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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "interseccion con cambio de
 coordenadas" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "ejemplo de calculo de multiplic
idad de interseccion" }}{PARA 0 "" 0 "" {TEXT -1 37 "donde ambas curva
s pasan por P1,P2,P3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "F:=
x*y+x*z+y*z;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG,(*&%\"xG\"\"\"%
\"yGF(F(*&F'F(%\"zGF(F(*&F)F(F+F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "G:=x^2*(y+z)+y^2*(x+z)+z^2*(x+y);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"GG,(*&)%\"xG\"\"#\"\"\",&%\"yGF*%\"zGF*F*F**&)F,F
)F*,&F(F*F-F*F*F**&)F-F)F*,&F(F*F,F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "cambio de coo
rdenadas x=x'+y'; y=y', z=z'  (llamo xx a x')" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 27 "FF:=expand(subs(x=xx+y,F));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#FFG,**&%\"yG\"\"\"%#xxGF(F(*$)F'\"\"#F(F(*&%\"zGF(F)
F(F(*(F,F(F'F(F.F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "GG:
=expand(subs(x=xx+y,G));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#GGG,2*&
)%#xxG\"\"#\"\"\"%\"yGF*F**&F'F*%\"zGF*F**(\"\"$F*)F+F)F*F(F*F***F)F*F
+F*F(F*F-F*F**&F)F*)F+F/F*F**(F)F*F0F*F-F*F**&)F-F)F*F(F*F**(F)F*F6F*F
+F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "resultant(FF,GG,y)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"*\"\"\")%\"zG\"\"%F&)%#xx
G\"\"#F&!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "si z^4=0" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "factor(subs(z=0,FF));factor(
subs(z=0,GG));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%#xxG\"\"\"%\"yG
F&F&F'F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(%\"yG\"\"\",&%#xxGF%F$F%
F%,&F'F%*&\"\"#F%F$F%F%F%" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "obtenemos los puntos P1=(1:0:0) y
 R=(1:-1:0) cuyas multiplicidades de intersecci\363n suman 4" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "si xx^2=0" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 44 "factor(subs(xx=0,FF));factor(subs(xx=0,GG));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"yG\"\"\",&F$F%*&\"\"#F%%\"zGF%F%F
%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"#\"\"\"%\"yGF&,(*$)F'F%F&
F&*&F'F&%\"zGF&F&*$)F,F%F&F&F&F&" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "obtenemos el punto P3=(0:0
:1) con multiplicidad 2" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "Pasamo
s a las coordenadas iniciales :los puntos de intersecci\363n son  " }}
{PARA 0 "" 0 "" {TEXT -1 14 "P1 queda igual" }}{PARA 0 "" 0 "" {TEXT 
-1 29 "R=(1:-1:0) pasa a  (0:1:0)=P2" }}{PARA 0 "" 0 "" {TEXT -1 15 "P
3 queda igual " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 105 "Por la simetr\355a del problema, la multiplicidad de int
ersecci\363n en cada uno de los puntos P1,P2,P3 es dos." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "Voy a variar un p
oco el problema, alterando los coeficientes" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 19 "F:=3*x*y-7*x*z+y*z;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"FG,(*(\"\"$\"\"\"%\"xGF(%\"yGF(F(*(\"\"(F(F)F(%\"zGF(!\"\"*&
F*F(F-F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "G:=x^2*(y+z)+
4*y^2*(x+z)-5*z^2*(x+y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"GG,(*&
)%\"xG\"\"#\"\"\",&%\"yGF*%\"zGF*F*F**(\"\"%F*)F,F)F*,&F(F*F-F*F*F**(
\"\"&F*)F-F)F*,&F(F*F,F*F*!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
42 "cambio de coordenadas x=x'+y'; y=y', z=z' " }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 27 "FF:=expand(subs(x=xx+y,F));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#FFG,**(\"\"$\"\"\"%\"yGF(%#xxGF(F(*&F'F()F)\"\"#F(
F(*(\"\"(F(%\"zGF(F*F(!\"\"*(\"\"'F(F)F(F0F(F1" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 27 "GG:=expand(subs(x=xx+y,G));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#GGG,2*&)%#xxG\"\"#\"\"\"%\"yGF*F**&F'F*%\"zGF*F**(
\"\"'F*)F+F)F*F(F*F***F)F*F+F*F(F*F-F*F**&\"\"&F*)F+\"\"$F*F**(F3F*F0F
*F-F*F**(F3F*)F-F)F*F(F*!\"\"*(\"#5F*F8F*F+F*F9" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 27 "factor(resultant(FF,GG,y));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#,$*.\"\"%\"\"\")%\"zG\"\"#F&%#xxGF&,&*&\"\"'F&F*F&F&*
&\"\"&F&F(F&F&F&,&*&F/F&F*F&F&*&\"#CF&F(F&F&F&,&*&F)F&F*F&F&*&\"#:F&F(
F&F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "si xx=0" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "factor(subs(xx=0,FF));factor(subs(x
x=0,GG));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"$\"\"\"%\"yGF&,&F
'F&*&\"\"#F&%\"zGF&!\"\"F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"
\"&\"\"\"%\"yGF&,&F'F&*&\"\"#F&%\"zGF&F&F&,&F'F&F+!\"\"F&F&" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "obtenemos el  punto P3=(0:0:1)con \+
 multiplicidad de intersecci\363n 1" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 8 "si z^2=0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "factor(su
bs(z=0,FF));factor(subs(z=0,GG));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,
$*(\"\"$\"\"\",&%#xxGF&%\"yGF&F&F)F&F&" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#*(%\"yG\"\"\",&%#xxGF%F$F%F%,&*&\"\"&F%F$F%F%F'F%F%" }}}{EXCHG 
{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 111 
"obtenemos los  puntos P_1=(1:0:0) y Q=(1:-1:0) con suma de multiplici
dades 2, i.e, cada uno con multiplicidad 1" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "si 0= 5z +6xx" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 54 "factor(subs(xx=-5*z/6,FF));factor(subs(xx
=-5*z/6,GG));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"'!\"\",&*&F%
\"\"\"%\"yGF)F)*&\"\"(F)%\"zGF)F&F),&*&\"\"$F)F*F)F)*&\"\"&F)F-F)F&F)F
)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,\"\"&\"\"\"\"#O!\"\",&%\"zGF(
*&\"\"#F&%\"yGF&F&F&,&*&\"\"'F&F-F&F&*&\"\"(F&F*F&F(F&,&*&F%F&F*F&F&*&
\"\"$F&F-F&F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "obtenemos  punto    R=(-5:7:6) con
 mult 1 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
78 "An\341logamente obtenemos dos puntos m\341s, cada uno con multipli
cidad uno cada uno" }}}{PARA 0 "" 0 "" {TEXT -1 35 "Pasamos a las coor
denadas iniciales" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "P3 ser\341 P3" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "P1 ser
\341 P1" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
18 "Q ser\341 (0:-1:0)=P2" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 68 "R ser\341 ( 2:7:6) y otros dos puntos m\341s, cada
 uno con multiplicidad 1" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "0
 0 0" 38 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 
}