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Infix to Postfix

how do you convert infix to postfix in case of exponents?

is 2^3^2 in postfix

23^2^

or

232^^

quite confused on this. thanks.
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third
Asked:
third
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2 Solutions
 
d-glitchCommented:
2^3^2 = (2^3)^2 = 8^2 = 64

The first is correct

(23^)2^  = 82^  = 64

But  232^^  = 2(3^2)^ = 2 9^ = 512
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mlmccCommented:
Actually the exponent has priority in this case.

2^3^2 = 2^(3^2) = 2^9 = 512

Therefore the second is correct.

mlmcc
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d-glitchCommented:
Matlab does infix calculatiosns.  Here is a screen paste:

>> 2^3^2

ans =

    64

My HP calculator does postfix

    23^2^  = 64

The two  exponent operators have equal precedence, so you work left to right.
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snoyes_jwCommented:
Type 2^3^2 into Google, and it restates it as 2^(3^2), which is 512.
The Windows calculator, which enforces order of operations (at least, entering 2+3*4 results in 14, not 20) says 64.
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aburrCommented:
when in doubt use ( )
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aburrCommented:
calculators use two main types of arithmatic which will produce different results if ( ) are not used.
TI calculators (and most others) use standard algrbraic operations.
HP and a few others use reverse polish notation which does operations in a different order if ( ) are not used.
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aburrCommented:
23^2^

or

232^^

On an HP calculator the last line would not work.
You use
2 enter
3 ^
2^
and the result is 64.
In your last line you have two operators in a row, which procedure does not work.
In your first line your notation is difficult in that you do not know whether you are dealing with 2 and 3 or 23. You could develop a computer program which would take care of this particular problem but you would still hve a problem with longer first numbers.
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d-glitchCommented:
There is a cute HP Calculator online:       http://www.hpmuseum.org/simulate/hp35sim/hp35sim.htm

Two operators in a row is not a problem.  You do have to use enter twice to terminate digit entry.

2
Enter
3
Enter
2
y^x          Returns 8
Y^x          Returns 64
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d-glitchCommented:
Ignore my last post, except for the HP link.
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GwynforWebCommented:
The answer is

23^2^

There are tons of converters on the web eg. http://webplaza.pt.lu/dostert/infixtopostfix.htm
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d-glitchCommented:
Part of the reason this is confusing is that your example is symmetric:

2^3^5  =  (2^3)^5  =  32768

2 3 ^ 5 ^  =  32768   on my HP-15C  where the exponential function is y^x


5 3 2 ^ ^  =  32768   on the HP-35  where the exponential function is x^y


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NovaDenizenCommented:
> how do you convert infix to postfix in case of exponents?
> is 2^3^2 in postfix
> 23^2^
> or
> 232^^

It depends on whether you have defined your exponent operator as left-associative or right-associative.  I don't think there's any  authoritative answer on this.  Without defining your exponent operator as left-associative or right associative, a^b^c results in an ambiguous expression.

Take a look at http://mathworld.wolfram.com/ExponentLaws.html .   Notice that there are no expressions like x^y^m.  However, there is an expression like (x^m)^n.  
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snoyes_jwCommented:
The TI-92, which allows entry of large equations using infix, evaluates 2^3^2 as 512.
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thirdAuthor Commented:
i guess i would go for 232^^ = 512

i found these websites and a book saying that exponents are evaluated right to left.
http://www.reed.edu/~mcphailb/applets/calc/
http://www.qiksearch.com/javascripts/infix-postfix.htm
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mlmccCommented:
Glad i could help

mlmcc
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