{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 1 "#" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 31 "# inicio del fichero RKUT44.MWS" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 1 "#" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 45 "# modelo para \+ estudiar metodos de Runge-Kutta" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 56 "# de cuatro evaluaciones k1, k2, k3 y k4 y orden 4 para " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 57 "# ecuaciones escalares aut\363nomas (EA) y no a ut\363nomas (EN)" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 53 "# y para sistema s aut\363nomos (SN) y no aut\363nomos (SN)." }}{PARA 0 "" 0 "" {MPLTEXT 0 21 37 "# Empezaremos con metodos explicitos." }}{PARA 0 "" 0 "" {MPLTEXT 0 21 1 "#" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 36 "# Empezam os con una ecuaci\363n escalar" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 28 "# \+ yp = f(x,y) , y(a) = " }{XPPEDIT 18 0 "alpha" "6#%&alphaG" } {MPLTEXT 0 21 2 " " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 8 "# o bien" }} {PARA 0 "" 0 "" {MPLTEXT 0 21 26 "# yp = f(y) , y(a) = " } {XPPEDIT 18 0 "alpha" "6#%&alphaG" }{MPLTEXT 0 21 15 " \+ " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 23 "# en el caso aut\363nomo. " }} {PARA 0 "" 0 "" {MPLTEXT 0 21 16 "# El m\351todo es " }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 19 "# k1:=f(x0,y0)" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 38 "# k2:=f(x0+c[2]*h,y0+a[2,1]*h*k1)" }} {PARA 0 "" 0 "" {MPLTEXT 0 21 50 "# k3:=f(x0+c[3]*h,y0+a[3,1]*h*k 1+a[3,2]*h*k2)" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 62 "# k4:=f(x0+c[ 4]*h,y0+a[4,1]*h*k1+a[4,2]*h*k2+a[4,3]*h*k3)" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 14 "# y finalmente" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 49 " # y1:=y0+h*(b[1]*k1+b[2]*k2+b[3]*k3+b[4]*k4)" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 28 "# o sea Fi0 que representa " }{XPPEDIT 18 0 "Phi(h) " "6#-%$PhiG6#%\"hG" }{MPLTEXT 0 21 3 " = " }{XPPEDIT 18 0 "Phi(x0,y0, h)" "6#-%$PhiG6%%#x0G%#y0G%\"hG" }{MPLTEXT 0 21 4 " es" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 44 "# Fi0:=b[1]*k1+b[2]*k2+b[3]*k3+b[4]*k4 " } }{PARA 0 "" 0 "" {MPLTEXT 0 21 51 "# y Fi1, Fi2, Fi3 son sus derivadas sucesivas, " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 54 "# mientras que, \+ por la parte de la verdadera soluci\363n," }}{PARA 0 "" 0 "" {MPLTEXT 0 21 22 "# fk que representa " }{XPPEDIT 18 0 "f^([k])" "6#)%\"fG7#% \"kG" }{MPLTEXT 0 21 14 " (x0,y0) vale" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 57 "# f(k+1):=diff(fk,x):=D[1](fk)+f0*D[2](fk) " }} {PARA 0 "" 0 "" {MPLTEXT 0 21 58 "# Para las condiciones de orden, lo \+ que se hace es imponer" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 16 "# sucesiva mente " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 16 "# Fik(0) = " } {XPPEDIT 18 0 "1/(k+1)" "6#*&\"\"\"F$,&%\"kGF$F$F$!\"\"" }{MPLTEXT 0 21 4 " fk " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# en este caso para k= 0,1,2,3" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 43 "# Para el t\351rmino del \+ error se calculan los" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 40 "# distintos coeficientes que aparecen en" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 7 "# \+ " }{XPPEDIT 18 0 "1/4!;" "6#*&\"\"\"F$-%*factorialG6#\"\"%!\"\"" } {MPLTEXT 0 21 10 " Fi4(0) - " }{XPPEDIT 18 0 "1/5!;" "6#*&\"\"\"F$-%*f actorialG6#\"\"&!\"\"" }{MPLTEXT 0 21 19 " f4 " }} {PARA 0 "" 0 "" {MPLTEXT 0 21 28 "# para el orden 4 del m\351todo" }} {PARA 0 "" 0 "" {MPLTEXT 0 21 1 "#" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 40 "# Para sistemas aut\363nomos y no aut\363nomos" }{TEXT -1 0 "" }} {PARA 0 "" 0 "" {MPLTEXT 0 21 45 "# Todo es similar, pero ahora las co ndiciones" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 19 "# Fik(0)[i] = " } {XPPEDIT 18 0 "1/(k+1)" "6#*&\"\"\"F$,&%\"kGF$F$F$!\"\"" }{MPLTEXT 0 21 37 " fk[i] " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 57 "# se imponen s\363lo sobre la primera componente i=1 , ya que" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 26 "# las otras son id\351nt icas " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 1 "#" }}}{EXCHG {PARA 0 "" 0 " " {MPLTEXT 0 21 35 "# PARA ECUACIONES NO AUTONOMAS (EN)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 26 "interface(labeling=false):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 37 "# desarrollo de la verdadera solucion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "y:=unapply(y(x),x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f:=unapply(f(x,y),x,y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f0:=f(x,y(x)):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 44 "f1:=subs(diff(y(x),x)=f(x,y(x)),diff(f0,x)): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "f2:=subs(diff(y(x),x)=f (x,y(x)),diff(f1,x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "f3 :=subs(diff(y(x),x)=f(x,y(x)),diff(f2,x)):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 45 "f0:=subs(\{y(x)=y0,x=x0\},f0):ENf0:=expand(f0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ENf0G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f1:=subs(\{y(x)=y0,x=x0\},f1):ENf1: =expand(f1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ENf1G,&--&%\"DG6#\" \"\"6#%\"fG6$%#x0G%#y0GF+*&--&F)6#\"\"#F,F.F+-F-F.F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f2:=subs(\{y(x)=y0,x=x0\},f2):ENf2: =expand(f2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ENf2G,,--&%\"DG6$\" \"\"F+6#%\"fG6$%#x0G%#y0GF+*(\"\"#F+--&F)6$F+F2F,F.F+-F-F.F+F+*&--&F)6 $F2F2F,F.F+)F7F2F+F+*&--&F)6#F2F,F.F+--&F)6#F+F,F.F+F+*&)F?F2F+F7F+F+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f3:=subs(\{y(x)=y0,x=x0 \},f3):ENf3:=expand(f3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%ENf3G,8 --&%\"DG6%\"\"\"F+F+6#%\"fG6$%#x0G%#y0GF+*(\"\"$F+--&F)6%F+F+\"\"#F,F. F+-F-F.F+F+*(F2F+--&F)6%F+F7F7F,F.F+)F8F7F+F+*(F2F+--&F)6$F+F7F,F.F+-- &F)6#F+F,F.F+F+**\"\"&F+F@F+--&F)6#F7F,F.F+F8F+F+*&--&F)6%F7F7F7F,F.F+ )F8F2F+F+**F2F+F8F+--&F)6$F7F7F,F.F+FDF+F+**\"\"%F+FUF+FJF+F>F+F+*&FJF +--&F)6$F+F+F,F.F+F+*&)FJF7F+FDF+F+*&)FJF2F+F8F+F+" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 23 "# desarrollo del m\351todo" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "k10:=f(x,y):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 32 "k20:=f(x+c[2]*h,y+a[2,1]*h*k10):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "k30:=f(x+c[3]*h,y+a[3,1]*h*k10+a[3,2]*h*k 20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "k40:=f(x+c[4]*h,y+a [4,1]*h*k10+a[4,2]*h*k20+a[4,3]*h*k30):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k100:=subs(h=0,k10):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k200:=subs(h=0,k20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k300:=subs(h=0,k30):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k400:=subs(h=0,k40):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "Fi0:=b[1]*k100+b[2]*k200+b[3]*k300+b[4]*k400:Fi0:=sub s(\{x=x0,y=y0\},Fi0):ENFi0:=expand(Fi0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&ENFi0G,**&&%\"bG6#\"\"\"F*-%\"fG6$%#x0G%#y0GF*F**&&F(6#\"\"#F *F+F*F**&&F(6#\"\"$F*F+F*F**&&F(6#\"\"%F*F+F*F*" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 17 "k11:=diff(k10,h):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 17 "k21:=diff(k20,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k31:=diff(k30,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k41:=diff(k40,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k110:=subs(h=0,k11):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k210:=subs(h=0,k21):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k310:=subs(h=0,k31):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k410:=subs(h=0,k41):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "Fi1:=b[1]*k110+b[2]*k210+b[3]*k310+b[4]*k410:Fi1:=sub s(\{x=x0,y=y0\},Fi1):ENFi1:=expand(Fi1);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&ENFi1G,4*(&%\"bG6#\"\"#\"\"\"--&%\"DG6#F+6#%\"fG6$%#x0G%#y0GF +&%\"cGF)F+F+**F'F+--&F/F)F1F3F+&%\"aG6$F*F+F+-F2F3F+F+*(&F(6#\"\"$F+F ,F+&F7FBF+F+**FAF+F9F+&F=6$FCF+F+F?F+F+**FAF+F9F+&F=6$FCF*F+F?F+F+*(&F (6#\"\"%F+F,F+&F7FMF+F+**FLF+F9F+&F=6$FNF+F+F?F+F+**FLF+F9F+&F=6$FNF*F +F?F+F+**FLF+F9F+&F=6$FNFCF+F?F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k12:=diff(k11,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k22:=diff(k21,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k32:=diff(k31,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k42:=diff(k41,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k120:=subs(h=0,k12):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k220:=subs(h=0,k22):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k320:=subs(h=0,k32):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k420:=subs(h=0,k42):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "Fi2:=b[1]*k120+b[2]*k220+b[3]*k320+b[4]*k420:Fi2:=sub s(\{x=x0,y=y0\},Fi2):ENFi2:=expand(Fi2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&ENFi2G,V*,&%\"bG6#\"\"%\"\"\"--&%\"DG6#\"\"#6#%\"fG6$%#x0G%#y 0GF+&%\"aG6$F*\"\"$F+--&F/6#F+F2F4F+&%\"cG6#F:F+F1*.F1F+F'F+F7F+)F,F1F +&F86$F:F+F+-F3F4F+F+*.F1F+F'F+F7F+FCF+&F86$F:F1F+FFF+F+*.F1F+F'F+--&F /6$F1F1F2F4F+&F86$F*F1F+)FFF1F+F7F+F+*.F1F+F'F+F,F+FOF+F;F+&F@F0F+F+*. F1F+F'F+FOF+FCF+&F86$F1F+F+FFF+F+**F'F+FKF+)FOF1F+FQF+F+**F'F+FKF+)F7F 1F+FQF+F+*.F1F+F'F+&F@F)F+--&F/6$F+F1F2F4F+FOF+FFF+F+*.F1F+F'F+FfnF+Fg nF+F7F+FFF+F+*.F1F+F'F+FKF+&F86$F*F+F+FQF+FOF+F+*.F1F+F'F+FKF+F]oF+FQF +F7F+F+*.F1F+F'F+FfnF+FgnF+F]oF+FFF+F+*(F'F+--&F/6$F+F+F2F4F+)FfnF1F+F +**F'F+FKF+)F]oF1F+FQF+F+*(&F(F0F+FboF+)FSF1F+F+*(&F(FAF+FboF+)F?F1F+F +**FjoF+)FUF1F+FQF+FKF+F+*.F1F+FjoF+FSF+FgnF+FUF+FFF+F+*.F1F+F]pF+F,F+ FHF+F;F+FSF+F+*.F1F+F]pF+FCF+FHF+FUF+FFF+F+**F]pF+FKF+)FDF1F+FQF+F+*.F 1F+F]pF+FKF+FDF+FQF+FHF+F+**F]pF+FKF+)FHF1F+FQF+F+*.F1F+F]pF+F?F+FgnF+ FHF+FFF+F+*.F1F+F]pF+F?F+FgnF+FDF+FFF+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k13:=diff(k12,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k23:=diff(k22,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k33:=diff(k32,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k43:=diff(k42,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k130:=subs(h=0,k13):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k230:=subs(h=0,k23):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k330:=subs(h=0,k33):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k430:=subs(h=0,k43):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "Fi3:=b[1]*k130+b[2]*k230+b[3]*k330+b[4]*k430:Fi3:=sub s(\{x=x0,y=y0\},Fi3):ENFi3:=expand(Fi3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&ENFi3G,`t*(&%\"bG6#\"\"#\"\"\"--&%\"DG6%F+F+F+6#%\"fG6$%#x0G% #y0GF+)&%\"cGF)\"\"$F+F+*.F9F+&F(6#\"\"%F+&F8FF+F?F+)&FE6$F=F*F*F+FGF+F+*.F9F +F;F+F>F+F?F+)&FE6$F=F9F*F+FGF+F+*0\"\"'F+F;F+--&F/6$F*F*F1F3F+FJF+--& F/F)F1F3F+&FE6$F*F+F+FGF+F+*2FRF+F;F+FSF+FKF+FWF+FZF+FGF+FOF+F+*2FRF+F ;F+FSF+FOF+--&F/6#F+F1F3F+&F86#F9F+FDF+FHF+F+*2FRF+F;F+FSF+FOF+FhnF+F \\oF+FKF+FHF+F+*0FRF+F;F+FSF+FNF+FhnF+F\\oF+FHF+F+*2FRF+F;F+FSF+FOF+FW F+&FE6$F9F+F+FGF+FDF+F+*2FRF+F;F+FSF+FOF+FWF+FaoF+FGF+FKF+F+*0FRF+F;F+ FSF+FNF+FWF+FaoF+FGF+F+*2FRF+F;F+FSF+FOF+FWF+&FE6$F9F*F+FGF+FDF+F+*2FR F+F;F+FSF+FOF+FWF+FfoF+FGF+FKF+F+*2FRF+F;F+FWF+FOF+F\\oF+--&F/6$F+F*F1 F3F+FfoF+FHF+F+*0FRF+F;F+F>F+F?F+FDF+FGF+FOF+F+*0FRF+F;F+F>F+F?F+FKF+F GF+FOF+F+*0FRF+F;F+F>F+FjoF+FKF+FhnF+F7F+F+*2FRF+F;F+F>F+FjoF+FKF+FWF+ FZF+FHF+F+*0FRF+F;F+F>F+FjoF+FOF+FhnF+F\\oF+F+*2FRF+F;F+F>F+FjoF+FOF+F WF+FaoF+FHF+F+*2FRF+F;F+F>F+FjoF+FOF+FWF+FfoF+FHF+F+*0FRF+F;F+F>F+F?F+ FDF+FGF+FKF+F+*.F9F+F;F+--&F/6%F*F*F*F1F3F+FCF+)FHF9F+FOF+F+*.F9F+F;F+ FgpF+FDF+F[qF+FJF+F+*.F9F+F;F+FgpF+FDF+F[qF+FNF+F+*.F9F+F;F+FgpF+FJF+F [qF+FOF+F+*.F9F+F;F+FgpF+FKF+F[qF+FNF+F+*.F9F+F;F+FWF+FKF+--&F/6$F+F+F 1F3F+)F7F*F+F+*.F9F+F;F+FWF+FOF+FaqF+)F\\oF*F+F+*.F9F+F;F+FgpF+FCF+F[q F+FKF+F+*.F9F+F;F+)F>F*F+--&F/6%F+F+F*F1F3F+FDF+FHF+F+*.F9F+F;F+FjqF+F [rF+FKF+FHF+F+*2FRF+F;F+FSF+FKF+FWF+FZF+FGF+FDF+F+*.F9F+F;F+FjqF+F[rF+ FOF+FHF+F+*0F9F+F;F+FWF+FOF+FSF+)FaoF*F+FGF+F+*2FRF+F;F+FWF+FOF+FSF+Fa oF+FGF+FfoF+F+*0F9F+F;F+FWF+FOF+FSF+)FfoF*F+FGF+F+*0FRF+F;F+FOF+)FWF*F +FfoF+FhnF+F7F+F+*0FRF+F;F+FOF+)FWF9F+FfoF+FZF+FHF+F+*2FRF+F;F+FWF+FKF +F7F+FjoF+FZF+FHF+F+*0F9F+F;F+FWF+FKF+)FZF*F+FGF+FSF+F+*2FRF+F;F+FWF+F OF+F\\oF+FjoF+FaoF+FHF+F+*0FRF+F;F+FSF+FNF+FWF+FfoF+FGF+F+*0FRF+F;F+Fg pF+FDF+F[qF+FKF+FOF+F+*2FRF+F;F+FSF+FKF+FhnF+F7F+FDF+FHF+F+*0FRF+F;F+F SF+FJF+FhnF+F7F+FHF+F+*2FRF+F;F+FSF+FKF+FhnF+F7F+FOF+FHF+F+**F;F+FgpF+ )FDF9F+F[qF+F+**F;F+FgpF+)FKF9F+F[qF+F+**F;F+FgpF+)FOF9F+F[qF+F+*2FRF+ &F(F]oF+FSF+FfoF+FWF+FZF+FGF+FaoF+F+*0FRF+F[tF+FSF+FfrF+FWF+FZF+FGF+F+ *2FRF+F[tF+FWF+FfoF+F7F+FjoF+FZF+FHF+F+*0F9F+F[tF+FWF+FfoF+F]sF+FGF+FS F+F+*0FRF+F[tF+F\\oF+F?F+FaoF+FGF+FfoF+F+*0FRF+F[tF+F\\oF+FjoF+FfoF+Fh nF+F7F+F+*2FRF+F[tF+F\\oF+FjoF+FfoF+FWF+FZF+FHF+F+*.F9F+F[tF+FgpF+FaoF +F[qF+FfrF+F+*.F9F+F[tF+FWF+FfoF+FaqF+FeqF+F+*.F9F+F[tF+FgqF+F[rF+FaoF +FHF+F+*.F9F+F[tF+FgqF+F[rF+FfoF+FHF+F+*.F9F+F[tF+F\\oF+F?F+FcrF+FGF+F +*.F9F+F[tF+F\\oF+F?F+FfrF+FGF+F+*.F9F+F[tF+FgpF+FcrF+F[qF+FfoF+F+*0FR F+F[tF+FSF+FfrF+FhnF+F7F+FHF+F+*(F[tF+F,F+)F\\oF9F+F+*2FRF+F[tF+FSF+Ff oF+FhnF+F7F+FaoF+FHF+F+**F[tF+FgpF+)FaoF9F+F[qF+F+**F[tF+FgpF+)FfoF9F+ F[qF+F+*.F9F+F'F+FeqF+F[rF+FZF+FHF+F+*.F9F+F'F+F7F+F]sF+FGF+F?F+F+*(F; F+F,F+)F>F9F+F+**F'F+)FZF9F+F[qF+FgpF+F+" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 24 "# consistencia y orden 1" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 53 "ENcond1a:=coeff(ENFi0,f(x0,y0))=coeff(ENf0,f(x0,y0) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENcond1aG/,*&%\"bG6#\"\"\"F*& F(6#\"\"#F*&F(6#\"\"$F*&F(6#\"\"%F*F*" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones para el orden 2" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 71 "ENcond2a:=coeff(ENFi1,D[1](f)(x0,y0))=coeff((1 /2)*ENf1,D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENcond 2aG/,(*&&%\"bG6#\"\"#\"\"\"&%\"cGF*F,F,*&&F)6#\"\"$F,&F.F1F,F,*&&F)6# \"\"%F,&F.F6F,F,#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "E Ncond2b:=coeff(coeff(ENFi1,D[2](f)(x0,y0)),f(x0,y0))=coeff(coeff((1/2) *ENf1,D[2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% )ENcond2bG/,.