20170629, 19:23  #23  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
Quote:
Frankly, the things you say seem to indicate you know very little about how computers actually work, and your talk about "endomorphisms" is equally meaningless from a mathematical perspective. You have no idea what you're doing, which is why you got such a snarky response to your initial post. 

20170629, 19:34  #24  
Jun 2017
1101_{2} Posts 
Quote:
But what is the problem with f: [Z][/2] > [Z][/2]. Well, I have been using homomorphisms(under * or +) on binary numbers. What is the problem with math? It is clear and very simple, is it not? Besides, this is an Algebra thread. Last fiddled with by manasi on 20170629 at 19:45 

20170629, 19:43  #25 
Aug 2006
175B_{16} Posts 
I don't mean that you shouldn't try, but that I don't see anything different. As far as I can tell your suggestion is to use binary, but everyone is using binary.

20170629, 20:35  #26  
Aug 2006
3·1,993 Posts 
Quote:
First are architectural limitations. I'm not sure what it is for GMP but for example in PARI/GP you can have t_REAL numbers up to almost 2^2^29 on 32bit systems and 2^2^61 on 64bit systems. Next there are memory limitations. If you want to store 2^10^15 directly you need 10^15 bits of memory. On 64bit systems this is more likely to cause trouble than architectural limitations. Finally there are practical limitations imposed by the algorithms used. If you want to factor the numbers, it doesn't matter if you could store billions of digits because you won't live long enough for a current computer running current software to factor such a beast. 

20170629, 20:56  #27 
Banned
"Luigi"
Aug 2002
Team Italia
7·691 Posts 
If the OP refers to Frobenius endomorphism of GF(N^2), this method is not deterministic. This was established by Grantham.
They are nothing more than PRP tests. And, owing to the work of Pomerance and Kim, they are not even as useful as a MR test. For the latter we have good estimates of the probability that the result of a test is in error. However, the Pomerance/Kim analysis will not work for your tests. Last fiddled with by ET_ on 20170629 at 20:57 
20170630, 15:48  #28 
Romulan Interpreter
"name field"
Jun 2011
Thailand
9859_{10} Posts 
@OP:
1. Click on "Start" button 2. Click on "All programs" 3. Click on "Accessories" 4. Click on "Calculator" 5. Click on "View" and select "Programmer" 6. Click on "Bin" radio button. 7. Voila! Enjoy! For how you talk, you seem not to be needing more... The only problem is that you may need to launch the magnifier program too (also in accessories) because as the binary number grows bigger, the digits become smaller, due to the limited space and nonsizeable window.. A real magnifier glass may do wonders... It can also be from plastic, it doesn't matter. Edit: tip: you can modify the numbers directly clicking on the powers of two on the gray area, you do not need to input all numbers bit by bit... Last fiddled with by LaurV on 20170630 at 15:53 