20170914, 22:26  #12  
Apr 2012
Gracie on alert.
3^{4}·5 Posts 
Quote:
Quote:
For example, the uniformization theorem and the geometrization conjecture are contexts that I have explored. As a nonspecialist such topics are heavy going but worth it. Quote:
Sometimes making something more complicated initially will simplify things drastically..or create a huge intractable swamp. As Laplace once stated, "Read Euler.." As will be noted through my posts I do have my weaknesses, however, what I have asked should be clear. Last fiddled with by jwaltos on 20170914 at 23:17 

20170914, 23:43  #13 
Apr 2012
Gracie on alert.
3^{4}·5 Posts 
I should have included this earlier as this is an aspect of testing and implementing certain results obtained relative to the question asked above;
Regarding computation, in addition to mainstream CAS's has anyone worked with ACL2 and/or Vermaseren's FORM? Last fiddled with by jwaltos on 20170914 at 23:52 
20170915, 00:18  #14  
"Forget I exist"
Jul 2009
Dumbassville
20C0_{16} Posts 
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20170915, 13:39  #15  
Aug 2006
175B_{16} Posts 
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20170915, 13:59  #16  
Aug 2006
3×1,993 Posts 
Quote:
You want Sage or MAGMA for stateoftheart integral or Sintegral computations on elliptic curves, or John Cremona's tables if you know the conductor and it's small enough (less than 400,000 at present). Look for integral_points/S_integral_points in Sage and IntegralPoints/SIntegralPoints in MAGMA. For subexponential algorithms on Diophantine quadratics  generalized Pell's equation and the like  PARI/GP is stateoftheart as far as I know. See the help for the functions quadunit, bnfisintnorm, and qfsolve. 

20170915, 14:11  #17 
Feb 2017
Nowhere
2^{2}×5×257 Posts 
F(x,y,a,b,c,d) = 2*x^3+(19/260*a60*b*y)*x^2+(21/2+314*a+30*d*y+30*c+314*b*y)*x+2+205*a+11*c+900*b*y*c+420*a*b*y+210*a^2+210*b^2*y^2+11*d*y+900*a*d*y+900*b*y^2*d+205*b*y+900*a*c
1) Does solving F(x,y,a,b,c,d) = N bear directly on factoring N? 2) If not, how does the value of N relate to the number to be factored? 3) Where does this function come from? Without an answer to his last question  which has already been asked twice, but not really answered  it seems pointless to try to proceed. Phrases like "part of an integer factorization toolkit," "derived in my attempts to develop a simple method of factoring integers," "an optimal and very specific entry point to a difficult set of questions," or "Every variable and operation has a very specific interpretation much like equations within general physics where dimensional analysis is applicable" don't really address the question. As examples of the sort of questions whose answers might actually be informative: Is F(x,y,a,b,c,d) obtained from a function in more variables by assigning values to some of them? If so, what was that function? Was F obtained from a homogeneous function? 
20170915, 16:22  #18  
Apr 2012
Gracie on alert.
625_{8} Posts 
Quote:
Thank you CR. I have used Sage but not MAGMA (yet). MAGMA has an implementation from Denis Simon which pertains to my question and I have looked at the originating paper. Years ago, John Cremona was gracious enough to answer a question of mine, again allied to the question here, providing guidance for a successful resolution to that query. I also use Pari and agree with your assessment regarding certain stateoftheart functionality. I am usually thorough researching a topic but I always try to account for blind spots, hence my posting. Again, thank you for your insights and bringing them to my attention. Quote:
1. Yes. 2. See above. 3. I invented it. Sardonicus, I sincerely appreciate the time taken to respond but I would be repeating myself if I were to address your questions fully. Sorry. Thank you to those who responded to my question as it has helped me to better understand how others view what I am looking at. Moderators, this thread can be closed anytime now. Thank you. Last fiddled with by jwaltos on 20170915 at 16:39 Reason: clarity 

20170915, 17:21  #19  
Aug 2006
3×1,993 Posts 
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20170915, 17:34  #20 
Aug 2006
13533_{8} Posts 

20170915, 17:53  #21 
"Robert Gerbicz"
Oct 2005
Hungary
7^{2}·31 Posts 

20170915, 18:20  #22  
Aug 2006
13533_{8} Posts 
I mentioned that in my post:
Quote:


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