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[F'/F4Q'prefixF'/F7Q%trueF'F9/F " 0 "" {MPLTEXT 1 206 20 "Con_M:=Matrix(14,9):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "for i from 1 to 8 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Con_M[i,i]:=1:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "end do:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "Con_M[9,5]:=3:Con_M[10,6]:=2 :Con_M[11,7]:=1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "Con_M[1 2,1]:=3:Con_M[13,2]:=2:Con_M[14,3]:=1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Con_M:" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 206 60 "pp,prim_list:=C_con_mulpoly([f,g,f1,g1],1,5,Con_M,W,'cofa'):" } {MPLTEXT 1 206 0 "" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }} {PARA 11 "" 1 "" {XPPMATH 20 "/I,error_orginG6\"$\"3y&)QFm%R%)\\'!#?" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I$numG6\"\"\"\"" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_m ulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I\"RG6\"$\"31)y_$Q)y>\\'!#?" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I$numG6\"\"\"\"" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_m ulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I(delta_xG6\"$\"36&z!=[!*)o, \"!#>" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I$numG6\"\"\"#" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_co n_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I\"RG6\"$\"3=*z=?.8#pV!#A " }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I$numG6\"\"\"#" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mu lpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I(delta_xG6\"$\"39l0P64Ho`!#@ " }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I$numG6\"\"\"$" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mu lpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I\"RG6\"$\"31vz!*R`'4e#!#C" } }{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I$numG6\"\"\"$" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mu lpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I(delta_xG6\"$\"31v@<^j%z<\"! #>" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I$numG6\"\"\"%" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_m ulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I\"RG6\"$\"3x\\o0Zd+:7!#@" } }{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I$numG6\"\"\"%" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mu lpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I(delta_xG6\"$\"3w_\"*)QEz.5 \"!#@" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I$numG6\"\"\"&" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_co n_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I\"RG6\"$\"3'G:dS!4w\"G\" !#D" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 " " {XPPMATH 20 "/I$numG6\"\"\"&" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_ mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I(delta_xG6\"$\"3=[%zhiMz4 \"!#@" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I$numG6\"\"\"'" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_co n_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I\"RG6\"$\"3gbVE&p&p&R\"! #D" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I$numG6\"\"\"'" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_m ulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I(delta_xG6\"$\"3/\"p<>-i%R( *!#C" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I8number~of~the~iterationG6\"\"\"'" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$IDche ck~the~distance~between~f~and~ffG6\"$\"//y,%QmY*!#=" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 206 1 " " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 206 114 "ff:=expand(pp*prim_list[1]):gg:=expand(pp*prim_lis t[2]):ff1:=expand(pp*prim_list[3]):gg1:=expand(pp*prim_list[4]):" } {MPLTEXT 1 206 0 "" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 206 39 "p p; ff; gg; prim_list[1]; prim_list[2];" }{MPLTEXT 1 206 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&,&$\"/C&*f6$R]\"!#;\"\"\"*&$\"/!pjt9I+\"!#8F '^#F'F'!\"\"F'*&,&$\"3c.++++++5!#)**! #9F'FEF'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ",0,&$\"/NBu\"*y.=!#;\"\"\" *&$\"/PP:gi15!#8F'^#F'F'!\"\"F'*&$\".Rb*)Q@#fF&F')I\"xG6\"\"\"#F'F'*&, $*&$\"/)\\kjiG5'!#)**!#=F'*&$\"3 %**f***p)H&)4\"!#?F'F+F'F'F')I\"xG6\"\"\"#F'F'*&,&$\"3W=\"eDGY?H\"F4! \"\"*&$\"3K9BQ\"3hR***F0F'F+F'F=F'F6F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(,&$\"/p$['3g.5!#8\"\"\"*&$\"/@*yivb$H!#sr6iw5)F?F'F,F'F6F'F8F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 206 39 "prim_part1:=polydiv(ff,expand(pp^2),x):" }{MPLTEXT 1 206 0 " " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 206 39 "prim_part2:=polydiv (gg,expand(pp^2),x):" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 206 83 "error_con:=norm(f-expand(pp^2*prim_part1),2)^2+norm(g-expand(pp^2*pri m_part2),2)^2;" }{MPLTEXT 1 206 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "> I*error_conG6\"$\"/tY,%QmY*!#=" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 206 0 "" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 206 15 "#check th e root" }{MPLTEXT 1 206 0 "" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 206 37 "norm(ff-expand(pp^2*prim_part1),2)^2;" }{MPLTEXT 1 206 0 "" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"/++++N\"y(!#S" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 206 37 "norm(gg-expand(pp^2*prim_part2),2)^2;" } {MPLTEXT 1 206 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"/,+S51!\\&!#R" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 217 51 "Case 2: using C_con_gcd with out linear constraints:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "p p,prim_list:=C_con_mulpoly([f,g,f1,g1],1,5,'default','default','cofa') :" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I,error_orginG6\"$\"3y&)QFm%R%)\\'!#?" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I$numG 6\"\"\"\"" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I\"RG6\"$\"3^28#z/;N]*!#J" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I$numG6 \"\"\"\"" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 " " 1 "" {XPPMATH 20 "/I(delta_xG6\"$\"3+R?N&H(yY9!#?" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I$numG 6\"\"\"#" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 " " 1 "" {XPPMATH 20 "/I\"RG6\"$\"3_09hU$z`L\"!#B" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I$numG6 \"\"\"#" }}{PARA 6 "" 1 "" {TEXT 216 14 "C_con_mulpoly:" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I(delta_xG6\"$\"3s)e]Y#o1p " 0 "" {MPLTEXT 1 0 165 "error_without_con:=norm(f-expand(pp*prim_list[1]),2)^2+norm( g-expand(pp*prim_list[2]),2)^2+norm(f1-expand(pp*prim_list[3]),2)^2+no rm(g1-expand(pp*prim_list[4]),2)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "> I2error_without_conG6\"$\"/^OEo\"***\\!#=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "pp;ff:=prim_list[1]; gg:=prim_list[2];" }}{PARA 11 " " 1 "" {XPPMATH 20 ",&,&$\"/Fq-q)[]'!#@!\"\"*&$\"/7()*)4,+5!#8\"\"\"^# F,F,F'F,*&,&$\"2/R*************!#I#ffG6\",(,&$\"/4^B.IUr!#?\" \"\"*&$\"/$Q_?x=](!#;F*^#F*F*F*F**&,&$\"2'*R'RJi******!#I#ggG6\" ,(,&$\"/^a30\\25!#8\"\"\"*&$\"/q_$=vf\"R!#?F*^#F*F*!\"\"F**&,&$\"3M3ix \"3#*\\(**!#=F**&$\"3&4Tqg-VMT#!#CF*F/F*F*F*)I\"xGF$\"\"#F*F**&,&$\"3; Y1lVs%Rk$F9F0*&$\"3UqEzF#>/*\\F.F*F/F*F0F*F;F*F*" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 206 38 "prim_part1:=polydiv(f,expand(pp^2),x):" } }}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 206 38 "prim_part2:=polydiv(g, expand(pp^2),x):" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 206 83 "err or_con:=norm(f-expand(pp^2*prim_part1),2)^2+norm(g-expand(pp^2*prim_pa rt2),2)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I*error_conG6\"$\"/7(>!>O (R\"!#<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }