Infix interpretation

[Matt Agajanian]

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

[Walter B]

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.

[Matt Agajanian]

Okay, got it. My OP says what I want it to say. Thanks.

[Bart (UK)]

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.).

[Dieter]

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:

• sin²x is the square of the sine of x
  
• sin x² is the sine of the square of x
  
• -x³ 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

[Marcus von Cube, Germany]

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 TI-92 which has a CAS that is supposedly derived from Derive doesn't allow this.

[Kiyoshi Akima]

Quote:

---

sin²x is the square of the sine of x

---

And of course sin^-1x 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 ln²x ?

[Marcus von Cube, Germany]

Quote:

---

Anyone ever seen something like ln²x ?

---

At least Derive accepts it as such.

[Walter B]

Quote:

---

And of course sin^-1x 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 HP-35 - 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?

[Kiyoshi Akima]

And it can get really messy sometimes. I've seen sin^-2x to mean the inverse of the square of the sine (csc squared), not the square of the arcsine or the arcsine of the arcsine.

[Matt Agajanian]

Quote:

---

Hi Matt,

Well, actually it is. ;-)

The textbooks I know of use the common mathematical notation which is quite unambigous:

• sin²x is the square of the sine of x
  
• sin x² is the sine of the square of x
  
• -x³ 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?

[Marcus von Cube, Germany]

Current algebraic calculators have two different minus signs, unary and binary. Unary minus binds stronger than binary minus.

[Dieter]

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 -(x³) equals (-x)³. ;-)

Dieter

[Matt Agajanian]

Thanks for the thorough analyses

[Paul Dale]

You can use [super]...[/super] and [sub]...[/sub] to get super and sub scripts.

- Pauli

[Matt Agajanian]

Thanks for the tip.

[peacecalc]

Hello Matt,

I miss another possible interpretation for

sin2(X) = sin(sin(X)) 

That is similar to the repeated useage of deriviation operator:

dn/dxn

Sincerely
peacecalc

[Nick_S]

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:

223

Result:

256

Nick

Edited: 20 Mar 2012, 3:56 a.m.

[Chris Randle (UK)]

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.

[Nick_S]

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.