only conceptual, as a value of -9 might be placed in ii as a result of this instruction, depending upon the actual implementation.]
There are several posts about this matter in old archives.
My objection to the EOS implementations is not in having a CHS and a minus. I don't like the fact that pressing a minus at the beginning of an expression on a new line automatically generates "ANS -", that is, subtract from previous answer. So "MINUS 3" becomes "ANS - 3" rather than "CHS 3". This causes all kinds of problems for students.
Note that some [not the latest] DAL/EOS SHARP calculators had a dual mode for their CHS operator. Before an expression or number, the CHS acted as a unary minus. After a number, it changed the sign of the preceding number by negating it and wrapping the number in parenthesis. I liked this implementation. It worked for individuals who were use to the previous generation of AOS calculators as well individuals who wished to enter an expression directly in textbook format. Unfortunately, the new implementation on DAL/EOS SHARP calculators does not seem to offer any direct way to enter an expression like "-3^2" because using CHS before or after the "3" results in "(-3)^2".