20060719, 16:51  #1 
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,877 Posts 
SQRT Problem
The linear algebra for 2,1044+ finished, but the first 4 dependencies all failed to compute the square root, so I stopped the code. Note that I did not say "resulted in trivial factorization". What I got each time was: Wrong number of factors (1) for polynomial 2. Dependency 1  Unable to take square roots Everything seemed OK up to the final CRT construction. Then the output started showing coefficients that were HUGE: much bigger than the C153 being factored.. The Final gidwant values looked reasonable up to the end. Then I hit: Starting Miscellaneous Lattice Ops Start Final CRT Construction The next lift that was shown showed: Left = (C1 alpha^5 + C2 alpha^4 + ...) where C1, C2, etc. were HUGE (much bigger than the number being factored) It then showed gfactorization = (1 mod alpha^6  alpha^3 + 1) X^2 + [polynomial in alpha with huge coefficients] ) mod (alpha^6  alpha^3 + 1) I then got the "Wrong number of factors" error. I suspect something is going wrong with Pari. I think it is hitting a stacksize limit or some other limit. Does anyone have their own windows executable that they could send me so I could try a different executable? Tracking down this problem will be a real pain, otherwise. I could try increasing some of the defined constants in the Pari code, but I would be shooting in the dark. Advice? Has anyone seen this problem? Bob 
20060719, 20:48  #2  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
10110110001010_{2} Posts 
Quote:
What I can suggest is trying to use a Linux box (possibly from a bootable CD if you don't want to find a new machine or build a dualboot machine) and then try using a recent CWI binary that I can supply (as I believe you already have permission to use the CWI toolkit. Alternatively, if you can get the dependencies, relations and polynomial files to me (email me for postal address and send me a CD, or perhaps put the files on a mutually accessible machine) I can run the SQRT here. Paul 

20060719, 21:43  #3  
Jun 2003
The Texas Hill Country
3^{2}·11^{2} Posts 
Quote:
I can only make a similar offer. I also have SQRT running on Mac OSX if that helps. Sorry that I cannot be more helpful. Richard 

20060719, 22:33  #4  
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,877 Posts 
Quote:
any ideas. Then I will try an older sqrt code. Then I will try increasing some of the array sizes in size Pari and recompile. If all else fails I will put the files on a couple of CD's and send them by snail mail to you or Richard. 

20060719, 22:39  #5  
"Bob Silverman"
Nov 2003
North of Boston
7508_{10} Posts 
Quote:
security restrictions keep me from modifying machines.... 

20060719, 23:30  #6 
Jan 2006
JHB, South Africa
157 Posts 
I've zipped the executable with the accompanying dlls & library for version 2.2.11 built 20 Oct 2005 if it will help you. You can download it from http://www.onyxsa.co.za/PARI.zip
I did not compile it, but downloaded the Installation file from the Pari Website quite a while ago. Regards Patrick 
20060719, 23:35  #7  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2×3×29×67 Posts 
Quote:
If you have a personal X86machine at home you could, presumably, boot that into Linux ... Paul 

20060720, 00:42  #8  
"Bob Silverman"
Nov 2003
North of Boston
7508_{10} Posts 
Quote:
PARI libraries) 

20060720, 13:43  #9  
Jan 2006
JHB, South Africa
157_{10} Posts 
Quote:
Regards Patrick 

20060720, 14:32  #10  
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,877 Posts 
2,1044+
Quote:
for all of the dependencies, I let the code run......... It succeeded on the 14th try. Weird. :surprised 2,1044+ C153 = p56.p98 p56 = 25582121116971797723434440295709382794690160485178612721 

20060720, 17:01  #11  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2·3·29·67 Posts 
Quote:
Do the primes used for CRT reconstruction overlap with the primes appearing in relations? They shouldn't, obviously, but if they do you would find that a dependency not using any CRT primes would succeed but the others would fail. I ran into something similar once when combining relations from Franke's lattice siever, which used large primes to 2^30, with CWIgenerated relations which were limited to 10^9. The CWI sqrt code uses primes just larger than 10^9 for CRT purposes... Paul 

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