*&&%\"bG6#\"\"#\"\"\"&%\"aG6$F+F,F,F,*&&F)6#\"\"$F,&F.6$F 3F,F,F,*&F1F,&F.6$F3F+F,F,*&&F)6#\"\"%F,&F.6$F " 0 "" {MPLTEXT 1 0 75 "ENcond3a:=coeff(ENFi2,D[1,1](f)(x0,y0))=coeff((1/3)*E Nf2,D[1,1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENcond3aG /,(*&&%\"bG6#\"\"$\"\"\")&%\"cGF*\"\"#F,F,*&&F)6#F0F,)&F/F3F0F,F,*&&F) 6#\"\"%F,)&F/F8F0F,F,#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "ENcond3b:=coeff(coeff(ENFi2,D[1,2](f)(x0,y0)),f(x0,y0))=coeff(coe ff((1/3)*ENf2,D[1,2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENcond3bG/,.*(&%\"bG6#\"\"%\"\"\"&%\"cGF*F,&%\"aG6$F +\"\"#F,F2**F2F,F(F,F-F,&F06$F+\"\"$F,F,**F2F,F(F,F-F,&F06$F+F,F,F,**F 2F,&F)6#F2F,&F.F " 0 "" {MPLTEXT 1 0 111 "ENcond3c:=coeff(coeff(ENFi2,D[2,2](f)(x0,y0)),f(x0,y0)^2)=coeff (coeff((1/3)*ENf2,D[2,2](f)(x0,y0)),f(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENcond3cG/,6*&&%\"bG6#\"\"%\"\"\")&%\"aG6$F+\"\"#F1F ,F,*&F(F,)&F/6$F+\"\"$F1F,F,**F1F,&F)6#F6F,&F/6$F6F,F,&F/6$F6F1F,F,**F 1F,F(F,&F/6$F+F,F,F4F,F,**F1F,F(F,F?F,F.F,F,**F1F,F(F,F.F,F4F,F,*&&F)6 #F1F,)&F/6$F1F,F1F,F,*&F(F,)F?F1F,F,*&F8F,)F:F1F,F,*&F8F,)F " 0 "" {MPLTEXT 1 0 115 "ENcond3d:=coeff(coeff (ENFi2,D[2](f)(x0,y0)),D[1](f)(x0,y0))=coeff(coeff((1/3)*ENf2,D[2](f)( x0,y0)),D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENcond3 dG/,(*(&%\"bG6#\"\"$\"\"\"&%\"aG6$F+\"\"#F,&%\"cG6#F0F,F0**F0F,&F)6#\" \"%F,&F.6$F7F0F,F1F,F,**F0F,F5F,&F.6$F7F+F,&F2F*F,F,#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "ENcond3e:=coeff(coeff(ENFi2,D[2](f )(x0,y0)^2),f(x0,y0))=coeff(coeff((1/3)*ENf2,D[2](f)(x0,y0)^2),f(x0,y0 ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENcond3eG/,**(&%\"bG6#\"\"% \"\"\"&%\"aG6$F+\"\"$F,&F.6$F0F,F,\"\"#**F3F,F(F,F-F,&F.6$F0F3F,F,**F3 F,F(F,&F.6$F+F3F,&F.6$F3F,F,F,**F3F,&F)6#F0F,F5F,F:F,F,#F,F0" }}} {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones para el orden 4 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "ENcond4a:=coeff(ENFi3,D [1,1,1](f)(x0,y0))=coeff((1/4)*ENf3,D[1,1,1](f)(x0,y0));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%)ENcond4aG/,(*&&%\"bG6#\"\"$\"\"\")&%\"cGF*F+F ,F,*&&F)6#\"\"%F,)&F/F2F+F,F,*&&F)6#\"\"#F,)&F/F8F+F,F,#F,F3" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "ENcond4b:=coeff(coeff(ENFi3 ,D[1,1,2](f)(x0,y0)),f(x0,y0))=coeff(coeff((1/4)*ENf3,D[1,1,2](f)(x0,y 0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENcond4bG/,.*(&% \"bG6#\"\"$\"\"\")&%\"cGF*\"\"#F,&%\"aG6$F+F,F,F+**F+F,F(F,F-F,&F26$F+ F0F,F,**F+F,&F)6#F0F,)&F/F9F0F,&F26$F0F,F,F,**F+F,&F)6#\"\"%F,)&F/F@F0 F,&F26$FAF,F,F,**F+F,F?F,FBF,&F26$FAF0F,F,**F+F,F?F,FBF,&F26$FAF+F,F,# F+FA" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "ENcond4c:=coeff(co eff(ENFi3,D[1,2,2](f)(x0,y0)),f(x0,y0)^2)=coeff(coeff((1/4)*ENf3,D[1,2 ,2](f)(x0,y0)),f(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENco nd4cG/,6*(&%\"bG6#\"\"%\"\"\"&%\"cGF*F,)&%\"aG6$F+F,\"\"#F,\"\"$**F4F, F(F,F-F,)&F16$F+F3F3F,F,**F4F,F(F,F-F,)&F16$F+F4F3F,F,**F4F,&F)6#F4F,& F.F?F,)&F16$F4F,F3F,F,**F4F,F>F,F@F,)&F16$F4F3F3F,F,**F4F,&F)6#F3F,&F. FJF,)&F16$F3F,F3F,F,*,\"\"'F,F(F,F-F,F0F,F;F,F,*,FPF,F(F,F-F,F7F,F;F,F ,*,FPF,F(F,F-F,F0F,F7F,F,*,FPF,F>F,F@F,FBF,FFF,F,#F4F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 119 "ENcond4d:=coeff(coeff(ENFi3,D[1,2] (f)(x0,y0)),D[1](f)(x0,y0))=coeff(coeff((1/4)*ENf3,D[1,2](f)(x0,y0)),D [1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENcond4dG/,(**&% \"bG6#\"\"%\"\"\"&%\"cGF*F,&%\"aG6$F+\"\"#F,&F.6#F2F,\"\"'*,F5F,F(F,F- F,&F06$F+\"\"$F,&F.6#F9F,F,*,F5F,&F)F;F,F:F,&F06$F9F2F,F3F,F,#F9F+" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 151 "ENcond4e:=coeff(coeff(coef f(ENFi3,D[1,2](f)(x0,y0)),D[2](f)(x0,y0)),f(x0,y0))=coeff(coeff(coeff( (1/4)*ENf3,D[1,2](f)(x0,y0)),D[2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%)ENcond4eG/,2**&%\"bG6#\"\"$\"\"\"&%\"cGF*F,&% \"aG6$F+\"\"#F,&F06$F2F,F,\"\"'*,F5F,&F)6#\"\"%F,&F06$F9F2F,&F.6#F2F,F 3F,F,*,F5F,F7F,&F06$F9F+F,F-F,&F06$F+F,F,F,*,F5F,F(F,F/F,F " 0 "" {MPLTEXT 1 0 115 "ENcond4f:=coeff(coeff(ENFi3,D[2,2,2](f)(x0,y0)),f(x0 ,y0)^3)=coeff(coeff((1/4)*ENf3,D[2,2,2](f)(x0,y0)),f(x0,y0)^3);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%)ENcond4fG/,@*&&%\"bG6#\"\"%\"\"\")& %\"aG6$F+\"\"$F1F,F,*&F(F,)&F/6$F+\"\"#F1F,F,*&F(F,)&F/6$F+F,F1F,F,**F 1F,F(F,)F9F6F,F4F,F,**F1F,F(F,F4F,)F.F6F,F,**F1F,F(F,)F4F6F,F.F,F,**F1 F,F(F,F9F,F>F,F,**F1F,F(F,F9F,F@F,F,**F1F,F(F,F " 0 "" {MPLTEXT 1 0 151 "ENcond4g:=coeff(coeff( coeff(ENFi3,D[2,2](f)(x0,y0)),D[1](f)(x0,y0)),f(x0,y0))=coeff(coeff(co eff((1/4)*ENf3,D[2,2](f)(x0,y0)),D[1](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENcond4gG/,2*(&%\"bG6#\"\"$\"\"\")&%\"aG6 $F+\"\"#F1F,&%\"cG6#F1F,\"\"'*,F5F,F(F,F.F,F2F,&F/6$F+F,F,F,*,F5F,&F)6 #\"\"%F,&F/6$F " 0 "" {MPLTEXT 1 0 155 "ENcond4h:=coeff(coeff(coeff(ENFi3,D[2,2](f)(x0,y0)),D[2](f)(x0, y0)),f(x0,y0)^2)=coeff(coeff(coeff((1/4)*ENf3,D[2,2](f)(x0,y0)),D[2](f )(x0,y0)),f(x0,y0)^2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)ENcond4hG /,B*(&%\"bG6#\"\"%\"\"\")&%\"aG6$F+\"\"#F1F,&F/6$F1F,F,\"\"'*,F4F,F(F, F.F,F2F,&F/6$F+\"\"$F,F,*,F4F,F(F,F6F,&F/6$F8F,F,&F/6$F+F,F,F,*,F4F,F( F,F6F,F:F,F.F,F,**F4F,F(F,)F6F1F,F:F,F,*,F4F,F(F,F6F,&F/6$F8F1F,F " 0 "" {MPLTEXT 1 0 119 " ENcond4i:=coeff(coeff(ENFi3,D[1,1](f)(x0,y0)),D[2](f)(x0,y0))=coeff(co eff((1/4)*ENf3,D[1,1](f)(x0,y0)),D[2](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENcond4iG/,(*(&%\"bG6#\"\"$\"\"\"&%\"aG6$F+\"\"#F,)& %\"cG6#F0F0F,F+**F+F,&F)6#\"\"%F,&F.6$F8F0F,F1F,F,**F+F,F6F,&F.6$F8F+F ,)&F3F*F0F,F,#F,F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 119 "ENco nd4j:=coeff(coeff(ENFi3,D[1](f)(x0,y0)),D[2](f)(x0,y0)^2)=coeff(coeff( (1/4)*ENf3,D[1](f)(x0,y0)),D[2](f)(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENcond4jG/,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F .6$F0\"\"#F,&%\"cG6#F3F,\"\"'#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "ENcond4k:=coeff(coeff(ENFi3,D[2](f)(x0,y0)^3),f(x0,y 0))=coeff(coeff((1/4)*ENf3,D[2](f)(x0,y0)^3),f(x0,y0));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%)ENcond4kG/,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\" \"$F,&F.6$F0\"\"#F,&F.6$F3F,F,\"\"'#F,F+" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 28 "# soluciones para el orden 4" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 154 "#ESsolve44:=solve(\{cond1a,cond2a,cond2b,cond 3a,cond3b,cond3c,cond3d,cond3e,cond4a,cond4b,cond4c,cond4d,cond4e,cond 4f,cond4g,cond4h,cond4i,cond4j,cond4k\}):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 26 "#ESsolve441:=ESsolve44[1];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "#ESsolve442:=ESsolve44[2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "#ESsolve443:=ESsolve44[3];" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 32 "# PARA ECUACIONES AUTONOMAS (EA)" }}} {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 37 "# desarrollo de la verdadera \+ solucion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "y:=unapply(y(x) ,x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=unapply(f(y),y): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "f0:=f(y(x)):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "f1:=subs(diff(y(x),x)=f(y(x) ),diff(f0,x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "f2:=subs( diff(y(x),x)=f(y(x)),diff(f1,x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "f3:=subs(diff(y(x),x)=f(y(x)),diff(f2,x)):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f0:=subs(\{y(x)=y0,x=x0\},f0 ):EAf0:=expand(f0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%EAf0G-%\"fG6 #%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f1:=subs(\{y(x)=y 0,x=x0\},f1):EAf1:=expand(f1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%E Af1G*&--%\"DG6#%\"fG6#%#y0G\"\"\"-F*F+F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f2:=subs(\{y(x)=y0,x=x0\},f2):EAf2:=expand(f2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%EAf2G,&*&---%#@@G6$%\"DG\"\"#6#%\"f G6#%#y0G\"\"\")-F/F0F-F2F2*&)--F,F.F0F-F2F4F2F2" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 45 "f3:=subs(\{y(x)=y0,x=x0\},f3):EAf3:=expand(f3) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%EAf3G,(*&---%#@@G6$%\"DG\"\"$6 #%\"fG6#%#y0G\"\"\")-F/F0F-F2F2**\"\"%F2---F*6$F,\"\"#F.F0F2)F4F;F2--F ,F.F0F2F2*&)F=F-F2F4F2F2" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 23 " # desarrollo del m\351todo" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "k10:=f(y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k20:=f(y+ a[2,1]*h*k10):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "k30:=f(y+ a[3,1]*h*k10+a[3,2]*h*k20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "k40:=f(y+a[4,1]*h*k10+a[4,2]*h*k20+a[4,3]*h*k30):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k100:=subs(h=0,k10):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k200:=subs(h=0,k20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k300:=subs(h=0,k30):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k400:=subs(h=0,k40):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "Fi0:=b[1]*k100+b[2]*k200+b[3]*k300+ b[4]*k400:Fi0:=subs(\{x=x0,y=y0\},Fi0):EAFi0:=expand(Fi0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&EAFi0G,**&&%\"bG6#\"\"\"F*-%\"fG6#%#y0GF* F**&&F(6#\"\"#F*F+F*F**&&F(6#\"\"$F*F+F*F**&&F(6#\"\"%F*F+F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k11:=diff(k10,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k21:=diff(k20,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k31:=diff(k30,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k41:=diff(k40,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k110:=subs(h=0,k11):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k210:=subs(h=0,k21):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k310:=subs(h=0,k31):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k410:=subs(h=0,k41):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "Fi1:=b[1]*k110+b[2]*k210+b[3 ]*k310+b[4]*k410:Fi1:=subs(\{x=x0,y=y0\},Fi1):EAFi1:=expand(Fi1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&EAFi1G,.