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{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 23 "read`multifac_1.3.mpl`:
" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 22 "# path:=\"debug_exs
\\/\":" }{MPLTEXT 1 204 20 "\npath:=\"examples\\/\":" }{MPLTEXT 1 204 
25 "\nread cat(path, \"exF18\"):" }}}{EXCHG {PARA 201 "> " 0 "" 
{MPLTEXT 1 204 38 "F18:=evalf(expand(cleanF18+noiseF18)):" }{MPLTEXT 
1 204 44 "norm(evalf(expand(noiseF18)),2)/norm(F18,2);" }{MPLTEXT 1 
204 16 "\nceil(log10(%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+FCSmw
!#<" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"(" }}}{EXCHG {PARA 201 "> " 
0 "" {MPLTEXT 1 204 12 "t18:=time():" }{MPLTEXT 1 204 27 "\nfacF18:=ap
pfac(F18,[x,y]);" }{MPLTEXT 1 204 17 "\nt18:=time()-t18;" }}{PARA 6 "
" 1 "" {TEXT -1 108 "` the biggest gap, the last r-th singular values \+
and the number of factors `, 1056104.077, .7823121207e-8, 2" }}{PARA 
6 "" 1 "" {TEXT -1 59 "` The time for computing the number of factors*
****`, 8.683" }}{PARA 6 "" 1 "" {TEXT -1 53 "`The time for the entire \+
factorization******`, 29.994" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'fac
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}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 13 "nops(facF18);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 201 "> " 0 "" 
{MPLTEXT 1 204 66 "berror18:=backward_error(expand(facF18[1]*facF18[2]
), F18, [x,y]);" }}{PARA 6 "" 1 "" {TEXT -1 50 "Approximate factorizat
ion is not a real polynomial" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"cG
^$$!+[818E!#7$\"+EV([W%F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)berror
18G$\"+S.+mH!#;" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 208 55 "save
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