20110413, 17:31  #1 
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3×419 Posts 
Inverse of functions
That website http://wims.unice.fr contains a plenty of useful online calculators,
really a lot, but I couldn't find out a place where inverse of functions is being sought. For example take up with 1. Can put with and then solve with that quadratic for . The inverse is being given by 2. The inverse of this function is given by just simply this case goes away within that way. 3. Writing with this function as The inverse can be given by OK, then what will be the inverses of these following functions? It seems that they cannot be solved by using all those elementary mathematical functions at all! (4) (5) (6) (7) (8) (9) e (10) Thanks for your help, if possible within any case Disclaimer: I had faced a problem which asked me to give an algorithm to check out if N is a perfect power, x^{y} where that value of y is ≥ 2. I told that it can be done by using checks of , , , , , , ... alternately, what value to check upto for base? Till N = z^{z}, for some value of z. Thus, how to write up with that value of z as a function of N? How does that way work out rather... Last fiddled with by Raman on 20110413 at 17:56 
20110413, 19:17  #2  
Aug 2006
3^{2}×5×7×19 Posts 
Quote:
Quote:
Last fiddled with by CRGreathouse on 20110413 at 19:20 

20110413, 19:58  #3  
"Forget I exist"
Jul 2009
Dumbassville
8384_{10} Posts 
Quote:
Last fiddled with by science_man_88 on 20110413 at 19:58 

20110413, 23:05  #4  
Aug 2006
3^{2}×5×7×19 Posts 
Quote:
You should look at the code for it some time, it's fascinating. They check for 2nd, 3rd, and 5th powers separately, then move on to general testing for larger bases. Some amount of trial division is also done so you don't have to check quite as high, IIRC. Incidentally, Bernstein has a nice paper about doing this test efficiently, in almostlinear time. Pretty impressive stuff. Last fiddled with by CRGreathouse on 20110413 at 23:06 

20110413, 23:22  #5  
"Forget I exist"
Jul 2009
Dumbassville
10000011000000_{2} Posts 
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20110413, 23:29  #6  
Aug 2006
3^{2}×5×7×19 Posts 
Quote:
http://cr.yp.to/ In particular, his math stuff is mostly in one of these: http://cr.yp.to/ntheory.html http://cr.yp.to/factorization.html http://cr.yp.to/arith.html 

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