**&%\"bG6#\"\"#\"\"\"--%\"D G6#%\"fG6#%#y0GF+&%\"aG6$F*F+F+-F0F1F+F+**&F(6#\"\"$F+F,F+&F46$F:F+F+F 6F+F+**F8F+F,F+&F46$F:F*F+F6F+F+**&F(6#\"\"%F+F,F+&F46$FCF+F+F6F+F+**F AF+F,F+&F46$FCF*F+F6F+F+**FAF+F,F+&F46$FCF:F+F6F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k12:=diff(k11,h):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 17 "k22:=diff(k21,h):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 17 "k32:=diff(k31,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k42:=diff(k41,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k120:=subs(h=0,k12):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k220:=subs(h=0,k22):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k320:=subs(h=0,k32):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k420:=subs(h=0,k42):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "Fi2:=b[1]*k120+b[2]*k220+b[3]*k320+b[4]*k420:Fi2:=sub s(\{x=x0,y=y0\},Fi2):EAFi2:=expand(Fi2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&EAFi2G,>**&%\"bG6#\"\"#\"\"\"---%#@@G6$%\"DGF*6#%\"fG6#%#y0GF +)&%\"aG6$F*F+F*F+)-F3F4F*F+F+**&F(6#\"\"$F+F,F+)&F86$F?F+F*F+F:F+F+*. F*F+F=F+F,F+FAF+F:F+&F86$F?F*F+F+**F=F+F,F+)FDF*F+F:F+F+*.F*F+F=F+)--F 1F2F4F*F+FDF+F7F+F;F+F+**&F(6#\"\"%F+F,F+)&F86$FOF+F*F+F:F+F+*.F*F+FMF +F,F+FQF+F:F+&F86$FOF*F+F+*.F*F+FMF+F,F+FQF+F:F+&F86$FOF?F+F+**FMF+F,F +)FTF*F+F:F+F+*.F*F+FMF+F,F+FTF+F:F+FWF+F+**FMF+F,F+)FWF*F+F:F+F+*.F*F +FMF+FTF+FIF+F7F+F;F+F+*.F*F+FMF+FWF+FIF+FAF+F;F+F+*.F*F+FMF+FWF+FIF+F DF+F;F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k13:=diff(k12, h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k23:=diff(k22,h):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k33:=diff(k32,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k43:=diff(k42,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k130:=subs(h=0,k13):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k230:=subs(h=0,k23):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k330:=subs(h=0,k33):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k430:=subs(h=0,k43):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "Fi3:=b[1]*k130+b[2]*k230+b[3 ]*k330+b[4]*k430:Fi3:=subs(\{x=x0,y=y0\},Fi3):EAFi3:=expand(Fi3);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%&EAFi3G,\\o**&%\"bG6#\"\"#\"\"\"---% #@@G6$%\"DG\"\"$6#%\"fG6#%#y0GF+)&%\"aG6$F*F+F2F+)-F4F5F2F+F+**&F(6#F2 F+F,F+)&F96$F2F+F2F+F;F+F+**F>F+F,F+)&F96$F2F*F2F+F;F+F+*.F2F+&F(6#\" \"%F+F,F+)&F96$FJF+F*F+F;F+&F96$FJF2F+F+*.F2F+FHF+F,F+FLF+F;F+)&F96$FJ F*F*F+F+*0\"\"'F+FHF+F,F+FLF+F;F+FRF+FNF+F+*.F2F+FHF+F,F+FLF+F;F+)FNF* F+F+*.F2F+FHF+F,F+FQF+F;F+FNF+F+*.F2F+FHF+F,F+FRF+F;F+FWF+F+*2FUF+FHF+ ---F/6$F1F*F3F5F+FLF+)FF+F,F+FhoF+F;F+FEF+F+*.F2F+F>F+F,F+FAF+F;F+F[pF+F+*2FUF+F> F+FenF+FEF+FjnF+F8F+FinF+FAF+F+*0FUF+F>F+FenF+F[pF+FjnF+F8F+FinF+F+*0F 2F+F>F+FjnF+FEF+FenF+FfoF+FinF+F+" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 24 "# consistencia y orden 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "EAcond1a:=coeff(EAFi0,f(y0))=coeff(EAf0,f(y0));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%)EAcond1aG/,*&%\"bG6#\"\"\"F*&F(6#\" \"#F*&F(6#\"\"$F*&F(6#\"\"%F*F*" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones para el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#EAcond2a" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "EAcond2b:=coeff(coeff(EAFi1,D(f)(y0)),f(y0))=coeff(coeff((1/2)*EAf 1,D(f)(y0)),f(y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)EAcond2bG/,. *&&%\"bG6#\"\"#\"\"\"&%\"aG6$F+F,F,F,*&&F)6#\"\"$F,&F.6$F3F,F,F,*&F1F, &F.6$F3F+F,F,*&&F)6#\"\"%F,&F.6$F " 0 "" {MPLTEXT 1 0 9 "#EAcon d3a" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#EAcond3b" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "EAcond3c:=coeff(coeff(EAFi2,(D@@2)( f)(y0)),f(y0)^2)=coeff(coeff((1/3)*EAf2,(D@@2)(f)(y0)),f(y0)^2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%)EAcond3cG/,6*&&%\"bG6#\"\"%\"\"\")& %\"aG6$F+\"\"#F1F,F,*&F(F,)&F/6$F+\"\"$F1F,F,**F1F,&F)6#F6F,&F/6$F6F,F ,&F/6$F6F1F,F,**F1F,F(F,&F/6$F+F,F,F4F,F,**F1F,F(F,F?F,F.F,F,**F1F,F(F ,F.F,F4F,F,*&&F)6#F1F,)&F/6$F1F,F1F,F,*&F(F,)F?F1F,F,*&F8F,)F:F1F,F,*& F8F,)F " 0 "" {MPLTEXT 1 0 9 "#EAcon d3d" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "EAcond3e:=coeff(coef f(EAFi2,D(f)(y0)^2),f(y0))=coeff(coeff((1/3)*EAf2,D(f)(y0)^2),f(y0)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)EAcond3eG/,**(&%\"bG6#\"\"%\"\" \"&%\"aG6$F+\"\"$F,&F.6$F0F,F,\"\"#**F3F,F(F,F-F,&F.6$F0F3F,F,**F3F,F( F,&F.6$F+F3F,&F.6$F3F,F,F,**F3F,&F)6#F0F,F5F,F:F,F,#F,F0" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones para el orden 4" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#EAcond4a" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#EAcond4b" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#EAcond4c" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#EAcond4d" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#EAcond4e" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "EAcond4f:=coeff(coeff(EAFi3, (D@@3)(f)(y0)),f(y0)^3)=coeff(coeff((1/4)*EAf3,(D@@3)(f)(y0)),f(y0)^3) ;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)EAcond4fG/,@*&&%\"bG6#\"\"%\" \"\")&%\"aG6$F+\"\"$F1F,F,*&F(F,)&F/6$F+\"\"#F1F,F,*&F(F,)&F/6$F+F,F1F ,F,**F1F,F(F,)F9F6F,F4F,F,**F1F,F(F,F4F,)F.F6F,F,**F1F,F(F,)F4F6F,F.F, F,**F1F,F(F,F9F,F>F,F,**F1F,F(F,F9F,F@F,F,**F1F,F(F,F " 0 "" {MPLTEXT 1 0 9 "#EAcond4g" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "EAcond4h:=coeff(coeff(coeff (EAFi3,(D@@2)(f)(y0)),D(f)(y0)),f(y0)^2)=coeff(coeff(coeff((1/4)*EAf3, (D@@2)(f)(y0)),D(f)(y0)),f(y0)^2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6# >%)EAcond4hG/,B*(&%\"bG6#\"\"%\"\"\")&%\"aG6$F+\"\"#F1F,&F/6$F1F,F,\" \"'*,F4F,F(F,F.F,F2F,&F/6$F+\"\"$F,F,*,F4F,F(F,F6F,&F/6$F8F,F,&F/6$F+F ,F,F,*,F4F,F(F,F6F,F:F,F.F,F,**F4F,F(F,)F6F1F,F:F,F,*,F4F,F(F,F6F,&F/6 $F8F1F,F " 0 "" {MPLTEXT 1 0 9 "#EAcond4i" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#EAcond4j" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "EAcond4k:=coe ff(coeff(EAFi3,D(f)(y0)^3),f(y0))=coeff(coeff((1/4)*EAf3,D(f)(y0)^3),f (y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)EAcond4kG/,$**&%\"bG6#\" \"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F.6$F3F,F,\"\"'#F,F+" }}} {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 33 "# PARA SISTEMAS NO AUTONOMOS \+ (SN)" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 37 "# desarrollo de la v erdadera solucion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "y[1]:= unapply(y[1](x),x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "y[2] :=unapply(y[2](x),x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f[ 1]:=unapply(f[1](x,y[1],y[2]),x,y[1],y[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f[2]:=unapply(f[2](x,y[1],y[2]),x,y[1],y[2]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f0[1]:=f[1](x,y[1](x),y[2](x )):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f0[2]:=f[2](x,y[1](x ),y[2](x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "f1[1]:=subs (\{diff(y[1](x),x)=f[1](x,y[1](x),y[2](x)),diff(y[2](x),x)=f[2](x,y[1] (x),y[2](x))\},diff(f0[1],x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "f1[2]:=subs(\{diff(y[1](x),x)=f[1](x,y[1](x),y[2](x)),diff(y[ 2](x),x)=f[2](x,y[1](x),y[2](x))\},diff(f0[2],x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "f2[1]:=subs(\{diff(y[1](x),x)=f[1](x,y[1]( x),y[2](x)),diff(y[2](x),x)=f[2](x,y[1](x),y[2](x))\},diff(f1[1],x)): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "f2[2]:=subs(\{diff(y[1 ](x),x)=f[1](x,y[1](x),y[2](x)),diff(y[2](x),x)=f[2](x,y[1](x),y[2](x) )\},diff(f1[2],x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "f3[ 1]:=subs(\{diff(y[1](x),x)=f[1](x,y[1](x),y[2](x)),diff(y[2](x),x)=f[2 ](x,y[1](x),y[2](x))\},diff(f2[1],x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "f3[2]:=subs(\{diff(y[1](x),x)=f[1](x,y[1](x),y[2](x) ),diff(y[2](x),x)=f[2](x,y[1](x),y[2](x))\},diff(f2[2],x)):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f0[1]:=subs(\{y[1](x)=y0[1], y[2](x)=y0[2],x=x0\},f0[1]):SNf0[1]:=expand(f0[1]);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>&%%SNf0G6#\"\"\"-&%\"fGF&6%%#x0G&%#y0GF&&F.6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f0[2]:=subs(\{y[1](x)=y0[ 1],y[2](x)=y0[2],x=x0\},f0[2]):SNf0[2]:=expand(f0[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f1[1]:=subs(\{y[1](x)=y0[1],y[2](x) =y0[2],x=x0\},f1[1]):SNf1[1]:=expand(f1[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%SNf1G6#\"\"\",(--&%\"DGF&6#&%\"fGF&6%%#x0G&%#y0GF&& F36#\"\"#F'*&--&F,F5F-F0F'-F.F0F'F'*&--&F,6#\"\"$F-F0F'-&F/F5F0F'F'" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f1[2]:=subs(\{y[1](x)=y0[1 ],y[2](x)=y0[2],x=x0\},f1[2]):SNf1[2]:=expand(f1[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f2[1]:=subs(\{y[1](x)=y0[1],y[2](x) =y0[2],x=x0\},f2[1]):SNf2[1]:=expand(f2[1]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%%SNf2G6#\"\"\",:--&%\"DG6$F'F'6#&%\"fGF&6%%#x0G&%#y0 GF&&F46#\"\"#F'*(F7F'--&F,6$F'F7F.F1F'-F/F1F'F'*(F7F'--&F,6$F'\"\"$F.F 1F'-&F0F6F1F'F'*&--&F,6$F7F7F.F1F')F=F7F'F'**F7F'F=F'--&F,6$F7FCF.F1F' FDF'F'*&--&F,F6F.F1F'--&F,F&F.F1F'F'*&)FRF7F'F=F'F'*(FRF'--&F,6#FCF.F1 F'FDF'F'*&--&F,6$FCFCF.F1F')FDF7F'F'*&FenF'--FW6#FEF1F'F'*(FenF'--FTFb oF1F'F=F'F'*(FenF'--FgnFboF1F'FDF'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f2[2]:=subs(\{y[1](x)=y0[1],y[2](x)=y0[2],x=x0\},f2[2 ]):SNf2[2]:=expand(f2[2]):" 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]dlF'FBF'FgrF'FJF'F`wF'F'*.F@F'F]dlF'F^tF'F`dlF'FUF'F`qF'F'*.F@F'F]dlF 'F^tF'F^dlF'FUF'F`qF'F'*.F@F'F]dlF'FgsF'FaoF'Ff[lF'F[[lF'F'*0FhnF'F]dl F'FitF'F`wF'F^vF'F`vF'FKF'F'*0F]tF'F]dlF'F^tF'FgrF'FUF'F`wF'F`qF'F'*0F ]tF'F]dlF'FctF'F`wF'FjoF'FgrF'FKF'F'*2FhnF'F]dlF'FitF'FaoF'F^vF'F`vF'F grF'FKF'F'*4FhnF'F]dlF'FfoF'FaoF'FarF'FcrF'FUF'FgrF'FKF'F'*2FhnF'F]dlF 'FfoF'F`wF'FarF'FcrF'FUF'FKF'F'*0F@F'F]dlF'FgsF'FaoF'FhxF'FjoF'FinF'F' *2FhnF'F]dlF'FgsF'FaoF'F`vF'FbsF'FcrF'FKF'F'*2FhnF'F]dlF'FgsF'FaoF'F`v F'FgqF'FcrF'FUF'F'*0F@F'F]dlF'FgsF'FaoF'FhxF'F`qF'FitF'F'*2FhnF'F]dlF' FgsF'FaoF'FhxF'FKF'FfoF'FUF'F'*4FhnF'F]dlF'FitF'FaoF'F[pF'FcrF'FUF'Fgr F'FKF'F'*0F]tF'F]dlF'FctF'FjvF'FjoF'FaoF'FKF'F'*2FhnF'F]dlF'FfoF'FaoF' F[rF'F`vF'FgrF'FKF'F'*0FhnF'F]dlF'FfoF'F`wF'F[rF'F`vF'FKF'F'*2FhnF'F]d lF'FfoF'FaoF'F]oF'FcrF'F`qF'FgrF'F'*0FhnF'F]dlF'FfoF'F`wF'F]oF'FcrF'F` qF'F'*2FhnF'F]dlF'FitF'FaoF'FgsF'FcrF'F`qF'FgrF'F'*0FhnF'F]dlF'F^rF'Fg qF'FaoF'F[rF'F`vF'F'*2FhnF'F]dlF'F^rF'FbsF'FaoF'F[pF'FcrF'FUF'F'*2F[sF 'F]dlF'F^rF'F\\sF'FgrF'FUF'FaoF'FKF'F'*2FhnF'F]dlF'F^rF'FgqF'FaoF'F]oF 'FcrF'FKF'F'*2FhnF'F]dlF'F^rF'FgqF'FaoF'FarF'FcrF'FUF'F'*0FhnF'F]dlF'F itF'F`wF'FgsF'FcrF'F`qF'F'*.F@F'F]dlF'F][lF'FablF'FgrF'FUF'F'*.F@F'F]d lF'F^rF'F\\qF'F`wF'F`qF'F'*.F@F'F]dlF'F^rF'F\\qF'FjvF'F`qF'F'*.F@F'F]d lF'F^rF'FfpF'F`wF'FjoF'F'*.F@F'F]dlF'F^rF'FfpF'FjvF'FjoF'F'*0F]tF'F]dl F'F^tF'FjvF'FUF'FaoF'F`qF'F'*.F@F'F]dlF'F][lF'FablF'FaoF'FUF'F'*.F@F'F ]dlF'F][lF'FapF'FgrF'FKF'F'*2FhnF'F]dlF'FitF'F`wF'F[pF'FcrF'FUF'FKF'F' *.F@F'F]dlF'F][lF'FapF'FaoF'FKF'F'*2FhnF'F]dlF'F^rF'FbsF'FaoF'FgsF'Fcr F'FKF'F'*0FhnF'F]dlF'F^rF'FbsF'FaoF'F^vF'F`vF'F'*0FhnF'F]dlF'F^rF'F\\s F'F`wF'FUF'FKF'F'*0FhnF'F]dlF'F^rF'F\\qF'FgrF'F`qF'FaoF'F'*0FhnF'F]dlF 'F^rF'F\\sF'FjvF'FUF'FKF'F'*0FhnF'F]dlF'F^rF'FfpF'FgrF'FjoF'FaoF'F'*.F @F'F]dlF'FctF'F`dlF'FjoF'FKF'F'*(F]dlF'F.F')F^rF@F'F'*(Ff\\lF'F.F')F`v F@F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "Fi3[2]:=b[1]*k13 0[2]+b[2]*k230[2]+b[3]*k330[2]+b[4]*k430[2]:Fi3[2]:=subs(\{x=x0,y[1]=y 0[1],y[2]=y0[2]\},Fi3[2]):SNFi3[1]:=expand(Fi3[1]):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 24 "# consistencia y orden 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "SNcond1a:=coeff(SNFi0[1],f[1](x0,y0[1],y0 [2]))=coeff(SNf0[1],f[1](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)SNcond1aG/,*&%\"bG6#\"\"\"F*&F(6#\"\"#F*&F(6#\"\"$F* &F(6#\"\"%F*F*" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condicio nes para el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "SNc ond2a:=coeff(SNFi1[1],D[1](f[1])(x0,y0[1],y0[2]))=coeff((1/2)*SNf1[1], D[1](f[1])(x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)SNc ond2aG/,(*&&%\"bG6#\"\"#\"\"\"&%\"cGF*F,F,*&&F)6#\"\"$F,&F.F1F,F,*&&F) 6#\"\"%F,&F.F6F,F,#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 158 "SNcond2b1:=coeff(coeff(SNFi1[1],D[2](f[1])(x0,y0[1],y0[2])),f[1](x0,y 0[1],y0[2]))=coeff(coeff((1/2)*SNf1[1],D[2](f[1])(x0,y0[1],y0[2])),f[1 ](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond2b1G/, .*&&%\"bG6#\"\"#\"\"\"&%\"aG6$F+F,F,F,*&&F)6#\"\"$F,&F.6$F3F,F,F,*&F1F ,&F.6$F3F+F,F,*&&F)6#\"\"%F,&F.6$F " 0 "" {MPLTEXT 1 0 158 "SNcond2b 2:=coeff(coeff(SNFi1[1],D[3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2 ]))=coeff(coeff((1/2)*SNf1[1],D[3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1 ],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond2b2G/,.*&&%\"bG 6#\"\"#\"\"\"&%\"aG6$F+F,F,F,*&&F)6#\"\"$F,&F.6$F3F,F,F,*&F1F,&F.6$F3F +F,F,*&&F)6#\"\"%F,&F.6$F " 0 "" {MPLTEXT 1 0 105 "SNcond3a:=co eff(SNFi2[1],D[1,1](f[1])(x0,y0[1],y0[2]))=coeff((1/3)*SNf2[1],D[1,1]( f[1])(x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)SNcond3a G/,(*&&%\"bG6#\"\"$\"\"\")&%\"cGF*\"\"#F,F,*&&F)6#F0F,)&F/F3F0F,F,*&&F )6#\"\"%F,)&F/F8F0F,F,#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 162 "SNcond3b1:=coeff(coeff(SNFi2[1],D[1,2](f[1])(x0,y0[1],y0[2])),f[1 ](x0,y0[1],y0[2]))=coeff(coeff((1/3)*SNf2[1],D[1,2](f[1])(x0,y0[1],y0[ 2])),f[1](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNco nd3b1G/,.