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What is the 9^1/2 equal to?

by Davewilliams
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1MileCrash
#19
Feb9-14, 07:53 PM
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Quote Quote by pwsnafu View Post
Why do you think the quadratic formula has the ##\pm## sign?
Clearly because the quadratic formula must account for adding the positive root, subtracting the negative root, adding the negative root, and subtracting the positive root.

lurflurf
#20
Feb9-14, 11:11 PM
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Quote Quote by 1MileCrash View Post
Please explain to me how I am to interpret 9^1/2 as √9 in terms of operation precedence.

I will send a bug report to Wolfram.
That is a feature not a bug. Clearly a^1/n should be interpreted as a^(1/n) because (a^1)/n would be better written as a/n. On the other hand a^b/n is interpreted as (a^b)/n when b!=1.
pwsnafu
#21
Feb9-14, 11:41 PM
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Quote Quote by lurflurf View Post
That is a feature not a bug. Clearly a^1/n should be interpreted as a^(1/n) because (a^1)/n would be better written as a/n. On the other hand a^b/n is interpreted as (a^b)/n.
Pretty much. One of devs gave a presentation at my uni, and as I understand it, the computation engine is nothing more than the Mathematica kernel. Unlike Mathematica however Alpha was designed to be used by non-scientists, hence they focused development on natural language interpretation.
olivermsun
#22
Feb10-14, 06:42 AM
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Quote Quote by pwsnafu View Post
Alpha is natural language interpreter, which is why it does this.
But using CAS as a citation is useless. Mathematica treats "xy" as a variable xy. If you want to multiply x and y you need to input "x y" with the space. They use spaces as context markers. It's a different environment than standard mathematics, which doesn't use spacing.
As far as I know, the '^' for exponentiation is not used in "standard mathematics"; instead it's just a way to enter mathematical expressions into computers. The issue is about how the string of characters containing '^' is processed into a "standard mathematics" expression. From there on, the usual order of operations appears to be preserved.

It's interesting that there are different behaviors for 9^1/2 and 9^3/2 (as lurflurf points out).
AlephZero
#23
Feb10-14, 02:28 PM
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Quote Quote by olivermsun View Post
It's interesting that there are different behaviors for 9^1/2 and 9^3/2 (as lurflurf points out).
This type of input is called DWIM (do what I mean), in contrast with the derogatory interpretation of WYSIWYG as "what you see is all you get".

Of course the problem with DWIM is that different people sometimes have different ideas about "meaning". Ideally, there should be a way to get the computer system to tell you exactly how it interpreted your input, e.g. by adding parentheses or whatever.
olivermsun
#24
Feb10-14, 02:35 PM
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One good thing about Alpha is that it shows you "what it thought you meant" (in "pretty" form) as an intermediate step.
glappkaeft
#25
Feb10-14, 03:26 PM
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Quote Quote by AlephZero View Post
Of course the problem with DWIM is that different people sometimes have different ideas about "meaning". Ideally, there should be a way to get the computer system to tell you exactly how it interpreted your input, e.g. by adding parentheses or whatever.
On of my favourite programming books says something like this (I'm paraphrasing):
"In C there are 23 rules of precedence. The smart programmer knows that multiplication and division comes before addition and subtraction and then puts parenthesis around everything else".


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