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{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 207 32 "read(\"../Src/multifac_1
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examples\\/\":" }{MPLTEXT 1 207 1 "\n" }{MPLTEXT 1 207 24 "read cat(pa
th, \"exF18\"):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Digits:=
floor(evalhf(Digits));" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#9" }}}
{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 207 38 "F18:=evalf(expand(cleanF
18+noiseF18)):" }{MPLTEXT 1 207 44 "norm(evalf(expand(noiseF18)),2)/no
rm(F18,2);" }{MPLTEXT 1 207 1 "\n" }{MPLTEXT 1 207 15 "ceil(log10(%));
" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"/e:CCSmw!#@" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "!\"(" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 207 12 "t1
8:=time():" }{MPLTEXT 1 207 1 "\n" }{MPLTEXT 1 207 26 "facF18:=appfac(
F18,[x,y]);" }{MPLTEXT 1 207 1 "\n" }{MPLTEXT 1 207 16 "t18:=time()-t1
8;" }}{PARA 6 "" 1 "" {TEXT 208 116 "` the biggest gap, the last r-th \+
singular values and the number of factors `, 1055930.3245364, .7824408
5000805e-8, 2" }}{PARA 6 "" 1 "" {TEXT 208 59 "` The time for computin
g the number of factors*****`, 7.406" }}{PARA 6 "" 1 "" {TEXT 208 53 "
`The time for the entire factorization******`, 31.829" }}{PARA 12 "" 1
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qrRF0F,F1F,F2F,)F7FIF,F,*&,&$\"3%)=%\\Q))*fS9F0F,*&$\"3r\\$pbJ,k?%F0F,
F1F,F,F,)F7\"\"%F,F,*&,&$\"3W*3&f,3hnKF0F,*&$\"3IM:4M*)[t6F0F,F1F,F,F,
)F4\"\"#F,F,*&,&$\"3172XcH4d]!#?F2*&$\"3#*od)yJk_>#F0F,F1F,F,F,)F7F]oF
,F,*&,&$\"3]72&R\"HJ#f\"F0F2*&$\"3W*3SzB\"RzBF0F,F1F,F,F,F3F,F,*&,&$\"
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YHBAA$3B]$F0F,F1F,F2F,F4F,F,*&,&$\"3YJAIIIZc7F0F2*&$\"39>'Q@!*fYm#F0F,
F1F,F2F,F7F,F,*(,&$\"3e)4$oN_@)z#F0F2*&$\"3e^Y(owK0[#F0F,F1F,F2F,F4F,F
foF,F,*(,&$\"3Kr7K!y7H.$F0F2*&$\"3+z$))3G6q#=F0F,F1F,F2F,F\\oF,F7F,F,*
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\"F0F,*&$\"33#3u8SfYm#F0F,F1F,F,F,F4F,F7F,F,,&$\"/uanr^jD!#9F,*&$\"/;G
I_0MJFbtF,F1F,F,F,*(,&$\"3&>!yl?(*fS9F0F,*&$\"3Xn\"Q[o,k?%F0F,F1F,F,F,
F4F,F?F,F,*(,&$\"3'zUmx!)fYm#F0F,*&$\"3mxs+_LZc7F0F,F1F,F2F,F\\oF,FYF,
F,*(,&$\"3@:j72D\"H.$F0F2*&$\"3HhOqb3,F=F0F,F1F,F2F,F\\qF,FfoF,F,*(,&$
\"3;(\\`uWoes\"F0F2*&$\"3#3N@;::wN\"F0F,F1F,F2F,F`sF,F7F,F,*(,&$\"3!HX
`-^P#)=%F+F,*&$\"3QaH/RH>#)))F+F,F1F,F,F,F4F,FYF,F,*(,&$\"3izRCSPZc7F0
F2*&$\"3#\\+xnRfYm#F0F,F1F,F2F,F\\oF,F6F,F,*(,&$\"3Qg3T-dhd8F0F2*&$\"3
88J)e#)oes\"F0F,F1F,F,F,F3F,FfoF,F,*(,&$\"3aUc=1#3B]$F0F,*&$\"3%>'zrO)
o'*>&F+F,F1F,F,F,F\\qF,F7F,F,*(,&$\"3u')[JR.yqyF+F,*&$\"3-rb&4)QqrRF0F