*(&%\"bG6#\"\"%\"\"\"&%\"cGF*F,&%\"aG6$F+\"\"#F,F2**F2F,F(F,F -F,&F06$F+\"\"$F,F,**F2F,F(F,F-F,&F06$F+F,F,F,**F2F,&F)6#F2F,&F.F " 0 "" {MPLTEXT 1 0 162 "SNcond3b2:=coe ff(coeff(SNFi2[1],D[1,3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]))= coeff(coeff((1/3)*SNf2[1],D[1,3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1], y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond3b2G/,.*(&%\"bG6# \"\"%\"\"\"&%\"cGF*F,&%\"aG6$F+\"\"#F,F2**F2F,F(F,F-F,&F06$F+\"\"$F,F, **F2F,F(F,F-F,&F06$F+F,F,F,**F2F,&F)6#F2F,&F.F " 0 "" {MPLTEXT 1 0 166 "SNcond3c1:=coeff(coeff(SNFi 2[1],D[2,2](f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2])^2)=coeff(coeff ((1/3)*SNf2[1],D[2,2](f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2])^2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond3c1G/,6*&&%\"bG6#\"\"%\" \"\")&%\"aG6$F+\"\"#F1F,F,*&F(F,)&F/6$F+\"\"$F1F,F,**F1F,&F)6#F6F,&F/6 $F6F,F,&F/6$F6F1F,F,**F1F,F(F,&F/6$F+F,F,F4F,F,**F1F,F(F,F?F,F.F,F,**F 1F,F(F,F.F,F4F,F,*&&F)6#F1F,)&F/6$F1F,F1F,F,*&F(F,)F?F1F,F,*&F8F,)F:F1 F,F,*&F8F,)F " 0 "" {MPLTEXT 1 0 166 "SNcond3c2:=coeff(coeff(SNFi2[1],D[3,3](f[1])(x0,y0[1],y0[2])),f[2 ](x0,y0[1],y0[2])^2)=coeff(coeff((1/3)*SNf2[1],D[3,3](f[1])(x0,y0[1],y 0[2])),f[2](x0,y0[1],y0[2])^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%* SNcond3c2G/,6*&&%\"bG6#\"\"%\"\"\")&%\"aG6$F+\"\"#F1F,F,*&F(F,)&F/6$F+ \"\"$F1F,F,**F1F,&F)6#F6F,&F/6$F6F,F,&F/6$F6F1F,F,**F1F,F(F,&F/6$F+F,F ,F4F,F,**F1F,F(F,F?F,F.F,F,**F1F,F(F,F.F,F4F,F,*&&F)6#F1F,)&F/6$F1F,F1 F,F,*&F(F,)F?F1F,F,*&F8F,)F:F1F,F,*&F8F,)F " 0 "" {MPLTEXT 1 0 218 "SNcond3c3:=coeff(coeff(coeff(SNFi2 [1],D[2,3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2])),f[1](x0,y0[1], y0[2]))=coeff(coeff(coeff((1/3)*SNf2[1],D[2,3](f[1])(x0,y0[1],y0[2])), f[2](x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond3c3G/,6*(&%\"bG6#\"\"%\"\"\"&%\"aG6$F+F,F,&F.6 $F+\"\"$F,F+**F+F,F(F,&F.6$F+\"\"#F,F0F,F,*(F6F,&F)6#F2F,)&F.6$F2F6F6F ,F,**F+F,F(F,F-F,F4F,F,*(F6F,F8F,)&F.6$F2F,F6F,F,*(F6F,F(F,)F-F6F,F,*( F6F,F(F,)F4F6F,F,*(F6F,F(F,)F0F6F,F,**F+F,F8F,F@F,F;F,F,*(F6F,&F)6#F6F ,)&F.6$F6F,F6F,F,#F6F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 170 " SNcond3d1:=coeff(coeff(SNFi2[1],D[2](f[1])(x0,y0[1],y0[2])),D[1](f[1]) (x0,y0[1],y0[2]))=coeff(coeff((1/3)*SNf2[1],D[2](f[1])(x0,y0[1],y0[2]) ),D[1](f[1])(x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*S Ncond3d1G/,(*(&%\"bG6#\"\"$\"\"\"&%\"aG6$F+\"\"#F,&%\"cG6#F0F,F0**F0F, &F)6#\"\"%F,&F.6$F7F0F,F1F,F,**F0F,F5F,&F.6$F7F+F,&F2F*F,F,#F,F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 170 "SNcond3d2:=coeff(coeff(SNFi 2[1],D[3](f[1])(x0,y0[1],y0[2])),D[1](f[2])(x0,y0[1],y0[2]))=coeff(coe ff((1/3)*SNf2[1],D[3](f[1])(x0,y0[1],y0[2])),D[1](f[2])(x0,y0[1],y0[2] ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond3d2G/,(*(&%\"bG6#\"\"$ \"\"\"&%\"aG6$F+\"\"#F,&%\"cG6#F0F,F0**F0F,&F)6#\"\"%F,&F.6$F7F0F,F1F, F,**F0F,F5F,&F.6$F7F+F,&F2F*F,F,#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 162 "SNcond3e1:=coeff(coeff(SNFi2[1],D[2](f[1])(x0,y0[1], y0[2])^2),f[1](x0,y0[1],y0[2]))=coeff(coeff((1/3)*SNf2[1],D[2](f[1])(x 0,y0[1],y0[2])^2),f[1](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond3e1G/,**(&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0F,F ,\"\"#**F3F,F(F,F-F,&F.6$F0F3F,F,**F3F,F(F,&F.6$F+F3F,&F.6$F3F,F,F,**F 3F,&F)6#F0F,F5F,F:F,F,#F,F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 226 "SNcond3e2:=coeff(coeff(coeff(SNFi2[1],D[2](f[1])(x0,y0[1],y0[2])) ,D[3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]))=coeff(coeff(coeff(( 1/3)*SNf2[1],D[2](f[1])(x0,y0[1],y0[2])),D[3](f[1])(x0,y0[1],y0[2])),f [2](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond3e2G /,**(&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0F,F,\"\"#**F3F,F(F,F-F ,&F.6$F0F3F,F,**F3F,F(F,&F.6$F+F3F,&F.6$F3F,F,F,**F3F,&F)6#F0F,F5F,F:F ,F,#F,F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 226 "SNcond3e3:=coe ff(coeff(coeff(SNFi2[1],D[3](f[1])(x0,y0[1],y0[2])),D[2](f[2])(x0,y0[1 ],y0[2])),f[1](x0,y0[1],y0[2]))=coeff(coeff(coeff((1/3)*SNf2[1],D[3](f [1])(x0,y0[1],y0[2])),D[2](f[2])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond3e3G/,**(&%\"bG6#\"\"% \"\"\"&%\"aG6$F+\"\"$F,&F.6$F0F,F,\"\"#**F3F,F(F,F-F,&F.6$F0F3F,F,**F3 F,F(F,&F.6$F+F3F,&F.6$F3F,F,F,**F3F,&F)6#F0F,F5F,F:F,F,#F,F0" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 226 "SNcond3e4:=coeff(coeff(coef f(SNFi2[1],D[3](f[1])(x0,y0[1],y0[2])),D[3](f[2])(x0,y0[1],y0[2])),f[2 ](x0,y0[1],y0[2]))=coeff(coeff(coeff((1/3)*SNf2[1],D[3](f[1])(x0,y0[1] ,y0[2])),D[3](f[2])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond3e4G/,**(&%\"bG6#\"\"%\"\"\"&%\"aG6 $F+\"\"$F,&F.6$F0F,F,\"\"#**F3F,F(F,F-F,&F.6$F0F3F,F,**F3F,F(F,&F.6$F+ F3F,&F.6$F3F,F,F,**F3F,&F)6#F0F,F5F,F:F,F,#F,F0" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones para el orden 4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "SNcond4a:=coeff(SNFi3[1],D[1,1,1](f[1])( x0,y0[1],y0[2]))=coeff((1/4)*SNf3[1],D[1,1,1](f[1])(x0,y0[1],y0[2])); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)SNcond4aG/,(*&&%\"bG6#\"\"$\"\" \")&%\"cGF*F+F,F,*&&F)6#\"\"%F,)&F/F2F+F,F,*&&F)6#\"\"#F,)&F/F8F+F,F,# F,F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 166 "SNcond4b1:=coeff(c oeff(SNFi3[1],D[1,1,2](f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]))=co eff(coeff((1/4)*SNf3[1],D[1,1,2](f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1], y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4b1G/,.*(&%\"bG6# \"\"$\"\"\")&%\"cGF*\"\"#F,&%\"aG6$F+F,F,F+**F+F,F(F,F-F,&F26$F+F0F,F, **F+F,&F)6#F0F,)&F/F9F0F,&F26$F0F,F,F,**F+F,&F)6#\"\"%F,)&F/F@F0F,&F26 $FAF,F,F,**F+F,F?F,FBF,&F26$FAF0F,F,**F+F,F?F,FBF,&F26$FAF+F,F,#F+FA" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 166 "SNcond4b2:=coeff(coeff(S NFi3[1],D[1,1,3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]))=coeff(co eff((1/4)*SNf3[1],D[1,1,3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4b2G/,.*(&%\"bG6#\"\"$ \"\"\")&%\"cGF*\"\"#F,&%\"aG6$F+F,F,F+**F+F,F(F,F-F,&F26$F+F0F,F,**F+F ,&F)6#F0F,)&F/F9F0F,&F26$F0F,F,F,**F+F,&F)6#\"\"%F,)&F/F@F0F,&F26$FAF, F,F,**F+F,F?F,FBF,&F26$FAF0F,F,**F+F,F?F,FBF,&F26$FAF+F,F,#F+FA" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 170 "SNcond4c1:=coeff(coeff(SNFi 3[1],D[1,2,2](f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2])^2)=coeff(coe ff((1/4)*SNf3[1],D[1,2,2](f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2])^ 2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4c1G/,6*(&%\"bG6#\"\"% \"\"\"&%\"cGF*F,)&%\"aG6$F+F,\"\"#F,\"\"$**F4F,F(F,F-F,)&F16$F+F3F3F,F ,**F4F,F(F,F-F,)&F16$F+F4F3F,F,**F4F,&F)6#F4F,&F.F?F,)&F16$F4F,F3F,F,* *F4F,F>F,F@F,)&F16$F4F3F3F,F,**F4F,&F)6#F3F,&F.FJF,)&F16$F3F,F3F,F,*, \"\"'F,F(F,F-F,F0F,F;F,F,*,FPF,F(F,F-F,F7F,F;F,F,*,FPF,F(F,F-F,F0F,F7F ,F,*,FPF,F>F,F@F,FBF,FFF,F,#F4F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 222 "SNcond4c2:=coeff(coeff(coeff(SNFi3[1],D[1,2,3](f[1]) (x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]))=coeff(co eff(coeff((1/4)*SNf3[1],D[1,2,3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1], y0[2])),f[1](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*S Ncond4c2G/,6**&%\"bG6#\"\"%\"\"\"&%\"cGF*F,&%\"aG6$F+F,F,&F06$F+\"\"$F ,\"#7*,F5F,F(F,F-F,&F06$F+\"\"#F,F2F,F,**\"\"'F,F(F,F-F,)F7F9F,F,**F;F ,F(F,F-F,)F/F9F,F,**F;F,&F)6#F9F,&F.FAF,)&F06$F9F,F9F,F,**F;F,F(F,F-F, )F2F9F,F,*,F5F,F(F,F-F,F/F,F7F,F,**F;F,&F)6#F4F,&F.FKF,)&F06$F4F9F9F,F ,*,F5F,FJF,FLF,&F06$F4F,F,FNF,F,**F;F,FJF,FLF,)FQF9F,F,#F4F9" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 170 "SNcond4c3:=coeff(coeff(SNFi 3[1],D[1,3,3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2])^2)=coeff(coe ff((1/4)*SNf3[1],D[1,3,3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2])^ 2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4c3G/,6*(&%\"bG6#\"\"% \"\"\"&%\"cGF*F,)&%\"aG6$F+F,\"\"#F,\"\"$**F4F,F(F,F-F,)&F16$F+F3F3F,F ,**F4F,F(F,F-F,)&F16$F+F4F3F,F,**F4F,&F)6#F4F,&F.F?F,)&F16$F4F,F3F,F,* *F4F,F>F,F@F,)&F16$F4F3F3F,F,**F4F,&F)6#F3F,&F.FJF,)&F16$F3F,F3F,F,*, \"\"'F,F(F,F-F,F0F,F;F,F,*,FPF,F(F,F-F,F7F,F;F,F,*,FPF,F(F,F-F,F0F,F7F ,F,*,FPF,F>F,F@F,FBF,FFF,F,#F4F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 174 "SNcond4d1:=coeff(coeff(SNFi3[1],D[1,2](f[1])(x0,y0[1 ],y0[2])),D[1](f[1])(x0,y0[1],y0[2]))=coeff(coeff((1/4)*SNf3[1],D[1,2] (f[1])(x0,y0[1],y0[2])),D[1](f[1])(x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4d1G/,(**&%\"bG6#\"\"%\"\"\"&%\"cGF*F,&%\"a G6$F+\"\"#F,&F.6#F2F,\"\"'*,F5F,F(F,F-F,&F06$F+\"\"$F,&F.6#F9F,F,*,F5F ,&F)F;F,F:F,&F06$F9F2F,F3F,F,#F9F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 174 "SNcond4d2:=coeff(coeff(SNFi3[1],D[1,3](f[1])(x0,y0[1 ],y0[2])),D[1](f[2])(x0,y0[1],y0[2]))=coeff(coeff((1/4)*SNf3[1],D[1,3] (f[1])(x0,y0[1],y0[2])),D[1](f[2])(x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4d2G/,(**&%\"bG6#\"\"%\"\"\"&%\"cGF*F,&%\"a G6$F+\"\"#F,&F.6#F2F,\"\"'*,F5F,F(F,F-F,&F06$F+\"\"$F,&F.6#F9F,F,*,F5F ,&F)F;F,F:F,&F06$F9F2F,F3F,F,#F9F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 230 "SNcond4e1:=coeff(coeff(coeff(SNFi3[1],D[1,2](f[1])(x 0,y0[1],y0[2])),D[2](f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]))=coef f(coeff(coeff((1/4)*SNf3[1],D[1,2](f[1])(x0,y0[1],y0[2])),D[2](f[1])(x 0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4e1G/,2**&%\"bG6#\"\"$\"\"\"&%\"cGF*F,&%\"aG6$F+\"\"#F, &F06$F2F,F,\"\"'*,F5F,&F)6#\"\"%F,&F06$F9F2F,&F.6#F2F,F3F,F,*,F5F,F7F, &F06$F9F+F,F-F,&F06$F+F,F,F,*,F5F,F(F,F/F,F " 0 "" {MPLTEXT 1 0 230 "SNc ond4e2:=coeff(coeff(coeff(SNFi3[1],D[1,2](f[1])(x0,y0[1],y0[2])),D[3]( f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]))=coeff(coeff(coeff((1/4)*S Nf3[1],D[1,2](f[1])(x0,y0[1],y0[2])),D[3](f[1])(x0,y0[1],y0[2])),f[2]( x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4e2G/,** *&%\"bG6#\"\"$\"\"\"&%\"cGF*F,&%\"aG6$F+\"\"#F,&F06$F2F,F,\"\"'*,F5F,& F)6#\"\"%F,&F.F8F,&F06$F9F+F,&F06$F+F,F,F,*,F5F,F7F,F:F,F;F,F/F,F,*,F5 F,F7F,F:F,&F06$F9F2F,F3F,F,#F+F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 230 "SNcond4e3:=coeff(coeff(coeff(SNFi3[1],D[1,2](f[2])(x 0,y0[1],y0[2])),D[3](f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]))=coef f(coeff(coeff((1/4)*SNf3[1],D[1,2](f[2])(x0,y0[1],y0[2])),D[3](f[1])(x 0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4e3G/,***&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"#F,&%\"cG6#F0 F,&F.6$F0F,F,\"\"'*,F6F,&F)6#\"\"$F,&F.6$F:F0F,F1F,F4F,F,*,F6F,F(F,&F. 6$F+F:F,&F2F9F,F;F,F,*,F6F,F(F,F>F,F@F,&F.6$F:F,F,F,#F,F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 230 "SNcond4e4:=coeff(coeff(coeff(SNFi3 [1],D[1,3](f[1])(x0,y0[1],y0[2])),D[2](f[1])(x0,y0[1],y0[2])),f[2](x0, y0[1],y0[2]))=coeff(coeff(coeff((1/4)*SNf3[1],D[1,3](f[1])(x0,y0[1],y0 [2])),D[2](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%*SNcond4e4G/,***&%\"bG6#\"\"%\"\"\"&%\"aG6$F+ \"\"#F,&%\"cG6#F0F,&F.6$F0F,F,\"\"'*,F6F,&F)6#\"\"$F,&F.6$F:F0F,F1F,F4 F,F,*,F6F,F(F,&F.6$F+F:F,&F2F9F,F;F,F,*,F6F,F(F,F>F,F@F,&F.6$F:F,F,F,# F,F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 230 "SNcond4e5:=coeff(c oeff(coeff(SNFi3[1],D[1,3](f[1])(x0,y0[1],y0[2])),D[2](f[2])(x0,y0[1], y0[2])),f[1](x0,y0[1],y0[2]))=coeff(coeff(coeff((1/4)*SNf3[1],D[1,3](f [1])(x0,y0[1],y0[2])),D[2](f[2])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4e5G/,***&%\"bG6#\"\"$ \"\"\"&%\"cGF*F,&%\"aG6$F+\"\"#F,&F06$F2F,F,\"\"'*,F5F,&F)6#\"\"%F,&F. F8F,&F06$F9F+F,&F06$F+F,F,F,*,F5F,F7F,F:F,F;F,F/F,F,*,F5F,F7F,F:F,&F06 $F9F2F,F3F,F,#F+F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 230 "SNco nd4e6:=coeff(coeff(coeff(SNFi3[1],D[1,3](f[1])(x0,y0[1],y0[2])),D[3](f [2])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]))=coeff(coeff(coeff((1/4)*SN f3[1],D[1,3](f[1])(x0,y0[1],y0[2])),D[3](f[2])(x0,y0[1],y0[2])),f[2](x 0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4e6G/,*** &%\"bG6#\"\"$\"\"\"&%\"cGF*F,&%\"aG6$F+\"\"#F,&F06$F2F,F,\"\"'*,F5F,&F )6#\"\"%F,&F.F8F,&F06$F9F+F,&F06$F+F,F,F,*,F5F,F7F,F:F,F;F,F/F,F,*,F5F ,F7F,F:F,&F06$F9F2F,F3F,F,#F+F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 230 "SNcond4e7:=coeff(coeff(coeff(SNFi3[1],D[1,3](f[2])(x0,y0[1],y 0[2])),D[3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]))=coeff(coeff(c oeff((1/4)*SNf3[1],D[1,3](f[2])(x0,y0[1],y0[2])),D[3](f[1])(x0,y0[1],y 0[2])),f[2](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SN cond4e7G/,***&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"#F,&%\"cG6#F0F,&F.6$F0F, F,\"\"'*,F6F,&F)6#\"\"$F,&F.6$F:F0F,F1F,F4F,F,*,F6F,F(F,&F.6$F+F:F,&F2 F9F,F;F,F,*,F6F,F(F,F>F,F@F,&F.6$F:F,F,F,#F,F0" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 170 "SNcond4f1:=coeff(coeff(SNFi3[1],D[2,2,2](f[1] )(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2])^3)=coeff(coeff((1/4)*SNf3[1],D [2,2,2](f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2])^3);" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#>%*SNcond4f1G/,@*&&%\"bG6#\"\"%\"\"\")&%\"aG6$F+ \"\"$F1F,F,*&F(F,)&F/6$F+\"\"#F1F,F,*&F(F,)&F/6$F+F,F1F,F,**F1F,F(F,)F 9F6F,F4F,F,**F1F,F(F,F4F,)F.F6F,F,**F1F,F(F,)F4F6F,F.F,F,**F1F,F(F,F9F ,F>F,F,**F1F,F(F,F9F,F@F,F,**F1F,F(F,F " 0 "" {MPLTEXT 1 0 226 "SNcond4f2:=coeff(coeff(coef f(SNFi3[1],D[2,2,3](f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2])^2),f[2 ](x0,y0[1],y0[2]))=coeff(coeff(coeff((1/4)*SNf3[1],D[2,2,3](f[1])(x0,y 0[1],y0[2])),f[1](x0,y0[1],y0[2])^2),f[2](x0,y0[1],y0[2]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SNcond4f2G/,@*(&%\"bG6#\"\"%\"\"\")&%\"aG 6$F+F,\"\"#F,&F/6$F+F1F,\"\"**,\"#=F,F(F,F.F,F2F,&F/6$F+\"\"$F,F,**F4F ,F(F,F2F,)F7F1F,F,**F4F,F(F,)F2F1F,F7F,F,*(F9F,F(F,)F2F9F,F,*(F9F,F(F, )F.F9F,F,**F4F,F(F,F-F,F7F,F,**F4F,F(F,F.F,F;F,F,**F4F,&F)6#F9F,)&F/6$ F9F,F1F,&F/6$F9F1F,F,*(F9F,&F)6#F1F,)&F/6$F1F,F9F,F,*(F9F,FEF,)FHF9F,F ,*(F9F,FEF,)FJF9F,F,**F4F,FEF,FHF,)FJF1F,F,**F4F,F(F,F.F,F=F,F,*(F9F,F (F,)F7F9F,F,#F9F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 226 "SNcon d4f3:=coeff(coeff(coeff(SNFi3[1],D[2,3,3](f[1])(x0,y0[1],y0[2])),f[2]( x0,y0[1],y0[2])^2),f[1](x0,y0[1],y0[2]))=coeff(coeff(coeff((1/4)*SNf3[ 1],D[2,3,3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2])^2),f[1](x0,y0[ 1],y0[2]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SNcond4f3G/,@*(&%\"b G6#\"\"%\"\"\")&%\"aG6$F+F,\"\"#F,&F/6$F+F1F,\"\"**,\"#=F,F(F,F.F,F2F, &F/6$F+\"\"$F,F,**F4F,F(F,F2F,)F7F1F,F,**F4F,F(F,)F2F1F,F7F,F,*(F9F,F( F,)F2F9F,F,*(F9F,F(F,)F.F9F,F,**F4F,F(F,F-F,F7F,F,**F4F,F(F,F.F,F;F,F, **F4F,&F)6#F9F,)&F/6$F9F,F1F,&F/6$F9F1F,F,*(F9F,&F)6#F1F,)&F/6$F1F,F9F ,F,*(F9F,FEF,)FHF9F,F,*(F9F,FEF,)FJF9F,F,**F4F,FEF,FHF,)FJF1F,F,**F4F, F(F,F.F,F=F,F,*(F9F,F(F,)F7F9F,F,#F9F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 170 "SNcond4f4:=coeff(coeff(SNFi3[1],D[3,3,3](f[1])(x0,y0 [1],y0[2])),f[2](x0,y0[1],y0[2])^3)=coeff(coeff((1/4)*SNf3[1],D[3,3,3] (f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2])^3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SNcond4f4G/,@*&&%\"bG6#\"\"%\"\"\")&%\"aG6$F+\"\"$F1 F,F,*&F(F,)&F/6$F+\"\"#F1F,F,*&F(F,)&F/6$F+F,F1F,F,**F1F,F(F,)F9F6F,F4 F,F,**F1F,F(F,F4F,)F.F6F,F,**F1F,F(F,)F4F6F,F.F,F,**F1F,F(F,F9F,F>F,F, **F1F,F(F,F9F,F@F,F,**F1F,F(F,F " 0 "" {MPLTEXT 1 0 230 "SNcond4g1:=coeff(coeff(coeff(SNFi3 [1],D[2,2](f[1])(x0,y0[1],y0[2])),D[1](f[1])(x0,y0[1],y0[2])),f[1](x0, y0[1],y0[2]))=coeff(coeff(coeff((1/4)*SNf3[1],D[2,2](f[1])(x0,y0[1],y0 [2])),D[1](f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%*SNcond4g1G/,2*(&%\"bG6#\"\"$\"\"\")&%\"aG6$F+ \"\"#F1F,&%\"cG6#F1F,\"\"'*,F5F,F(F,F.F,F2F,&F/6$F+F,F,F,*,F5F,&F)6#\" \"%F,&F/6$F " 0 "" {MPLTEXT 1 0 230 "SNcond4g2:=coeff(coeff(coeff(SNFi3[1],D[2,3](f[1])(x0,y0[1],y0[2] )),D[1](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]))=coeff(coeff(coeff ((1/4)*SNf3[1],D[2,3](f[1])(x0,y0[1],y0[2])),D[1](f[1])(x0,y0[1],y0[2] )),f[2](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond 4g2G/,2*(&%\"bG6#\"\"$\"\"\")&%\"aG6$F+\"\"#F1F,&%\"cG6#F1F,\"\"'*,F5F ,F(F,F.F,F2F,&F/6$F+F,F,F,*,F5F,&F)6#\"\"%F,&F/6$F " 0 "" {MPLTEXT 1 0 230 "SNcond4g3:=coeff(coeff(coef f(SNFi3[1],D[2,3](f[1])(x0,y0[1],y0[2])),D[1](f[2])(x0,y0[1],y0[2])),f [1](x0,y0[1],y0[2]))=coeff(coeff(coeff((1/4)*SNf3[1],D[2,3](f[1])(x0,y 0[1],y0[2])),D[1](f[2])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4g3G/,2*(&%\"bG6#\"\"$\"\"\") &%\"aG6$F+\"\"#F1F,&%\"cG6#F1F,\"\"'*,F5F,F(F,F.F,F2F,&F/6$F+F,F,F,*,F 5F,&F)6#\"\"%F,&F/6$F " 0 "" {MPLTEXT 1 0 230 "SNcond4g4:=coeff(coeff(coeff(SNFi3[1],D[3,3](f[1])(x 0,y0[1],y0[2])),D[1](f[2])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]))=coef f(coeff(coeff((1/4)*SNf3[1],D[3,3](f[1])(x0,y0[1],y0[2])),D[1](f[2])(x 0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4g4G/,2*(&%\"bG6#\"\"$\"\"\")&%\"aG6$F+\"\"#F1F,&%\"cG6 #F1F,\"\"'*,F5F,F(F,F.F,F2F,&F/6$F+F,F,F,*,F5F,&F)6#\"\"%F,&F/6$F " 0 "" {MPLTEXT 1 0 234 "SNcond4h1:=c oeff(coeff(coeff(SNFi3[1],D[2,2](f[1])(x0,y0[1],y0[2])),D[2](f[1])(x0, y0[1],y0[2])),f[1](x0,y0[1],y0[2])^2)=coeff(coeff(coeff((1/4)*SNf3[1], D[2,2](f[1])(x0,y0[1],y0[2])),D[2](f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1 ],y0[2])^2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SNcond4h1G/,B*(&%\" bG6#\"\"%\"\"\")&%\"aG6$F+\"\"#F1F,&F/6$F1F,F,\"\"'*,F4F,F(F,F.F,F2F,& F/6$F+\"\"$F,F,*,F4F,F(F,F6F,&F/6$F8F,F,&F/6$F+F,F,F,*,F4F,F(F,F6F,F:F ,F.F,F,**F4F,F(F,)F6F1F,F:F,F,*,F4F,F(F,F6F,&F/6$F8F1F,F " 0 "" {MPLTEXT 1 0 286 "SNcond4h2 :=coeff(coeff(coeff(coeff(SNFi3[1],D[2,2](f[1])(x0,y0[1],y0[2])),D[3]( f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]))=coe ff(coeff(coeff(coeff((1/4)*SNf3[1],D[2,2](f[1])(x0,y0[1],y0[2])),D[3]( f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]));" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SNcond4h2G/,8**&%\"bG6#\"\"%\"\"\" &%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F.6$F+F,F,\"\"'*,F6F,F(F,F-F,F1F,&F.6$ F+F3F,F,*,F6F,F(F,F8F,&F.6$F3F,F,F-F,F,*,F6F,F(F,F-F,&F.6$F0F,F,F4F,F, *,F6F,F(F,F-F,F>F,F8F,F,**F6F,F(F,)F-F3F,F>F,F,*,F6F,&F)6#F0F,F1F,F;F, F>F,F,**F6F,F(F,FBF,F1F,F,*,F6F,F(F,F8F,F;F,F4F,F,**F6F,F(F,)F8F3F,F;F ,F,**F6F,FDF,)F1F3F,F;F,F,#F0F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 234 "SNcond4h3:=coeff(coeff(coeff(SNFi3[1],D[2,2](f[2])(x0,y0[1],y 0[2])),D[3](f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2])^2)=coeff(coeff (coeff((1/4)*SNf3[1],D[2,2](f[2])(x0,y0[1],y0[2])),D[3](f[1])(x0,y0[1] ,y0[2])),f[1](x0,y0[1],y0[2])^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %*SNcond4h3G/,,*(&%\"bG6#\"\"$\"\"\"&%\"aG6$F+\"\"#F,)&F.6$F0F,F0F,F+* *F+F,&F)6#\"\"%F,&F.6$F7F+F,)&F.6$F+F,F0F,F,**F+F,F5F,&F.6$F7F0F,F1F,F ,**F+F,F5F,F8F,)F-F0F,F,*,\"\"'F,F5F,F8F,F;F,F-F,F,#F,F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 286 "SNcond4h4:=coeff(coeff(coeff(coeff (SNFi3[1],D[2,3](f[1])(x0,y0[1],y0[2])),D[2](f[1])(x0,y0[1],y0[2])),f[ 1](x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]))=coeff(coeff(coeff(coeff((1/4 )*SNf3[1],D[2,3](f[1])(x0,y0[1],y0[2])),D[2](f[1])(x0,y0[1],y0[2])),f[ 1](x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SNcond4h4G/,B*(&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,) &F.6$F0F,\"\"#F,\"\"'*,\"#7F,F(F,F-F,F2F,&F.6$F0F4F,F,**F5F,&F)6#F0F,F 8F,)&F.6$F4F,F4F,F,**F5F,F(F,)&F.6$F+F4F4F,F>F,F,*,F5F,F(F,F-F,F2F,FBF ,F,*,F5F,F(F,F-F,F8F,&F.6$F+F,F,F,*,F5F,F(F,FBF,F>F,FFF,F,**F5F,F;F,)F 8F4F,F>F,F,*,F5F,F;F,F8F,F>F,F2F,F,*,F5F,F(F,F-F,F2F,FFF,F,*,F5F,F(F,F -F,F8F,FBF,F,**F5F,F(F,FBF,F=F,F,*,F5F,F(F,FBF,F>F,F-F,F,**F5F,F(F,)F- F4F,F2F,F,**F5F,F(F,FQF,F8F,F,**F5F,F(F,F-F,FJF,F,#\"\"&F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 234 "SNcond4h5:=coeff(coeff(coeff(SNFi3 [1],D[2,3](f[1])(x0,y0[1],y0[2])),D[2](f[2])(x0,y0[1],y0[2])),f[1](x0, y0[1],y0[2])^2)=coeff(coeff(coeff((1/4)*SNf3[1],D[2,3](f[1])(x0,y0[1], y0[2])),D[2](f[2])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2])^2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SNcond4h5G/,8**&%\"bG6#\"\"%\"\"\"&%\"aG6 $F+\"\"$F,&F.6$F0\"\"#F,&F.6$F+F,F,\"\"'*,F6F,F(F,F-F,F1F,&F.6$F+F3F,F ,*,F6F,F(F,F8F,&F.6$F3F,F,F-F,F,*,F6F,F(F,F-F,&F.6$F0F,F,F4F,F,*,F6F,F (F,F-F,F>F,F8F,F,**F6F,F(F,)F-F3F,F>F,F,*,F6F,&F)6#F0F,F1F,F;F,F>F,F,* *F6F,F(F,FBF,F1F,F,*,F6F,F(F,F8F,F;F,F4F,F,**F6F,F(F,)F8F3F,F;F,F,**F6 F,FDF,)F1F3F,F;F,F,#F0F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 234 "SNcond4h6:=coeff(coeff(coeff(SNFi3[1],D[2,3](f[1])(x0,y0[1],y0[2] )),D[3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2])^2)=coeff(coeff(coe ff((1/4)*SNf3[1],D[2,3](f[1])(x0,y0[1],y0[2])),D[3](f[1])(x0,y0[1],y0[ 2])),f[2](x0,y0[1],y0[2])^2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SN cond4h6G/,8**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F.6$F+ F,F,\"\"'*,F6F,F(F,F-F,F1F,&F.6$F+F3F,F,*,F6F,F(F,F8F,&F.6$F3F,F,F-F,F ,*,F6F,F(F,F-F,&F.6$F0F,F,F4F,F,*,F6F,F(F,F-F,F>F,F8F,F,**F6F,F(F,)F-F 3F,F>F,F,*,F6F,&F)6#F0F,F1F,F;F,F>F,F,**F6F,F(F,FBF,F1F,F,*,F6F,F(F,F8 F,F;F,F4F,F,**F6F,F(F,)F8F3F,F;F,F,**F6F,FDF,)F1F3F,F;F,F,#F0F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 286 "SNcond4h7:=coeff(coeff(coef f(coeff(SNFi3[1],D[2,3](f[1])(x0,y0[1],y0[2])),D[3](f[2])(x0,y0[1],y0[ 2])),f[1](x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]))=coeff(coeff(coeff(coe ff((1/4)*SNf3[1],D[2,3](f[1])(x0,y0[1],y0[2])),D[3](f[2])(x0,y0[1],y0[ 2])),f[1](x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SNcond4h7G/,8**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,& F.6$F0\"\"#F,&F.6$F+F,F,\"\"'*,F6F,F(F,F-F,F1F,&F.6$F+F3F,F,*,F6F,F(F, F8F,&F.6$F3F,F,F-F,F,*,F6F,F(F,F-F,&F.6$F0F,F,F4F,F,*,F6F,F(F,F-F,F>F, F8F,F,**F6F,F(F,)F-F3F,F>F,F,*,F6F,&F)6#F0F,F1F,F;F,F>F,F,**F6F,F(F,FB F,F1F,F,*,F6F,F(F,F8F,F;F,F4F,F,**F6F,F(F,)F8F3F,F;F,F,**F6F,FDF,)F1F3 F,F;F,F,#F0F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 286 "SNcond4h8 :=coeff(coeff(coeff(coeff(SNFi3[1],D[2,3](f[2])(x0,y0[1],y0[2])),D[3]( f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]))=coe ff(coeff(coeff(coeff((1/4)*SNf3[1],D[2,3](f[2])(x0,y0[1],y0[2])),D[3]( f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]));" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4h8G/,,*(&%\"bG6#\"\"$\"\"\" &%\"aG6$F+\"\"#F,)&F.6$F0F,F0F,\"\"'**F4F,&F)6#\"\"%F,&F.6$F8F0F,F1F,F ,*,\"#7F,F6F,&F.6$F8F+F,&F.6$F+F,F,F-F,F,**F4F,F6F,F=F,)F?F0F,F,**F4F, F6F,F=F,)F-F0F,F,#F,F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 234 " SNcond4h9:=coeff(coeff(coeff(SNFi3[1],D[3,3](f[1])(x0,y0[1],y0[2])),D[ 2](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2])^2)=coeff(coeff(coeff((1 /4)*SNf3[1],D[3,3](f[1])(x0,y0[1],y0[2])),D[2](f[1])(x0,y0[1],y0[2])), f[2](x0,y0[1],y0[2])^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4 h9G/,,*(&%\"bG6#\"\"$\"\"\"&%\"aG6$F+\"\"#F,)&F.6$F0F,F0F,F+**F+F,&F)6 #\"\"%F,&F.6$F7F+F,)&F.6$F+F,F0F,F,**F+F,F5F,&F.6$F7F0F,F1F,F,**F+F,F5 F,F8F,)F-F0F,F,*,\"\"'F,F5F,F8F,F;F,F-F,F,#F,F7" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 287 "SNcond4h10:=coeff(coeff(coeff(coeff(SNFi3[1], D[3,3](f[1])(x0,y0[1],y0[2])),D[2](f[2])(x0,y0[1],y0[2])),f[1](x0,y0[1 ],y0[2])),f[2](x0,y0[1],y0[2]))=coeff(coeff(coeff(coeff((1/4)*SNf3[1], D[3,3](f[1])(x0,y0[1],y0[2])),D[2](f[2])(x0,y0[1],y0[2])),f[1](x0,y0[1 ],y0[2])),f[2](x0,y0[1],y0[2]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>% +SNcond4h10G/,8**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F. 6$F+F,F,\"\"'*,F6F,F(F,F-F,F1F,&F.6$F+F3F,F,*,F6F,F(F,F8F,&F.6$F3F,F,F -F,F,*,F6F,F(F,F-F,&F.6$F0F,F,F4F,F,*,F6F,F(F,F-F,F>F,F8F,F,**F6F,F(F, )F-F3F,F>F,F,*,F6F,&F)6#F0F,F1F,F;F,F>F,F,**F6F,F(F,FBF,F1F,F,*,F6F,F( F,F8F,F;F,F4F,F,**F6F,F(F,)F8F3F,F;F,F,**F6F,FDF,)F1F3F,F;F,F,#F0F+" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 235 "SNcond4h11:=coeff(coeff(c oeff(SNFi3[1],D[3,3](f[1])(x0,y0[1],y0[2])),D[3](f[2])(x0,y0[1],y0[2]) ),f[2](x0,y0[1],y0[2])^2)=coeff(coeff(coeff((1/4)*SNf3[1],D[3,3](f[1]) (x0,y0[1],y0[2])),D[3](f[2])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2])^2); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%+SNcond4h11G/,8**&%\"bG6#\"\"%\" \"\"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F.6$F+F,F,\"\"'*,F6F,F(F,F-F,F1F,& F.6$F+F3F,F,*,F6F,F(F,F8F,&F.6$F3F,F,F-F,F,*,F6F,F(F,F-F,&F.6$F0F,F,F4 F,F,*,F6F,F(F,F-F,F>F,F8F,F,**F6F,F(F,)F-F3F,F>F,F,*,F6F,&F)6#F0F,F1F, F;F,F>F,F,**F6F,F(F,FBF,F1F,F,*,F6F,F(F,F8F,F;F,F4F,F,**F6F,F(F,)F8F3F ,F;F,F,**F6F,FDF,)F1F3F,F;F,F,#F0F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 235 "SNcond4h12:=coeff(coeff(coeff(SNFi3[1],D[3,3](f[2])( x0,y0[1],y0[2])),D[3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2])^2)=c oeff(coeff(coeff((1/4)*SNf3[1],D[3,3](f[2])(x0,y0[1],y0[2])),D[3](f[1] )(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2])^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+SNcond4h12G/,,*(&%\"bG6#\"\"$\"\"\"&%\"aG6$F+\"\"#F, )&F.6$F0F,F0F,F+**F+F,&F)6#\"\"%F,&F.6$F7F+F,)&F.6$F+F,F0F,F,**F+F,F5F ,&F.6$F7F0F,F1F,F,**F+F,F5F,F8F,)F-F0F,F,*,\"\"'F,F5F,F8F,F;F,F-F,F,#F ,F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 174 "SNcond4i1:=coeff(co eff(SNFi3[1],D[1,1](f[1])(x0,y0[1],y0[2])),D[2](f[1])(x0,y0[1],y0[2])) =coeff(coeff((1/4)*SNf3[1],D[1,1](f[1])(x0,y0[1],y0[2])),D[2](f[1])(x0 ,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4i1G/,(*(& %\"bG6#\"\"$\"\"\"&%\"aG6$F+\"\"#F,)&%\"cG6#F0F0F,F+**F+F,&F)6#\"\"%F, &F.6$F8F0F,F1F,F,**F+F,F6F,&F.6$F8F+F,)&F3F*F0F,F,#F,F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 174 "SNcond4i2:=coeff(coeff(SNFi3[1],D[ 1,1](f[2])(x0,y0[1],y0[2])),D[3](f[1])(x0,y0[1],y0[2]))=coeff(coeff((1 /4)*SNf3[1],D[1,1](f[2])(x0,y0[1],y0[2])),D[3](f[1])(x0,y0[1],y0[2])); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4i2G/,(*(&%\"bG6#\"\"$\" \"\"&%\"aG6$F+\"\"#F,)&%\"cG6#F0F0F,F+**F+F,&F)6#\"\"%F,&F.6$F8F0F,F1F ,F,**F+F,F6F,&F.6$F8F+F,)&F3F*F0F,F,#F,F8" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 174 "SNcond4j1:=coeff(coeff(SNFi3[1],D[2](f[1])(x0,y0[1 ],y0[2])^2),D[1](f[1])(x0,y0[1],y0[2]))=coeff(coeff((1/4)*SNf3[1],D[2] (f[1])(x0,y0[1],y0[2])^2),D[1](f[1])(x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4j1G/,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\" \"$F,&F.6$F0\"\"#F,&%\"cG6#F3F,\"\"'#F,F+" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 238 "SNcond4j2:=coeff(coeff(coeff(SNFi3[1],D[2](f[1])(x 0,y0[1],y0[2])),D[3](f[1])(x0,y0[1],y0[2])),D[1](f[2])(x0,y0[1],y0[2]) )=coeff(coeff(coeff((1/4)*SNf3[1],D[2](f[1])(x0,y0[1],y0[2])),D[3](f[1 ])(x0,y0[1],y0[2])),D[1](f[2])(x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4j2G/,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,& F.6$F0\"\"#F,&%\"cG6#F3F,\"\"'#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 238 "SNcond4j3:=coeff(coeff(coeff(SNFi3[1],D[2](f[2])(x0, y0[1],y0[2])),D[3](f[1])(x0,y0[1],y0[2])),D[1](f[1])(x0,y0[1],y0[2]))= coeff(coeff(coeff((1/4)*SNf3[1],D[2](f[2])(x0,y0[1],y0[2])),D[3](f[1]) (x0,y0[1],y0[2])),D[1](f[1])(x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4j3G/,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,& F.6$F0\"\"#F,&%\"cG6#F3F,\"\"'#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 238 "SNcond4j4:=coeff(coeff(coeff(SNFi3[1],D[3](f[1])(x0, y0[1],y0[2])),D[3](f[2])(x0,y0[1],y0[2])),D[1](f[2])(x0,y0[1],y0[2]))= coeff(coeff(coeff((1/4)*SNf3[1],D[3](f[1])(x0,y0[1],y0[2])),D[3](f[2]) (x0,y0[1],y0[2])),D[1](f[2])(x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4j4G/,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,& F.6$F0\"\"#F,&%\"cG6#F3F,\"\"'#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 162 "SNcond4k1:=coeff(coeff(SNFi3[1],D[2](f[1])(x0,y0[1], y0[2])^3),f[1](x0,y0[1],y0[2]))=coeff(coeff((1/4)*SNf3[1],D[2](f[1])(x 0,y0[1],y0[2])^3),f[1](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4k1G/,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0\" \"#F,&F.6$F3F,F,\"\"'#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 230 "SNcond4k2:=coeff(coeff(coeff(SNFi3[1],D[2](f[1])(x0,y0[1],y0[2])^ 2),D[3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]))=coeff(coeff(coeff ((1/4)*SNf3[1],D[2](f[1])(x0,y0[1],y0[2])^2),D[3](f[1])(x0,y0[1],y0[2] )),f[2](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond 4k2G/,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F.6$F3F,F, \"\"'#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 294 "SNcond4k3:=c oeff(coeff(coeff(coeff(SNFi3[1],D[2](f[1])(x0,y0[1],y0[2])),D[3](f[1]) (x0,y0[1],y0[2])),D[2](f[2])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]))=co eff(coeff(coeff(coeff((1/4)*SNf3[1],D[2](f[1])(x0,y0[1],y0[2])),D[3](f [1])(x0,y0[1],y0[2])),D[2](f[2])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4k3G/,$**&%\"bG6#\"\"% \"\"\"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F.6$F3F,F,\"#7#F,F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 294 "SNcond4k4:=coeff(coeff(coeff(coeff (SNFi3[1],D[2](f[1])(x0,y0[1],y0[2])),D[3](f[1])(x0,y0[1],y0[2])),D[3] (f[2])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]))=coeff(coeff(coeff(coeff( (1/4)*SNf3[1],D[2](f[1])(x0,y0[1],y0[2])),D[3](f[1])(x0,y0[1],y0[2])), D[3](f[2])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%*SNcond4k4G/,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F ,&F.6$F0\"\"#F,&F.6$F3F,F,\"\"'#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 230 "SNcond4k5:=coeff(coeff(coeff(SNFi3[1],D[2](f[2])(x0, y0[1],y0[2])),D[3](f[1])(x0,y0[1],y0[2])^2),f[2](x0,y0[1],y0[2]))=coef f(coeff(coeff((1/4)*SNf3[1],D[2](f[2])(x0,y0[1],y0[2])),D[3](f[1])(x0, y0[1],y0[2])^2),f[2](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4k5G/,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0\" \"#F,&F.6$F3F,F,\"\"'#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 294 "SNcond4k6:=coeff(coeff(coeff(coeff(SNFi3[1],D[2](f[2])(x0,y0[1],y 0[2])),D[3](f[1])(x0,y0[1],y0[2])),D[3](f[2])(x0,y0[1],y0[2])),f[1](x0 ,y0[1],y0[2]))=coeff(coeff(coeff(coeff((1/4)*SNf3[1],D[2](f[2])(x0,y0[ 1],y0[2])),D[3](f[1])(x0,y0[1],y0[2])),D[3](f[2])(x0,y0[1],y0[2])),f[1 ](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4k6G/, $**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F.6$F3F,F,\"\"'# F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 230 "SNcond4k7:=coeff(c oeff(coeff(SNFi3[1],D[3](f[1])(x0,y0[1],y0[2])),D[3](f[2])(x0,y0[1],y0 [2])^2),f[2](x0,y0[1],y0[2]))=coeff(coeff(coeff((1/4)*SNf3[1],D[3](f[1 ])(x0,y0[1],y0[2])),D[3](f[2])(x0,y0[1],y0[2])^2),f[2](x0,y0[1],y0[2]) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond4k7G/,$**&%\"bG6#\"\"% \"\"\"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F.6$F3F,F,\"\"'#F,F+" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 28 "# soluciones para el orden 4" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "#SNsolve44:=solve(\{cond1a, cond2a,cond2b1,cond2b2,cond3a,cond3b1,cond3b2,cond3c1,cond3c2,cond3c3, cond3d1,cond3d2,cond3e1,cond3e2,cond3e3,cond3e4\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "#SNsolve441:=SNsolve44[1];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "#SNsolve442:=SNsolve44[2];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "#SNsolve443:=SNsolve44[3];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "#SNsolve444:=SNsolve44[4] ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "#SNsolve445:=SNsolve44 [5];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "#SNsolve446:=SNsolv e44[6];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "#SNsolve447:=SNs olve44[7];" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 30 "# PARA SISTEMA S AUTONOMOS (SA)" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 37 "# desarr ollo de la verdadera solucion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "y[1]:=unapply(y[1](x),x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "y[2]:=unapply(y[2](x),x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "f[1]:=unapply(f[1](y[1],y[2]),y[1],y[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "f[2]:=unapply(f[2](y[1],y[2]),y[1], y[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "f0[1]:=f[1](y[1]( x),y[2](x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "f0[2]:=f[2] (y[1](x),y[2](x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "f1[1 ]:=subs(\{diff(y[1](x),x)=f[1](y[1](x),y[2](x)),diff(y[2](x),x)=f[2](y [1](x),y[2](x))\},diff(f0[1],x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "f1[2]:=subs(\{diff(y[1](x),x)=f[1](y[1](x),y[2](x)), diff(y[2](x),x)=f[2](y[1](x),y[2](x))\},diff(f0[2],x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "f2[1]:=subs(\{diff(y[1](x),x)=f[1] (y[1](x),y[2](x)),diff(y[2](x),x)=f[2](y[1](x),y[2](x))\},diff(f1[1],x )):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "f2[2]:=subs(\{diff( y[1](x),x)=f[1](y[1](x),y[2](x)),diff(y[2](x),x)=f[2](y[1](x),y[2](x)) \},diff(f1[2],x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "f3[1 ]:=subs(\{diff(y[1](x),x)=f[1](y[1](x),y[2](x)),diff(y[2](x),x)=f[2](y [1](x),y[2](x))\},diff(f2[1],x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "f3[2]:=subs(\{diff(y[1](x),x)=f[1](y[1](x),y[2](x)), diff(y[2](x),x)=f[2](y[1](x),y[2](x))\},diff(f2[2],x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f0[1]:=subs(\{y[1](x)=y0[1],y[2](x) =y0[2],x=x0\},f0[1]):SAf0[1]:=expand(f0[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%SAf0G6#\"\"\"-&%\"fGF&6$&%#y0GF&&F-6#\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f0[2]:=subs(\{y[1](x)=y0[1], y[2](x)=y0[2],x=x0\},f0[2]):SAf0[2]:=expand(f0[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f1[1]:=subs(\{y[1](x)=y0[1],y[2](x)=y0[2] ,x=x0\},f1[1]):SAf1[1]:=expand(f1[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%SAf1G6#\"\"\",&*&--&%\"DGF&6#&%\"fGF&6$&%#y0GF&&F36#\"\"#F'- F/F1F'F'*&--&F-F5F.F1F'-&F0F5F1F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f1[2]:=subs(\{y[1](x)=y0[1],y[2](x)=y0[2],x=x0\},f1[2 ]):SAf1[2]:=expand(f1[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f2[1]:=subs(\{y[1](x)=y0[1],y[2](x)=y0[2],x=x0\},f2[1]):SAf2[1]:=e xpand(f2[1]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%%SAf2G6#\"\"\",0*& --&%\"DG6$F'F'6#&%\"fGF&6$&%#y0GF&&F46#\"\"#F')-F0F2F7F'F'**F7F'F9F'-- &F-6$F'F7F/F2F'-&F1F6F2F'F'*&)--&F-F&F/F2F7F'F9F'F'*(FCF'--&F-F6F/F2F' F?F'F'*&--&F-6$F7F7F/F2F')F?F7F'F'*(FGF'--FE6#F@F2F'F9F'F'*(FGF'--FIFS F2F'F?F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f2[2]:=subs( \{y[1](x)=y0[1],y[2](x)=y0[2],x=x0\},f2[2]):SAf2[2]:=expand(f2[2]):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f3[1]:=subs(\{y[1](x)=y0[1 ],y[2](x)=y0[2],x=x0\},f3[1]):SAf3[1]:=expand(f3[1]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%%SAf3G6#\"\"\",P**-&%\"fGF&6$&%#y0GF&&F/6#\"\"# F'--&%\"DG6$F'F26#F+F-F'--&F6F16#&F,F1F-F'-F=F-F'\"\"$*,F?F'F*F'--&F66 $F'F'F8F-F'--F;F8F-F'F>F'F'*,F2F'--&F6F&F8F-F'FEF'--FJFF'FHF'F*F'F'**FHF'FEF'F9F'F>F'F'*,F?F'F>F'--&F66$F2F2F8F-F' FKF'F*F'F'*,F2F'FEF'F*F'--F5FF'F'**F?F')F*F2F'--&F66%F'F'F2F8F- F'F>F'F'*&--&F66%F'F'F'F8F-F')F*F?F'F'**\"\"%F'FAF'FHF'FYF'F'**FEF'F9F 'FKF'F*F'F'**F?F'F*F'--&F66%F'F2F2F8F-F')F>F2F'F'**F?F'F3F'FKF'FYF'F'* &)FHF?F'F*F'F'*(FHF'FQF'FfoF'F'*()FHF2F'FEF'F>F'F'**F?F'F3F'FfoF'FEF'F '**F?F'FQF'F9F'FfoF'F'*&--&F66%F2F2F2F8F-F')F>F?F'F'*(FEF'--FCFF'F'*(FEF'--FSFF'F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f3[2]:=subs(\{y[1](x)=y0[1], y[2](x)=y0[2],x=x0\},f3[2]):SAf3[2]:=expand(f3[2]):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 23 "# desarrollo del m\351todo" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "k10[1]:=f[1](y[1],y[2]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "k10[2]:=f[2](y[1],y[2]):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "k20[1]:=f[1](y[1]+a[2,1]*h* k10[1],y[2]+a[2,1]*h*k10[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "k20[2]:=f[2](y[1]+a[2,1]*h*k10[1],y[2]+a[2,1]*h*k10[2]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "k30[1]:=f[1](y[1]+a[3,1]*h*k 10[1]+a[3,2]*h*k20[1],y[2]+a[3,1]*h*k10[2]+a[3,2]*h*k20[2]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "k30[2]:=f[2](y[1]+a[3,1]*h*k 10[1]+a[3,2]*h*k20[1],y[2]+a[3,1]*h*k10[2]+a[3,2]*h*k20[2]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "k40[1]:=f[1](y[1]+a[4,1]*h* k10[1]+a[4,2]*h*k20[1]+a[4,3]*h*k30[1],y[2]+a[4,1]*h*k10[2]+a[4,2]*h*k 20[2]+a[4,3]*h*k30[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "k40[2]:=f[2](y[1]+a[4,1]*h*k10[1]+a[4,2]*h*k20[1]+a[4,3]*h*k30[1],y[2 ]+a[4,1]*h*k10[2]+a[4,2]*h*k20[2]+a[4,3]*h*k30[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k100[1]:=subs(h=0,k10[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k100[2]:=subs(h=0,k10[2]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k200[1]:=subs(h=0,k20[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k200[2]:=subs(h=0,k20[2]) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k300[1]:=subs(h=0,k30[ 1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k300[2]:=subs(h=0,k 30[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k400[1]:=subs(h= 0,k40[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k400[2]:=subs (h=0,k40[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "Fi0[1]:=b [1]*k100[1]+b[2]*k200[1]+b[3]*k300[1]+b[4]*k400[1]:Fi0[1]:=subs(\{x=x0 ,y[1]=y0[1],y[2]=y0[2]\},Fi0[1]):SAFi0[1]:=expand(Fi0[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&SAFi0G6#\"\"\",**&&%\"bGF&F'-&%\"fGF&6$& %#y0GF&&F16#\"\"#F'F'*&&F+F3F'F,F'F'*&&F+6#\"\"$F'F,F'F'*&&F+6#\"\"%F' F,F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "Fi0[2]:=b[1]*k10 0[2]+b[2]*k200[2]+b[3]*k300[2]+b[4]*k400[2]:Fi0[2]:=subs(\{x=x0,y[1]=y 