> restart;
> read`multifac_1.3.mpl`:
> # path:="debug_exs\/":
> path:="examples\/":
> read cat(path, "exF18"):
> F18:=evalf(expand(cleanF18+noiseF18)):norm(evalf(expand(noiseF18)),2)/
> norm(F18,2);
> ceil(log10(%));

                                         -7
                          0.7666402427 10


                                  -7

> t18:=time():
> facF18:=appfac(F18,[x,y]);
> t18:=time()-t18;
` the biggest gap, the last r-th singular values and the number of
factors `, 1056104.077, .7823121207e-8, 2
` The time for computing the number of factors*****`, 8.683
`The time for the entire factorization******`, 29.994

                                                                4
  facF18 := [-(0.0478441052867338430 + 0.442024273781976895 I) y

                                                             5
         + (0.0265606573147074282 + 0.346161490089326118 I) x

                                                            5
         + (0.330155261998031746 + 0.127875278834704730 I) y

                                                             6
         + (0.442024293424868375 - 0.0478440885595998108 I) x

         - 0.1809965365 - 0.3621677487 I

                                                            3
         + (0.159713129592526398 + 0.266304939554199482 I) y

                                                             4
         - (0.0320125256239235448 - 0.308871842102679540 I) x

         - (0.127875221713060426 - 0.330155274219456507 I) x

         + (0.0638503070688524050 + 0.287588412354781830 I) y

                                                            2
         - (0.292865604788136003 + 0.186448409517893432 I) x

                                                             2
         + (0.0532958991469199839 - 0.213009055666190966 I) y

                                                            3
         + (0.207731818403916608 - 0.197002848595488140 I) x

                                                             2  4
         - (0.287588409822200130 - 0.0638503398721431138 I) x  y

                                                               5
         - (0.0478440808336138904 + 0.442024306601188910 I) x y

                                                             3  3
         - (0.0745793334654765022 - 0.117146192024187662 I) x  y

                                                              2
         + (0.218286252904517310 + 0.303594603989917999 I) x y

                                                            2
         + (0.255575896172862194 + 0.245021544002062970 I) x  y

                                                            3
         + (0.207731802830405404 - 0.197002772943852988 I) x  y

                                                            2  2
         - (0.143706932454258085 + 0.420740854883492221 I) x  y

                                                               3
         + (0.0107289933412350654 - 0.404734633790436616 I) x y

                                                            4
         - (0.330155247682365538 + 0.127875290704780292 I) x  y

                                                            3  2
         + (0.170442187380067056 - 0.138429690713380960 I) x  y

                                                             2  3
         + (0.0638503881390497520 + 0.287588378991266880 I) x  y

                                                                4
         - (0.0212833920991547243 + 0.0958627252528246044 I) x y

                                                            5
         + (0.138429664998634738 + 0.170442125311147580 I) x  y

                                                            4  2
         + (0.255575878208181062 + 0.245021494908587878 I) x  y

         - (0.0638503728628057738 + 0.287588375485235636 I) x y

                                                             6
         - (0.0107290379462734316 - 0.404734684849957228 I) y ,

                                                             5
        -(0.0663120689681781367 - 0.225262337486092922 I) x y

                                                             2  4
         + (0.0663121048266673424 - 0.225262316373411958 I) x  y

                                                            3  3
         - (0.143154587571759889 - 0.153685092029216097 I) x  y

                                                            4  2
         - (0.212099203850915158 - 0.304737460087111390 I) x  y

                                                            5
         - (0.135256695527558562 - 0.376314752744864146 I) x  y

                                                               4
         - (0.0794751327887399106 + 0.145787188810887202 I) x y

                                                             2  3
         + (0.368416939865846392 - 0.0873729339132224558 I) x  y

                                                            3  2
         - (0.307370119060317414 + 0.286309101569445502 I) x  y

                                                             4
         + (0.219997037658822642 - 0.0821077228259704389 I) x  y

                                                              3
         - (0.230527443690630496 + 0.214731847148739274 I) x y

                                                            2  2
         + (0.140521841279242360 - 0.227894879532995892 I) x  y

                                                              3
         + (0.222629716442359321 - 0.00789782795435714676 I) x  y

                                                            2
         + (0.135256692702430680 - 0.376314794302377632 I) x  y

                                                               2
         + (0.296839652305793956 - 0.0105304429865572570 I) x y

         + 0.007897890873 + 0.2226296524 I

         + (0.00263257897360078550 + 0.0742098881533463234 I) x y

                                                             6
         + (0.0636794172030864526 - 0.299472257531392892 I) y

                                                             4
         - (0.299472204989360222 + 0.0636794248324432238 I) y

                                                             5
         + (0.294206963377170283 - 0.0847404050596708426 I) x

                                                            5
         - (0.161582876174276357 + 0.365784261110501220 I) y

                                                            6
         - (0.378947350720218566 + 0.209466557829527554 I) x

         - (0.288941681558735008 - 0.233160183800132204 I) x

         + (0.373682123194210958 + 0.0610468054224255971 I) y

                                                             2
         + (0.299472266814685804 + 0.0636793972440788808 I) x

                                                            2
         - (0.233160195963755118 + 0.288941732020515428 I) y

                                                            3
         + (0.217364463391447050 - 0.156317660326506014 I) x

                                                              3
         - (0.0768425290487625564 + 0.0715773261661077770 I) y

                                                             4
         - (0.373682099222375885 + 0.0610467804978594777 I) x ]


                            t18 := 30.034

> nops(facF18);

                                  2

> berror18:=backward_error(expand(facF18[1]*facF18[2]), F18, [x,y]);
Approximate factorization is not a real polynomial

                c = -0.002613061348 + 0.004444874326 I


                                               -6
                    berror18 := 0.2966000340 10

> save facF18, t18, berror18, cat(path, "exF18-factors");
> 
> 
> 
> 
> 
> 
> 
# 
#