Re: Order of operations (was: Eigenvalues &/or eigenvectors,
Re: Order of operations (was: Eigenvalues &/or eigenvectors,
- Subject: Re: Order of operations (was: Eigenvalues &/or eigenvectors,
- From: Doug McNutt <email@hidden>
- Date: Tue, 13 May 2003 21:25:59 -0600
With a few snips:
At 10:06 -1000 5/13/03, Reinhold Penner wrote:
>
On Tuesday, May 13, 2003, at 09:23 Pacific/Honolulu, Gary Lists wrote:
>
>Having taught high school math and algebra, I can tell you that you no one
>
>should expect a square to be negative.
>
You better apologize to your students... ;-)
I am seriously considering writing a paper on this subject. Just when was this high school course taught? Was it part of the "new math" system? I graduated from HS in 1952 and at that time it certainly was not the "rule". It also certainly was not the rule when I graduated from college in 1956 or when I got my PhD in physics, with a minor in math, in 1962.
Sometime it changed, possibly as a result of the rise of Computer Science as an academic subject. I used a Control Data 1604 with that modern concept - a compiler - in 1963+ and FORTRAN figured -x^2 my way, the same as 0-x^2 or (1-x)(1+x)-1, at that time.
It's deadly serious and I worry that a bridge might fall down because working engineers have not been advised of the changed paradigm. I'd like to do my part to prevent that..
So far I have found only three "compilers" that advance unary minus forward of exponentiation. They are AppleScript / Hypercard, Microsoft Excel Worksheet functions (macros in Visual Basic get it "right" though), and the UNIX "bc" calculator. There are a variety of pocket calculators that finesse the question by providing separate buttons for unary minus (change sign) and binary subtraction. Reverse Polish compilers like UNIX dc, Forth, and Postscript intrinsically avoid the problem. I solicit reports of other examples.
It's no longer AppleScript fodder though. Chris has given the final answer for that. Please reply to:
<
mailto://email@hidden>
I will compile (no pun intended) and report the results.
<
http://mathworld.wolfram.com/Unitary.html> is recommended for further study.
--
--> If you are presented a number as a percentage, and you do not clearly understand the numerator and the denominator involved, you are surely being lied to. <--
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