0[1],y[2]=y0[2]\},Fi0[2]):SAFi0[2]:=expand(Fi0[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k11[1]:=diff(k10[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k11[2]:=diff(k10[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k21[1]:=diff(k20[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k21[2]:=diff(k20[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k31[1]:=diff(k30[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k31[2]:=diff(k30[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k41[1]:=diff(k40[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k41[2]:=diff(k40[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k110[1]:=subs(h=0,k11[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k110[2]:=subs(h=0,k11[2]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k210[1]:=subs(h=0,k21[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k210[2]:=subs(h=0,k21[2]) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k310[1]:=subs(h=0,k31[ 1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k310[2]:=subs(h=0,k 31[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k410[1]:=subs(h= 0,k41[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k410[2]:=subs (h=0,k41[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "Fi1[1]:=b [1]*k110[1]+b[2]*k210[1]+b[3]*k310[1]+b[4]*k410[1]:Fi1[1]:=subs(\{x=x0 ,y[1]=y0[1],y[2]=y0[2]\},Fi1[1]):SAFi1[1]:=expand(Fi1[1]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%&SAFi1G6#\"\"\",:**&%\"bG6#\"\"#F'--&%\"D GF&6#&%\"fGF&6$&%#y0GF&&F7F,F'&%\"aG6$F-F'F'-F3F5F'F'**F*F'--&F1F,F2F5 F'F9F'-&F4F,F5F'F'**&F+6#\"\"$F'F.F'&F:6$FFF'F'FF'FGF'FAF'F'**FDF'F>F'FJF'FAF'F'**&F+6#\"\"%F'F.F'&F :6$FQF'F'FF'FRF'FAF'F'**FOF'F>F'FUF'FAF'F'**FOF'F>F'FXF'FAF'F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "Fi1[2]:=b[1]*k110[2]+b[2]*k 210[2]+b[3]*k310[2]+b[4]*k410[2]:Fi1[2]:=subs(\{x=x0,y[1]=y0[1],y[2]=y 0[2]\},Fi1[2]):SAFi1[2]:=expand(Fi1[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k12[1]:=diff(k11[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k12[2]:=diff(k11[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k22[1]:=diff(k21[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k22[2]:=diff(k21[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k32[1]:=diff(k31[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k32[2]:=diff(k31[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k42[1]:=diff(k41[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k42[2]:=diff(k41[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k120[1]:=subs(h=0,k12[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k120[2]:=subs(h=0,k12[2]):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 26 "k220[1]:=subs(h=0,k22[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k220[2]:=subs(h=0,k22[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k320[1]:=subs(h=0,k32[1]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k320[2]:=subs(h=0,k32[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k420[1]:=subs(h=0,k42[1]) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k420[2]:=subs(h=0,k42[ 2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "Fi2[1]:=b[1]*k120[ 1]+b[2]*k220[1]+b[3]*k320[1]+b[4]*k420[1]:Fi2[1]:=subs(\{x=x0,y[1]=y0[ 1],y[2]=y0[2]\},Fi2[1]):SAFi2[1]:=expand(Fi2[1]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%&SAFi2G6#\"\"\",hp*,&%\"bG6#\"\"$F'--&%\"DG6$F'F'6#& %\"fGF&6$&%#y0GF&&F86#\"\"#F'&%\"aG6$F-F'F')-F4F6F;F'&F=6$F-F;F'F;*.F; F'F*F'--&F16$F'F;F3F6F')F " 0 "" {MPLTEXT 1 0 135 "Fi2[2]:=b[1]*k120[2]+b[2]*k 220[2]+b[3]*k320[2]+b[4]*k420[2]:Fi2[2]:=subs(\{x=x0,y[1]=y0[1],y[2]=y 0[2]\},Fi2[2]):SAFi2[1]:=expand(Fi2[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k13[1]:=diff(k12[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k13[2]:=diff(k12[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k23[1]:=diff(k22[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k23[2]:=diff(k22[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k33[1]:=diff(k32[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k33[2]:=diff(k32[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k43[1]:=diff(k42[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k43[2]:=diff(k42[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k130[1]:=subs(h=0,k13[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k130[2]:=subs(h=0,k13[2]):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 26 "k230[1]:=subs(h=0,k23[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k230[2]:=subs(h=0,k23[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k330[1]:=subs(h=0,k33[1]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k330[2]:=subs(h=0,k33[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k430[1]:=subs(h=0,k43[1]) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k430[2]:=subs(h=0,k43[ 2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "Fi3[1]:=b[1]*k130[ 1]+b[2]*k230[1]+b[3]*k330[1]+b[4]*k430[1]:Fi3[1]:=subs(\{x=x0,y[1]=y0[ 1],y[2]=y0[2]\},Fi3[1]):SAFi3[1]:=expand(Fi3[1]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%&SAFi3G6#\"\"\",^bl*.&%\"bG6#\"\"%F'--&%\"DG6%F'F'\" \"#6#&%\"fGF&6$&%#y0GF&&F96#F3F'&%\"aG6$F-F'F'-&F6F;F7F')&F=6$F-\"\"$F 3F')-F5F7F3F'\"\"**4\"\"'F'F*F'--&F16$F3F3F4F7F'FBF'--&F1F&6#F@F7F'&F= 6$FDF3F'FFF'F " 0 "" {MPLTEXT 1 0 135 "Fi3[2]:=b[1]*k130[2]+b[2]*k230[2]+b[3]*k330[2]+ b[4]*k430[2]:Fi3[2]:=subs(\{x=x0,y[1]=y0[1],y[2]=y0[2]\},Fi3[2]):SAFi3 [1]:=expand(Fi3[1]):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 24 "# co nsistencia y orden 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "SAc ond1a:=coeff(SAFi0[1],f[1](y0[1],y0[2]))=coeff(SAf0[1],f[1](y0[1],y0[2 ]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)SAcond1aG/,*&%\"bG6#\"\"\"F *&F(6#\"\"#F*&F(6#\"\"$F*&F(6#\"\"%F*F*" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones para el orden 2" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 9 "#SAcond2a" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "SAcond2b1:=coeff(coeff(SAFi1[1],D[1](f[1])(y0[1],y0[ 2])),f[1](y0[1],y0[2]))=coeff(coeff((1/2)*SAf1[1],D[1](f[1])(y0[1],y0[ 2])),f[1](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond2 b1G/,.*&&%\"bG6#\"\"#\"\"\"&%\"aG6$F+F,F,F,*&&F)6#\"\"$F,&F.6$F3F,F,F, *&F1F,&F.6$F3F+F,F,*&&F)6#\"\"%F,&F.6$F " 0 "" {MPLTEXT 1 0 146 "SAc ond2b2:=coeff(coeff(SAFi1[1],D[2](f[1])(y0[1],y0[2])),f[2](y0[1],y0[2] ))=coeff(coeff((1/2)*SAf1[1],D[2](f[1])(y0[1],y0[2])),f[2](y0[1],y0[2] ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond2b2G/,.*&&%\"bG6#\"\"# \"\"\"&%\"aG6$F+F,F,F,*&&F)6#\"\"$F,&F.6$F3F,F,F,*&F1F,&F.6$F3F+F,F,*& &F)6#\"\"%F,&F.6$F " 0 "" {MPLTEXT 1 0 9 "#SAcond3a" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond3b1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond3b2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "SAcond3c1:=coeff(coeff(SAFi2[1],D[1,1](f[1])(y0[1],y 0[2])),f[1](y0[1],y0[2])^2)=coeff(coeff((1/3)*SAf2[1],D[1,1](f[1])(y0[ 1],y0[2])),f[1](y0[1],y0[2])^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% *SAcond3c1G/,6*&&%\"bG6#\"\"%\"\"\")&%\"aG6$F+\"\"#F1F,F,*&F(F,)&F/6$F +\"\"$F1F,F,**F1F,&F)6#F6F,&F/6$F6F,F,&F/6$F6F1F,F,**F1F,F(F,&F/6$F+F, F,F4F,F,**F1F,F(F,F?F,F.F,F,**F1F,F(F,F.F,F4F,F,*&&F)6#F1F,)&F/6$F1F,F 1F,F,*&F(F,)F?F1F,F,*&F8F,)F:F1F,F,*&F8F,)F " 0 "" {MPLTEXT 1 0 154 "SAcond3c2:=coeff(coeff(SAFi2[1],D[ 2,2](f[1])(y0[1],y0[2])),f[2](y0[1],y0[2])^2)=coeff(coeff((1/3)*SAf2[1 ],D[2,2](f[1])(y0[1],y0[2])),f[2](y0[1],y0[2])^2);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%*SAcond3c2G/,6*&&%\"bG6#\"\"%\"\"\")&%\"aG6$F+\"\"# F1F,F,*&F(F,)&F/6$F+\"\"$F1F,F,**F1F,&F)6#F6F,&F/6$F6F,F,&F/6$F6F1F,F, **F1F,F(F,&F/6$F+F,F,F4F,F,**F1F,F(F,F?F,F.F,F,**F1F,F(F,F.F,F4F,F,*&& F)6#F1F,)&F/6$F1F,F1F,F,*&F(F,)F?F1F,F,*&F8F,)F:F1F,F,*&F8F,)F " 0 "" {MPLTEXT 1 0 200 "SAcond3c3:=coeff(c oeff(coeff(SAFi2[1],D[1,2](f[1])(y0[1],y0[2])),f[2](y0[1],y0[2])),f[1] (y0[1],y0[2]))=coeff(coeff(coeff((1/3)*SAf2[1],D[1,2](f[1])(y0[1],y0[2 ])),f[2](y0[1],y0[2])),f[1](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond3c3G/,6*(&%\"bG6#\"\"%\"\"\"&%\"aG6$F+F,F,&F.6 $F+\"\"$F,F+**F+F,F(F,&F.6$F+\"\"#F,F0F,F,*(F6F,&F)6#F2F,)&F.6$F2F6F6F ,F,**F+F,F(F,F-F,F4F,F,*(F6F,F8F,)&F.6$F2F,F6F,F,*(F6F,F(F,)F-F6F,F,*( F6F,F(F,)F4F6F,F,*(F6F,F(F,)F0F6F,F,**F+F,F8F,F@F,F;F,F,*(F6F,&F)6#F6F ,)&F.6$F6F,F6F,F,#F6F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "# SAcond3d1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond3d2" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "SAcond3e1:=coeff(coeff(SAF i2[1],D[1](f[1])(y0[1],y0[2])^2),f[1](y0[1],y0[2]))=coeff(coeff((1/3)* SAf2[1],D[1](f[1])(y0[1],y0[2])^2),f[1](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond3e1G/,**(&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\" \"$F,&F.6$F0F,F,\"\"#**F3F,F(F,F-F,&F.6$F0F3F,F,**F3F,F(F,&F.6$F+F3F,& F.6$F3F,F,F,**F3F,&F)6#F0F,F5F,F:F,F,#F,F0" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 208 "SAcond3e2:=coeff(coeff(coeff(SAFi2[1],D[1](f[1])(y 0[1],y0[2])),D[2](f[1])(y0[1],y0[2])),f[2](y0[1],y0[2]))=coeff(coeff(c oeff((1/3)*SAf2[1],D[1](f[1])(y0[1],y0[2])),D[2](f[1])(y0[1],y0[2])),f [2](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond3e2G/,* *(&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0F,F,\"\"#**F3F,F(F,F-F,&F .6$F0F3F,F,**F3F,F(F,&F.6$F+F3F,&F.6$F3F,F,F,**F3F,&F)6#F0F,F5F,F:F,F, #F,F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 208 "SAcond3e3:=coeff( coeff(coeff(SAFi2[1],D[2](f[1])(y0[1],y0[2])),D[1](f[2])(y0[1],y0[2])) ,f[1](y0[1],y0[2]))=coeff(coeff(coeff((1/3)*SAf2[1],D[2](f[1])(y0[1],y 0[2])),D[1](f[2])(y0[1],y0[2])),f[1](y0[1],y0[2]));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%*SAcond3e3G/,**(&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F ,&F.6$F0F,F,\"\"#**F3F,F(F,F-F,&F.6$F0F3F,F,**F3F,F(F,&F.6$F+F3F,&F.6$ F3F,F,F,**F3F,&F)6#F0F,F5F,F:F,F,#F,F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 208 "SAcond3e4:=coeff(coeff(coeff(SAFi2[1],D[2](f[1])(y0[ 1],y0[2])),D[2](f[2])(y0[1],y0[2])),f[2](y0[1],y0[2]))=coeff(coeff(coe ff((1/3)*SAf2[1],D[2](f[1])(y0[1],y0[2])),D[2](f[2])(y0[1],y0[2])),f[2 ](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond3e4G/,**( &%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0F,F,\"\"#**F3F,F(F,F-F,&F.6 $F0F3F,F,**F3F,F(F,&F.6$F+F3F,&F.6$F3F,F,F,**F3F,&F)6#F0F,F5F,F:F,F,#F ,F0" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones para el orden 4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#SAcond4a" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4b1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4b2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4c1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4c2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4c 3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4d1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4d2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4e1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4e2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4e3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4e 4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4e5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4e6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4e7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 158 "SAcond4f1:=coeff(coeff(SAFi3[1],D[1,1,1](f[1])(y0[1] ,y0[2])),f[1](y0[1],y0[2])^3)=coeff(coeff((1/4)*SAf3[1],D[1,1,1](f[1]) (y0[1],y0[2])),f[1](y0[1],y0[2])^3);" }}{PARA 12 "" 1 "" {XPPMATH 20 " 6#>%*SAcond4f1G/,@*&&%\"bG6#\"\"%\"\"\")&%\"aG6$F+\"\"$F1F,F,*&F(F,)&F /6$F+\"\"#F1F,F,*&F(F,)&F/6$F+F,F1F,F,**F1F,F(F,)F9F6F,F4F,F,**F1F,F(F ,F4F,)F.F6F,F,**F1F,F(F,)F4F6F,F.F,F,**F1F,F(F,F9F,F>F,F,**F1F,F(F,F9F ,F@F,F,**F1F,F(F,F " 0 " " {MPLTEXT 1 0 208 "SAcond4f2:=coeff(coeff(coeff(SAFi3[1],D[1,1,2](f[1 ])(y0[1],y0[2])),f[1](y0[1],y0[2])^2),f[2](y0[1],y0[2]))=coeff(coeff(c oeff((1/4)*SAf3[1],D[1,1,2](f[1])(y0[1],y0[2])),f[1](y0[1],y0[2])^2),f [2](y0[1],y0[2]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SAcond4f2G/,@ *(&%\"bG6#\"\"%\"\"\")&%\"aG6$F+F,\"\"#F,&F/6$F+F1F,\"\"**,\"#=F,F(F,F .F,F2F,&F/6$F+\"\"$F,F,**F4F,F(F,F2F,)F7F1F,F,**F4F,F(F,)F2F1F,F7F,F,* (F9F,F(F,)F2F9F,F,*(F9F,F(F,)F.F9F,F,**F4F,F(F,F-F,F7F,F,**F4F,F(F,F.F ,F;F,F,**F4F,&F)6#F9F,)&F/6$F9F,F1F,&F/6$F9F1F,F,*(F9F,&F)6#F1F,)&F/6$ F1F,F9F,F,*(F9F,FEF,)FHF9F,F,*(F9F,FEF,)FJF9F,F,**F4F,FEF,FHF,)FJF1F,F ,**F4F,F(F,F.F,F=F,F,*(F9F,F(F,)F7F9F,F,#F9F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 