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
1011101100011_{2} Posts 
Quote:
Quote:
Last fiddled with by CRGreathouse on 20110413 at 19:20 

20110413, 19:58  #3  
"Forget I exist"
Jul 2009
Dartmouth NS
2·3·23·61 Posts 
Quote:
Last fiddled with by science_man_88 on 20110413 at 19:58 

20110413, 23:05  #4  
Aug 2006
1763_{16} 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
Dartmouth NS
2·3·23·61 Posts 
Quote:


20110413, 23:29  #6  
Aug 2006
5,987 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 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Inverse of Smoothness Probability  paul0  Math  6  20170725 16:41 
mi64: inverse does not exist  wreck  NFS@Home  1  20160508 15:44 
Lurid Obsession with Mod Inverse  only_human  Miscellaneous Math  26  20120810 02:47 
Electricity, GIMPS, and inverse relationships  stars10250  Soap Box  31  20120410 15:41 
Inverse Laplace Transform  flouran  Math  1  20100118 23:48 