Topology with bertini_real + poly_Top about bertini_real

[ofloveandhate]

use block code formatting, and edit your previous post please.

[ofloveandhate]

another thought just occurred to me. there is another set of tolerances we can play with, that determine when two points are classified as the same. let me roust my memory on that part of the program.

[tjstrunk]

Here is a sample input file:

CONFIG
tracktype: 1;
mptype: 2;
tracktolbeforeeg: 1e-50;
tracktolduringeg: 1e-51;
endgamenum: 2
sharpendigits: 40;
END;

INPUT
variable_group x,y,z,w;
function f1,f2;
f1 = (2672629601432955*w*y^2)/4503599627370496 - (5264871816214999*w^2*x)/2251799813685248 - (1936766882093563*w*x^2)/9007199254740992 + (2486516577644593*w^2*y)/4503599627370496 - (2202506525151075*w*z^2)/562949953421312 - (799415115089593*x*y^2)/2251799813685248 + (7152576441995337*w^2*z)/2251799813685248 + (5495560963472431*x^2*y)/2251799813685248 + (5658489086262587*x*z^2)/4503599627370496 + (90783840814235*x^2*z)/35184372088832 - (3382218688193493*y*z^2)/4503599627370496 + (436143035268931*y^2*z)/70368744177664 + (4842875058618353*w^3)/9007199254740992 + (6382467225033903*x^3)/4503599627370496 + (6236217787907793*y^3)/2251799813685248 + (3882883444338651*z^3)/4503599627370496 - (5564729308787463*w*x*y)/36028797018963968 + (4184977779251709*w*x*z)/562949953421312 - (7212895511779849*w*y*z)/2251799813685248 + (7884701419519699*x*y*z)/4503599627370496;
f2 = x^2 + y^2 + z^2 + w^2 - 1;
END;

[ofloveandhate]

your input file contains a syntax error. concatenation is not multiplication -- it must be explicit

[tjstrunk]

My input file doesn't contain that error. The input file itself has the '*' for multiplication. GitHub just wasn't displaying the asterisk for some reason. You have to use backslash asterisk. (I am disappointed, because that would have been such a simple fix if the error was in the actual input file...)

[tjstrunk]

I think the previous post formatting is fixed!

[ofloveandhate]

hey Tanner, would you mind please summing up the things we talked about at CBMS Applications of Polynomial Systems, and how they turned out?

[ofloveandhate]

triple backticks make a codeblock, yo

[tjstrunk]

I ended up using

CONFIG
tracktype: 1;
mptype: 2;
sharpenDigits: 30;
endgameNum: 2;
trackTolBeforeEG: 1e-11;
trackTolDuringEG: 1e-12;
endgameBdry: 0.000001;
finaltol: 1e-12;
functiontolerance:1e-14;
MaxStepsBeforeNewton: 0;
MaxNewtonIts: 1;
odepredictor: 8;
securitylevel: 1;
END;

to get some reasonable output for all but one of the samples. That one sample still would not give the correct h^2 (and presumably h^1--I didn't check, actually). In particular I changed the endgamebdry parameter, Newton iteration numbers, and ODE predictor. I also added -g 1 to my call to bertini_real to make it use the gamma trick.

[ofloveandhate]

can you post the complete input file for the problematic example?

[ofloveandhate]

also, remember to fix randomseed, to help with reproducibility.

[ofloveandhate]

you should make that functiontolerance larger, too. when evaluated, expressions are considered 0 if their abs is smaller than that tolerance. smaller than computed tolerances seems incorrect. maybe 1e-7?

[tjstrunk]

I made the function tolerance smaller in an effort to get better output. I don't still have the original input file that started this issue. I'll try running things again with the bigger function tolerance and see what difference that makes. I was having some qualms with the output in the last batch anyway...

[ofloveandhate]

do a run, collect all the problematic input files (and hopefully .mat files too from the matlab component), and that will go a long way to finding out what is the problem here.

[ofloveandhate]

there's probably some stupid bug in the decomposition that we are dancing around here. fixing the value of randomseed in the bertini_real input files will at least give us the ability to replicate the problem, if we also have the input files.