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Here's an illustration in favor of RPN:
I cannot simulate super/subscript so imagine my examples written in the natural typography.
How would I know to interpret
2
sin x as X [SQ] [SIN] and not x [SIN] [SQ] ?
Shouldn't x [SIN] [SQ] be written in tech notes, textbooks, etc as:
2
sin x ?
On another note, what's clarifying
3
x as x 3 [y^x] [CHS] and not x [CHS] 3 [y^x] ?
Edited: 18 Mar 2012, 2:37 p.m. after one or more responses were posted
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Hi Matt,
It will help if you use [pre] in formatting your text input. Please see here.
Edit: OK, you were faster in editing your mail than I was in pointing you to the link about formatting ;)
Nevertheless, you're preaching to the choir emphasizing the advantages of RPN to the members of this forum IMHO.
Edited: 18 Mar 2012, 2:25 p.m.
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Okay, got it. My OP says what I want it to say. Thanks.
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When you are typing a message, below the message box are test formatting buttons, if you click "more" you can see a whole array of formatting marks you can use in your post (heading, underlines, super and subscripts, lists etc.).
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Hi Matt,
Quote:
Shouldn't x [SIN] [SQ] be written in tech notes, textbooks, etc as:
2
sin x ?
Well, actually it is. ;)
The textbooks I know of use the common mathematical notation which is quite unambigous:
 sin^{2}x is the square of the sine of x
 sin x^{2} is the sine of the square of x
 x^{3} is 1 times the cube of x
 (x)^{3} is the cube of x
Although the one or other calculator manufacturer may claim that the user can enter expressions just the way they are found in the textbook, this usually is not true for cases like the ones you mentioned. At least I do not know of a device that accepts something like sin^2(x) instead of the transscription (sin(x))^2 that is also used in most programming languages. Or have I missed something?
Yes, of course that's an advantage of RPN. ;)
Dieter
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Quote:
At least I do not know of a device that accepts something like sin^2(x) instead of the transscription (sin(x))^2 that is also used in most programming languages. Or have I missed something?
I just detected one: Derive 6 on Windows allows the entry of sin^2x which is then transformed to SIN(x) ^{2}. The interpretation of the latter is unambiguous because the opening parenthesis is tied to the function name SIN. The TI92 which has a CAS that is supposedly derived from Derive doesn't allow this.
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Quote:
sin^{2}x is the square of the sine of x
And of course sin^{1}x is the sine of x raised to the 1 power. Oh, no, that's csc x. The superscript 1 means something completely different in this case.
Does the power appear between the function name and its argument in anything other than trig (and hyperbolic) functions? Anyone ever seen something like ln^{2}x ?
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Quote:
Anyone ever seen something like ln^{2}x ?
At least Derive accepts it as such.
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Quote:
And of course sin^{1}x is the sine of x raised to the 1 power. Oh, no, that's csc x. The superscript 1 means something completely different in this case.
AFAIK, that use of superscript 1 for the inverse is special for trig and hyperbolic (and some more functions of advanced math). We were taught earlier its called e.g. arcsin  compare the HP35  or arcosh. Personally, I observed the notation tan ^{1} meaning arctan the first time on scientific calculators and remember it confused me  I think TI (horribile dictu) found a better solution with their key INV. Would be interesting to know who invented sin ^{1} = arcsin  any experts here from the old days?
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And it can get really messy sometimes. I've seen sin^{2}x to mean the inverse of the square of the sine (csc squared), not the square of the arcsine or the arcsine of the arcsine.
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Quote:
Hi Matt,
Well, actually it is. ;)
The textbooks I know of use the common mathematical notation which is quite unambigous:
 sin^{2}x is the square of the sine of x
 sin x^{2} is the sine of the square of x
 x^{3} is 1 times the cube of x
 (x)^{3} is the cube of x
Although the one or other calculator manufacturer may claim that the user can enter expressions just the way they are found in the textbook, this usually is not true for cases like the ones you mentioned. At least I do not know of a device that accepts something like sin^2(x) instead of the transscription (sin(x))^2 that is also used in most programming languages. Or have I missed something?
Yes, of course that's an advantage of RPN. ;)
Dieter
But, what's preventing #3 from being interpreted as x raised to the third power?
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Current algebraic calculators have two different minus signs, unary and binary. Unary minus binds stronger than binary minus.
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Quote:
But, what's preventing #3 from being interpreted as x raised to the third power?
The missing parentheses.
By the way, in this case it doesn't matter  both expressions are equivalent since (x^{3}) equals (x)^{3}. ;)
Dieter
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Thanks for the thorough analyses
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You can use [super]...[/super] and [sub]...[/sub] to get super and sub scripts.
 Pauli
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Hello Matt,
I miss another possible interpretation for
sin^{2}(X) = sin(sin(X))
That is similar to the repeated useage of deriviation operator:
d^{n}/dx^{n}
Sincerely
peacecalc
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On a similar theme, yesterday I was looking at the differences in the order of evaluation of powers, which appears to be a potential trap.
In RPL:
'2^2^3' EVAL
1: 64
in R
2^2^3
[1] 256
and in Wolfram Alpha
2^2^3 =
Input:
2^{23}
Result:
256
Nick
Edited: 20 Mar 2012, 3:56 a.m.
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I don't see the same result on my 50g:
'2^2^3' EVAL
256
but my 48SX:
'2^2^3' EVAL
64
Never noticed that before.
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I get a result of 64 on both my 28S and 48GX calculators. It is interesting to see that HP changed the order of evaluation for the 50g.
Nick
Edited: 21 Mar 2012, 3:21 a.m.