,F1F,F,F,F4F,F6F,F,*(,&$\"3P&HpI6?)GBF0F,*&$\"39TIRqqd(y$F0F,F1F,F,F,F
\\oF,FfoF,F,,Z*(,&$\"3#o&=pRu!pB\"F0F,*&$\"3'[6+K(=*3]$F0F,F1F,F2F,F
\\qF,FfoF,F,*&,&$\"3?)e'QTwN-=F+F,*&$\"3i:z@I')[cIF0F,F1F,F,F,FQF,F,*&
,&$\"3nIFn%3_\"GDF0F,*&$\"3/j\"o%GXX)4$F0F,F1F,F,F,F?F,F,*&,&$\"3/RXHD
LY4UF0F,*&$\"3&yv!p0aq95F0F,F1F,F,F,FHF,F,*&,&$\"3bN\"*yIW37EF0F2*&$\"
3)Q/\\C1ztf\"F0F,F1F,F,F,F`sF,F,*&,&$\"33Uf`W\")[cIF0F,*&$\"3IO]zocN-=
F+F,F1F,F2F,FYF,F,*&,&$\"3O1AMmjt2$*F+F,*&$\"3'e2@4I-P'[F+F,F1F,F,F,F6
F,F,*&,&$\"3/H\")zS'f]w$F0F,*&$\"31RQsydPCSF+F,F1F,F2F,F\\qF,F,*&,&$\"
3Q-bqX/on@F0F,*&$\"3T_f(3*>_9IF0F,F1F,F2F,F4F,F,*&,&$\"3i'=6c%*f]w$F0F
2*&$\"3O]im%=uV-%F+F,F1F,F,F,F7F,F,*&,&$\"3S0^EWA_9IF0F,*&$\"3WEU6%*3o
n@F0F,F1F,F,F,FfoF,F,*&,&$\"3)z@Y/D68o\"F0F2*&$\"3wk\\J&o[P3#F0F,F1F,F
,F,F3F,F,*(,&$\"31JMco5k'>%FboF,*&$\"3W:_b0p\"zM#F0F,F1F,F2F,F4F,F?F,F
,*(,&$\"35`9rV4o'>%FboF2*&$\"3#Rxr*)y;zM#F0F,F1F,F,F,F\\oF,FYF,F,*(,&$
\"31uP\"yE(RF(*F+F,*&$\"391dfMuah=F0F,F1F,F2F,F3F,F6F,F,*(,&$\"3++)oE&
4MhIF+F,*&$\"3!*))48E=E()RF0F,F1F,F2F,F`sF,F7F,F,*(,&$\"3)3AP&4_(H:\"F
0F,*&$\"3Y@F.E:%\\>\"F0F,F1F,F,F,F4F,FYF,F,*(,&$\"3=!oZW-d1K$F0F2*&$\"
3iGsW5-e>=F0F,F1F,F,F,F\\oF,F6F,F,*(,&$\"3pr`>TS4BPF0F,*&$\"3?qH'p$*ya
%>F0F,F1F,F,F,F3F,FfoF,F,*(,&$\"3(4I\\'>F^.>F0F2*&$\"3cR8W'ew^P\"F0F,F
1F,F,F,F\\qF,F7F,F,*(,&$\"3'f.)3%>>Bz#F0F,*&$\"31R\"3sy4\"f9F0F,F1F,F,
F,F4F,F6F,F,*(,&$\"3&oB<d()p`](F+F2*&$\"3->-'ej<,d#F0F,F1F,F,F,F\\oF,F
foF,F,*(,&$\"3-(yhX&R,AAF+F2*&$\"3-+!f31;d3(F+F,F1F,F2F,F4F,F7F,F,*(,&
$\"3\\LT<\"4:d7#F0F2*&$\"3w\\\\%ev^gm'F+F,F1F,F,F,F3F,F7F,F,,&$\"/'y^9
cgm'!#:F2*&$\"/Xi5VrD@FbtF,F1F,F2F,*(,&$\"3LTSYgqGMGF0F2*&$\"3!Qtw+Zq!
))))F+F,F1F,F,F,F4F,FfoF,F,*&,&$\"3')3zXt')[cIF0F2*&$\"3d6H/G)fB!=F+F,
F1F,F,F,F\\oF,F,*(,&$\"3A4UU*[R81$F+F2*&$\"3'*RNR3AE()RF0F,F1F,F,F,F
\\oF,F7F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$t18G$\"&H=$!\"$" }}}
{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 207 13 "nops(facF18);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 202 "> " 0 "" 
{MPLTEXT 1 207 69 "berror18:=backward_error(expand(facF18[1]*facF18[2]
), F18, [x,y])[2];" }}{PARA 6 "" 1 "" {TEXT 208 50 "Approximate factor
ization is not a real polynomial" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%
\"cG,&$\"/V#))RG'3@!#<!\"\"*&$\"/;u(*R<_^!#;\"\"\"^#F.F.F." }}{PARA 11
 "" 1 "" {XPPMATH 20 "6#>%)berror18G$\"/8?xg3cH!#?" }}}{EXCHG {PARA 
202 "> " 0 "" {MPLTEXT 1 202 55 "save facF18, t18, berror18, cat(path,
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{EXCHG {PARA 202 "" 0 "" {TEXT 209 0 "" }}}{PARA 206 "" 0 "" {TEXT 
210 0 "" }}}
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