208 "SAcond4f3:=coeff(coeff(coeff(SAFi3[1],D[1,2,2]( f[1])(y0[1],y0[2])),f[2](y0[1],y0[2])^2),f[1](y0[1],y0[2]))=coeff(coef f(coeff((1/4)*SAf3[1],D[1,2,2](f[1])(y0[1],y0[2])),f[2](y0[1],y0[2])^2 ),f[1](y0[1],y0[2]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SAcond4f3G /,@*(&%\"bG6#\"\"%\"\"\")&%\"aG6$F+F,\"\"#F,&F/6$F+F1F,\"\"**,\"#=F,F( F,F.F,F2F,&F/6$F+\"\"$F,F,**F4F,F(F,F2F,)F7F1F,F,**F4F,F(F,)F2F1F,F7F, F,*(F9F,F(F,)F2F9F,F,*(F9F,F(F,)F.F9F,F,**F4F,F(F,F-F,F7F,F,**F4F,F(F, F.F,F;F,F,**F4F,&F)6#F9F,)&F/6$F9F,F1F,&F/6$F9F1F,F,*(F9F,&F)6#F1F,)&F /6$F1F,F9F,F,*(F9F,FEF,)FHF9F,F,*(F9F,FEF,)FJF9F,F,**F4F,FEF,FHF,)FJF1 F,F,**F4F,F(F,F.F,F=F,F,*(F9F,F(F,)F7F9F,F,#F9F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 158 "SAcond4f4:=coeff(coeff(SAFi3[1],D[2,2,2](f[1 ])(y0[1],y0[2])),f[2](y0[1],y0[2])^3)=coeff(coeff((1/4)*SAf3[1],D[2,2, 2](f[1])(y0[1],y0[2])),f[2](y0[1],y0[2])^3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SAcond4f4G/,@*&&%\"bG6#\"\"%\"\"\")&%\"aG6$F+\"\"$F1 F,F,*&F(F,)&F/6$F+\"\"#F1F,F,*&F(F,)&F/6$F+F,F1F,F,**F1F,F(F,)F9F6F,F4 F,F,**F1F,F(F,F4F,)F.F6F,F,**F1F,F(F,)F4F6F,F.F,F,**F1F,F(F,F9F,F>F,F, **F1F,F(F,F9F,F@F,F,**F1F,F(F,F " 0 "" {MPLTEXT 1 0 10 "#SAcond4g1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4g2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4g3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4g4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 216 "SAcond4h 1:=coeff(coeff(coeff(SAFi3[1],D[1,1](f[1])(y0[1],y0[2])),D[1](f[1])(y0 [1],y0[2])),f[1](y0[1],y0[2])^2)=coeff(coeff(coeff((1/4)*SAf3[1],D[1,1 ](f[1])(y0[1],y0[2])),D[1](f[1])(y0[1],y0[2])),f[1](y0[1],y0[2])^2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SAcond4h1G/,B*(&%\"bG6#\"\"%\"\" \")&%\"aG6$F+\"\"#F1F,&F/6$F1F,F,\"\"'*,F4F,F(F,F.F,F2F,&F/6$F+\"\"$F, F,*,F4F,F(F,F6F,&F/6$F8F,F,&F/6$F+F,F,F,*,F4F,F(F,F6F,F:F,F.F,F,**F4F, F(F,)F6F1F,F:F,F,*,F4F,F(F,F6F,&F/6$F8F1F,F " 0 "" {MPLTEXT 1 0 262 "SAcond4h2:=coeff(coeff (coeff(coeff(SAFi3[1],D[1,1](f[1])(y0[1],y0[2])),D[2](f[1])(y0[1],y0[2 ])),f[1](y0[1],y0[2])),f[2](y0[1],y0[2]))=coeff(coeff(coeff(coeff((1/4 )*SAf3[1],D[1,1](f[1])(y0[1],y0[2])),D[2](f[1])(y0[1],y0[2])),f[1](y0[ 1],y0[2])),f[2](y0[1],y0[2]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*S Acond4h2G/,8**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F.6$F +F,F,\"\"'*,F6F,F(F,F-F,F1F,&F.6$F+F3F,F,*,F6F,F(F,F8F,&F.6$F3F,F,F-F, F,*,F6F,F(F,F-F,&F.6$F0F,F,F4F,F,*,F6F,F(F,F-F,F>F,F8F,F,**F6F,F(F,)F- F3F,F>F,F,*,F6F,&F)6#F0F,F1F,F;F,F>F,F,**F6F,F(F,FBF,F1F,F,*,F6F,F(F,F 8F,F;F,F4F,F,**F6F,F(F,)F8F3F,F;F,F,**F6F,FDF,)F1F3F,F;F,F,#F0F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 216 "SAcond4h3:=coeff(coeff(coef f(SAFi3[1],D[1,1](f[2])(y0[1],y0[2])),D[2](f[1])(y0[1],y0[2])),f[1](y0 [1],y0[2])^2)=coeff(coeff(coeff((1/4)*SAf3[1],D[1,1](f[2])(y0[1],y0[2] )),D[2](f[1])(y0[1],y0[2])),f[1](y0[1],y0[2])^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond4h3G/,,*(&%\"bG6#\"\"$\"\"\"&%\"aG6$F+\"\"#F,) &F.6$F0F,F0F,F+**F+F,&F)6#\"\"%F,&F.6$F7F+F,)&F.6$F+F,F0F,F,**F+F,F5F, &F.6$F7F0F,F1F,F,**F+F,F5F,F8F,)F-F0F,F,*,\"\"'F,F5F,F8F,F;F,F-F,F,#F, F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 262 "SAcond4h4:=coeff(coe ff(coeff(coeff(SAFi3[1],D[1,2](f[1])(y0[1],y0[2])),D[1](f[1])(y0[1],y0 [2])),f[1](y0[1],y0[2])),f[2](y0[1],y0[2]))=coeff(coeff(coeff(coeff((1 /4)*SAf3[1],D[1,2](f[1])(y0[1],y0[2])),D[1](f[1])(y0[1],y0[2])),f[1](y 0[1],y0[2])),f[2](y0[1],y0[2]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>% *SAcond4h4G/,B*(&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,)&F.6$F0F,\"\"#F, \"\"'*,\"#7F,F(F,F-F,F2F,&F.6$F0F4F,F,**F5F,&F)6#F0F,F8F,)&F.6$F4F,F4F ,F,**F5F,F(F,)&F.6$F+F4F4F,F>F,F,*,F5F,F(F,F-F,F2F,FBF,F,*,F5F,F(F,F-F ,F8F,&F.6$F+F,F,F,*,F5F,F(F,FBF,F>F,FFF,F,**F5F,F;F,)F8F4F,F>F,F,*,F5F ,F;F,F8F,F>F,F2F,F,*,F5F,F(F,F-F,F2F,FFF,F,*,F5F,F(F,F-F,F8F,FBF,F,**F 5F,F(F,FBF,F=F,F,*,F5F,F(F,FBF,F>F,F-F,F,**F5F,F(F,)F-F4F,F2F,F,**F5F, F(F,FQF,F8F,F,**F5F,F(F,F-F,FJF,F,#\"\"&F+" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 216 "SAcond4h5:=coeff(coeff(coeff(SAFi3[1],D[1,2](f[1]) (y0[1],y0[2])),D[1](f[2])(y0[1],y0[2])),f[1](y0[1],y0[2])^2)=coeff(coe ff(coeff((1/4)*SAf3[1],D[1,2](f[1])(y0[1],y0[2])),D[1](f[2])(y0[1],y0[ 2])),f[1](y0[1],y0[2])^2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SAcon d4h5G/,8**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F.6$F+F,F ,\"\"'*,F6F,F(F,F-F,F1F,&F.6$F+F3F,F,*,F6F,F(F,F8F,&F.6$F3F,F,F-F,F,*, F6F,F(F,F-F,&F.6$F0F,F,F4F,F,*,F6F,F(F,F-F,F>F,F8F,F,**F6F,F(F,)F-F3F, F>F,F,*,F6F,&F)6#F0F,F1F,F;F,F>F,F,**F6F,F(F,FBF,F1F,F,*,F6F,F(F,F8F,F ;F,F4F,F,**F6F,F(F,)F8F3F,F;F,F,**F6F,FDF,)F1F3F,F;F,F,#F0F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 216 "SAcond4h6:=coeff(coeff(coef f(SAFi3[1],D[1,2](f[1])(y0[1],y0[2])),D[2](f[1])(y0[1],y0[2])),f[2](y0 [1],y0[2])^2)=coeff(coeff(coeff((1/4)*SAf3[1],D[1,2](f[1])(y0[1],y0[2] )),D[2](f[1])(y0[1],y0[2])),f[2](y0[1],y0[2])^2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SAcond4h6G/,8**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,& F.6$F0\"\"#F,&F.6$F+F,F,\"\"'*,F6F,F(F,F-F,F1F,&F.6$F+F3F,F,*,F6F,F(F, F8F,&F.6$F3F,F,F-F,F,*,F6F,F(F,F-F,&F.6$F0F,F,F4F,F,*,F6F,F(F,F-F,F>F, F8F,F,**F6F,F(F,)F-F3F,F>F,F,*,F6F,&F)6#F0F,F1F,F;F,F>F,F,**F6F,F(F,FB F,F1F,F,*,F6F,F(F,F8F,F;F,F4F,F,**F6F,F(F,)F8F3F,F;F,F,**F6F,FDF,)F1F3 F,F;F,F,#F0F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 262 "SAcond4h7 :=coeff(coeff(coeff(coeff(SAFi3[1],D[1,2](f[1])(y0[1],y0[2])),D[2](f[2 ])(y0[1],y0[2])),f[1](y0[1],y0[2])),f[2](y0[1],y0[2]))=coeff(coeff(coe ff(coeff((1/4)*SAf3[1],D[1,2](f[1])(y0[1],y0[2])),D[2](f[2])(y0[1],y0[ 2])),f[1](y0[1],y0[2])),f[2](y0[1],y0[2]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*SAcond4h7G/,8**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,& F.6$F0\"\"#F,&F.6$F+F,F,\"\"'*,F6F,F(F,F-F,F1F,&F.6$F+F3F,F,*,F6F,F(F, F8F,&F.6$F3F,F,F-F,F,*,F6F,F(F,F-F,&F.6$F0F,F,F4F,F,*,F6F,F(F,F-F,F>F, F8F,F,**F6F,F(F,)F-F3F,F>F,F,*,F6F,&F)6#F0F,F1F,F;F,F>F,F,**F6F,F(F,FB F,F1F,F,*,F6F,F(F,F8F,F;F,F4F,F,**F6F,F(F,)F8F3F,F;F,F,**F6F,FDF,)F1F3 F,F;F,F,#F0F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 262 "SAcond4h8 :=coeff(coeff(coeff(coeff(SAFi3[1],D[1,2](f[2])(y0[1],y0[2])),D[2](f[1 ])(y0[1],y0[2])),f[1](y0[1],y0[2])),f[2](y0[1],y0[2]))=coeff(coeff(coe ff(coeff((1/4)*SAf3[1],D[1,2](f[2])(y0[1],y0[2])),D[2](f[1])(y0[1],y0[ 2])),f[1](y0[1],y0[2])),f[2](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond4h8G/,,*(&%\"bG6#\"\"$\"\"\"&%\"aG6$F+\"\"#F,) &F.6$F0F,F0F,\"\"'**F4F,&F)6#\"\"%F,&F.6$F8F0F,F1F,F,*,\"#7F,F6F,&F.6$ F8F+F,&F.6$F+F,F,F-F,F,**F4F,F6F,F=F,)F?F0F,F,**F4F,F6F,F=F,)F-F0F,F,# F,F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 216 "SAcond4h9:=coeff(c oeff(coeff(SAFi3[1],D[2,2](f[1])(y0[1],y0[2])),D[1](f[1])(y0[1],y0[2]) ),f[2](y0[1],y0[2])^2)=coeff(coeff(coeff((1/4)*SAf3[1],D[2,2](f[1])(y0 [1],y0[2])),D[1](f[1])(y0[1],y0[2])),f[2](y0[1],y0[2])^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond4h9G/,,*(&%\"bG6#\"\"$\"\"\"&%\"aG6 $F+\"\"#F,)&F.6$F0F,F0F,F+**F+F,&F)6#\"\"%F,&F.6$F7F+F,)&F.6$F+F,F0F,F ,**F+F,F5F,&F.6$F7F0F,F1F,F,**F+F,F5F,F8F,)F-F0F,F,*,\"\"'F,F5F,F8F,F; F,F-F,F,#F,F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 263 "SAcond4h1 0:=coeff(coeff(coeff(coeff(SAFi3[1],D[2,2](f[1])(y0[1],y0[2])),D[1](f[ 2])(y0[1],y0[2])),f[1](y0[1],y0[2])),f[2](y0[1],y0[2]))=coeff(coeff(co eff(coeff((1/4)*SAf3[1],D[2,2](f[1])(y0[1],y0[2])),D[1](f[2])(y0[1],y0 [2])),f[1](y0[1],y0[2])),f[2](y0[1],y0[2]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%+SAcond4h10G/,8**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F, &F.6$F0\"\"#F,&F.6$F+F,F,\"\"'*,F6F,F(F,F-F,F1F,&F.6$F+F3F,F,*,F6F,F(F ,F8F,&F.6$F3F,F,F-F,F,*,F6F,F(F,F-F,&F.6$F0F,F,F4F,F,*,F6F,F(F,F-F,F>F ,F8F,F,**F6F,F(F,)F-F3F,F>F,F,*,F6F,&F)6#F0F,F1F,F;F,F>F,F,**F6F,F(F,F BF,F1F,F,*,F6F,F(F,F8F,F;F,F4F,F,**F6F,F(F,)F8F3F,F;F,F,**F6F,FDF,)F1F 3F,F;F,F,#F0F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 217 "SAcond4h 11:=coeff(coeff(coeff(SAFi3[1],D[2,2](f[1])(y0[1],y0[2])),D[2](f[2])(y 0[1],y0[2])),f[2](y0[1],y0[2])^2)=coeff(coeff(coeff((1/4)*SAf3[1],D[2, 2](f[1])(y0[1],y0[2])),D[2](f[2])(y0[1],y0[2])),f[2](y0[1],y0[2])^2); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%+SAcond4h11G/,8**&%\"bG6#\"\"%\" \"\"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F.6$F+F,F,\"\"'*,F6F,F(F,F-F,F1F,& F.6$F+F3F,F,*,F6F,F(F,F8F,&F.6$F3F,F,F-F,F,*,F6F,F(F,F-F,&F.6$F0F,F,F4 F,F,*,F6F,F(F,F-F,F>F,F8F,F,**F6F,F(F,)F-F3F,F>F,F,*,F6F,&F)6#F0F,F1F, F;F,F>F,F,**F6F,F(F,FBF,F1F,F,*,F6F,F(F,F8F,F;F,F4F,F,**F6F,F(F,)F8F3F ,F;F,F,**F6F,FDF,)F1F3F,F;F,F,#F0F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 217 "SAcond4h12:=coeff(coeff(coeff(SAFi3[1],D[2,2](f[2])( y0[1],y0[2])),D[2](f[1])(y0[1],y0[2])),f[2](y0[1],y0[2])^2)=coeff(coef f(coeff((1/4)*SAf3[1],D[2,2](f[2])(y0[1],y0[2])),D[2](f[1])(y0[1],y0[2 ])),f[2](y0[1],y0[2])^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+SAcond 4h12G/,,*(&%\"bG6#\"\"$\"\"\"&%\"aG6$F+\"\"#F,)&F.6$F0F,F0F,F+**F+F,&F )6#\"\"%F,&F.6$F7F+F,)&F.6$F+F,F0F,F,**F+F,F5F,&F.6$F7F0F,F1F,F,**F+F, F5F,F8F,)F-F0F,F,*,\"\"'F,F5F,F8F,F;F,F-F,F,#F,F7" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 10 "#SAcond4i1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4i2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4j1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4j 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4j3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAcond4j4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "SAcond4k1:=coeff(coeff(SAFi3[1],D[1](f[1])(y0[1 ],y0[2])^3),f[1](y0[1],y0[2]))=coeff(coeff((1/4)*SAf3[1],D[1](f[1])(y0 [1],y0[2])^3),f[1](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %*SAcond4k1G/,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F. 6$F3F,F,\"\"'#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 212 "SAco nd4k2:=coeff(coeff(coeff(SAFi3[1],D[1](f[1])(y0[1],y0[2])^2),D[2](f[1] )(y0[1],y0[2])),f[2](y0[1],y0[2]))=coeff(coeff(coeff((1/4)*SAf3[1],D[1 ](f[1])(y0[1],y0[2])^2),D[2](f[1])(y0[1],y0[2])),f[2](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond4k2G/,$**&%\"bG6#\"\"%\"\" \"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F.6$F3F,F,\"\"'#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 270 "SAcond4k3:=coeff(coeff(coeff(coeff (SAFi3[1],D[1](f[1])(y0[1],y0[2])),D[2](f[1])(y0[1],y0[2])),D[1](f[2]) (y0[1],y0[2])),f[1](y0[1],y0[2]))=coeff(coeff(coeff(coeff((1/4)*SAf3[1 ],D[1](f[1])(y0[1],y0[2])),D[2](f[1])(y0[1],y0[2])),D[1](f[2])(y0[1],y 0[2])),f[1](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcon d4k3G/,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F.6$F3F,F ,\"#7#F,F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 270 "SAcond4k4:=c oeff(coeff(coeff(coeff(SAFi3[1],D[1](f[1])(y0[1],y0[2])),D[2](f[1])(y0 [1],y0[2])),D[2](f[2])(y0[1],y0[2])),f[2](y0[1],y0[2]))=coeff(coeff(co eff(coeff((1/4)*SAf3[1],D[1](f[1])(y0[1],y0[2])),D[2](f[1])(y0[1],y0[2 ])),D[2](f[2])(y0[1],y0[2])),f[2](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond4k4G/,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,& F.6$F0\"\"#F,&F.6$F3F,F,\"\"'#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 212 "SAcond4k5:=coeff(coeff(coeff(SAFi3[1],D[1](f[2])(y0[ 1],y0[2])),D[2](f[1])(y0[1],y0[2])^2),f[2](y0[1],y0[2]))=coeff(coeff(c oeff((1/4)*SAf3[1],D[1](f[2])(y0[1],y0[2])),D[2](f[1])(y0[1],y0[2])^2) ,f[2](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond4k5G/ ,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F.6$F3F,F,\"\"' #F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 270 "SAcond4k6:=coeff( coeff(coeff(coeff(SAFi3[1],D[1](f[2])(y0[1],y0[2])),D[2](f[1])(y0[1],y 0[2])),D[2](f[2])(y0[1],y0[2])),f[1](y0[1],y0[2]))=coeff(coeff(coeff(c oeff((1/4)*SAf3[1],D[1](f[2])(y0[1],y0[2])),D[2](f[1])(y0[1],y0[2])),D [2](f[2])(y0[1],y0[2])),f[1](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond4k6G/,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,& F.6$F0\"\"#F,&F.6$F3F,F,\"\"'#F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 212 "SAcond4k7:=coeff(coeff(coeff(SAFi3[1],D[2](f[1])(y0[ 1],y0[2])),D[2](f[2])(y0[1],y0[2])^2),f[2](y0[1],y0[2]))=coeff(coeff(c oeff((1/4)*SAf3[1],D[2](f[1])(y0[1],y0[2])),D[2](f[2])(y0[1],y0[2])^2) ,f[2](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond4k7G/ ,$**&%\"bG6#\"\"%\"\"\"&%\"aG6$F+\"\"$F,&F.6$F0\"\"#F,&F.6$F3F,F,\"\"' #F,F+" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }