negative number raised to even power

[Wes Loewer]

(05-07-2015 10:40 AM)Gerald H Wrote:  

(05-06-2015 07:56 PM)Wes Loewer Wrote:  -2^2 = (a) -4 (b) 4
2^3^2 = (a) 512 (b) 64
1/2pi = (a) 1.57 (b) 0.159
...
??-: Lotus 123 (can someone test this)
ab-: Lotus Improv (anybody remember this spreadsheet?)

Lotus 123, 2.4: aba

Thanks, I suspected it would be ab.

I should have explained what I was testing on the last one: 1/2pi. On Casio's, older TIs, and some software, implied multiplication is given a higher priority than explicit multiplication and division. They treat 1/2pi as 1/(2*pi) but 1/2*pi as (1/2)*pi. I put dashes for things that don't support implied multiplication.

Am I correct that 123 requires explicit multiplication like other spreadsheets?

[Thomas Radtke]

(05-08-2015 02:27 AM)Dave Britten Wrote:  I find it much more elegant to consider the negation prefix as an inseparable part of the number [...]

It isn't, since you cannot consistently do what generations of studens did before: Rewriting an equation

-2^2 = -4

to

0 = -4 + 2^2

I bet most people would just do it this way without giving it a second thought.

[Dave Britten]

(05-08-2015 05:15 AM)Thomas Radtke Wrote:  

(05-08-2015 02:27 AM)Dave Britten Wrote:  I find it much more elegant to consider the negation prefix as an inseparable part of the number [...]

It isn't, since you cannot consistently do what generations of studens did before: Rewriting an equation

-2^2 = -4

to

0 = -4 + 2^2

I bet most people would just do it this way without giving it a second thought.

Yeah, that does make for an ugly little pitfall. Maybe we need to just start writing it like fractions/division: base under the caret, power directly over it. Then you'd have to either put the negation sign unambiguously next to either operand, or the caret itself.

[Gerald H]

(05-08-2015 04:31 AM)Wes Loewer Wrote:  

(05-07-2015 10:40 AM)Gerald H Wrote:  Lotus 123, 2.4: aba

Thanks, I suspected it would be ab.

I should have explained what I was testing on the last one: 1/2pi. On Casio's, older TIs, and some software, implied multiplication is given a higher priority than explicit multiplication and division. They treat 1/2pi as 1/(2*pi) but 1/2*pi as (1/2)*pi. I put dashes for things that don't support implied multiplication.

Am I correct that 123 requires explicit multiplication like other spreadsheets?

Yes, actual entry was 1/2*@PI as 1/2@PI produces an error.

[Thomas Radtke]

(05-08-2015 11:14 AM)Dave Britten Wrote:  Maybe we need to just start writing it like fractions/division: base under the caret, power directly over it. Then you'd have to either put the negation sign unambiguously next to either operand, or the caret itself.

I know RPN-people like to save strokes of any kind, but there are brackets to make it clear and to keep the set of symbols orthogonal ;-).

[Dave Britten]

(05-08-2015 01:56 PM)Thomas Radtke Wrote:  

(05-08-2015 11:14 AM)Dave Britten Wrote:  Maybe we need to just start writing it like fractions/division: base under the caret, power directly over it. Then you'd have to either put the negation sign unambiguously next to either operand, or the caret itself.

I know RPN-people like to save strokes of any kind, but there are brackets to make it clear and to keep the set of symbols orthogonal ;-).

Hey, we've got two division symbols, with one intended to prevent ambiguity, so let's do the same with powers.

Or better yet, no more powers. Only EXP(Y*LN(X)).

(This is all more proof that RPN is better.)

[Thomas Radtke]

(05-08-2015 02:03 PM)Dave Britten Wrote:  (This is all more proof that RPN is better.)

By far!

[Gerald H]

(05-08-2015 03:21 PM)Thomas Radtke Wrote:  

(05-08-2015 02:03 PM)Dave Britten Wrote:  (This is all more proof that RPN is better.)

By far!

I alert you to post #7 in this thread.

[Joe Horn]

(05-08-2015 02:03 PM)Dave Britten Wrote:  (This is all more proof that RPN is better.)

This proof more all is that RPN better is, to say you meant?

[Mark Hardman]

(05-08-2015 04:08 PM)Joe Horn Wrote:  This proof more all is that RPN better is, to say you meant?

That would have been funnier four days ago.

[DrD]

Grammars Joe from, laughter it caused. Humorous, he is!

[Thomas Radtke]

May the forth be with you, Joeda. I bet this joke has been made before, but ... CNR.

[StephenG1CMZ]

(05-03-2015 04:47 PM)Dirk. Wrote:  Hi,
checking three "algebraic" calculators for the -2²-bug leads to interesing results:

CASIO CFX-9850GB PLUS:
There is no (+/-)-key but a special (-)-key to change sign. The algebraic (-)-sign of a number can be distinguished from the (-)-operation by a shorter symbol in front of the number.
*) 2(-)² -> Syn ERROR
*) -2² -> -4

SHARP EL-512S and SHARP EL-520V:
Both also have a special character so distingusih subtration from negarive numbers when pressing (+/-) to change sign.
*) 2(+/-)² -> -2² -> 4 at the EL-512
*) 2(+/-)² -> (-2)² -> 4 at the EL-520
*) (+/-)2² -> -2² -> 4
Pressing the (-)-key as the first key of a calculation leads to "0-" in the algebraic line of the display (on the prime it leads to "ANS-")
*) -2² -> 0-2² -> -4

-> On SHARP calculators it works like expected. The 520 even adds the brackets automatically to make this point even more clear.

Adding brackets to "explain" how a result is obtained seems an excellent idea.
Much clearer than expecting a user to see a difference between two minus signs - and knowing which is which and how to translate that onto a system having just one, in order to use a calculation.


I had thought I knew what -2^2 was, now I simply don't - and I would never have read -2^2 in C and thought EXOR rather than exponentiate.