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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "with(plots):with(lin
alg):" }{TEXT 2 58 "  carica le librerie per i grafici e per l'algebra
 lineare" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 7 "Coniche" }}{SECT 1 
{PARA 4 "" 0 "" {TEXT -1 9 "Esempio 1" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "A:=matrix([[1,1/2],[1/2,1]]); h:=[1,1/2]; k:=0;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "conica1:=simplify(evalm([x,y
] &* A &* [x,y])+2*evalm(h &* [x,y])+k);  " }}{PARA 0 "" 0 "" {TEXT 
-1 131 " equazione della conica con parte quadratica definita dalla ma
trice simmetrica A, parte lineare definita dal vettore h e costante k
" }{MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 73 "implicitplot(conica1,x=-3..3,y=-2..2,scaling=CONSTRAI
NED,numpoints=1000);" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 26 "Riduzion
e a forma canonica" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "R:=mat
rix(evalm(1/sqrt(2)*[[1,1],[-1,1]])); " }{TEXT -1 20 "matrice di rotaz
ione" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "conica1_R:=simplify
(subs( x=evalm(R&*[X,Y])[1],y=evalm(R&*[X,Y])[2],conica1));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "implicitplot(conica1_R,X=-3.
.3,Y=-2..2,scaling=CONSTRAINED,numpoints=1000);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 68 "conica1_RT:=simplify(subs(X=x1-sqrt(2)/2,Y=y1-
sqrt(2)/2,conica1_R));" }}{PARA 0 "" 0 "" {TEXT -1 35 "conica rototras
lata (centro=(-1,0))" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "imp
licitplot(conica1_RT,x1=-3..3,y1=-2..2,scaling=CONSTRAINED,numpoints=1
000);" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Esempio 2" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "A:=matrix([[0,1/2],[1/2,0]]); h:=[
1,1/2]; k:=0;\nconica2:=simplify(evalm([x,y]&*A&*[x,y])+2*evalm(h&*[x,
y])+k);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "implicitplot(con
ica2,x=-6..5,y=-6..5,scaling=CONSTRAINED,numpoints=1000);" }}}{SECT 1 
{PARA 5 "" 0 "" {TEXT -1 26 "Riduzione a forma canonica" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "R:=matrix(evalm(1/sqrt(2)*[[1,-1],[
1,1]])); " }{TEXT -1 20 "matrice di rotazione" }{MPLTEXT 1 0 1 " " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "conica2_R:=simplify(subs( x=
evalm(R&*[X,Y])[1],y=evalm(R&*[X,Y])[2],conica2));" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 75 "implicitplot(conica2_R,X=-6..3,Y=-4..3,scal
ing=CONSTRAINED,numpoints=1000);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 76 "conica2_RT:=simplify(1/2*subs( X=x1-3*sqrt(2)/2,Y=y1-
sqrt(2)/2,conica2_R)); " }{TEXT -1 36 "conica rototraslata (centro=(-1
,-2))" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "implicitplot(conic
a2_RT,x1=-4..4,y1=-3..3,scaling=CONSTRAINED,numpoints=1000);" }}}}}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Esempio 3" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 106 "A:=matrix([[1,1],[1,1]]); h:=[1/2,0]; k:=0;\nco
nica3:=simplify(evalm([x,y]&*A&*[x,y])+2*evalm(h&*[x,y])+k);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "implicitplot(conica3,x=-3..1
,y=-1..3,scaling=CONSTRAINED,numpoints=1000);" }}}{SECT 1 {PARA 5 "" 
0 "" {TEXT -1 26 "Riduzione a forma canonica" }}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 44 "R:=matrix(evalm(1/sqrt(2)*[[1,-1],[1,1]])); " }
{TEXT -1 20 "matrice di rotazione" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 78 "conica3_R:=simplify(subs( x=evalm(R&*[X,Y])[1],y=eval
m(R&*[X,Y])[2],conica3));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
75 "implicitplot(conica3_R,X=-2..1,Y=-1..2,scaling=CONSTRAINED,numpoin
ts=1000);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "conica3_RT:=si
mplify(1/2*subs( X=x1-1/(4*sqrt(2)),Y=y1-sqrt(2)/16,conica3_R));" }
{TEXT -1 23 " parabola rototraslata " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 78 "implicitplot(conica3_RT,x1=-1..1,y1=-1..2,scaling=CON
STRAINED,numpoints=1000);" }}}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Q
uadriche" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 7 "Esempio" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "A:=matrix([[1,0,0],[0,2,0],[0,0,3]
]); h:=[1,1,0]; k:=1;\nquadrica1:=simplify(evalm([x,y,z]&*A&*[x,y,z])+
2*evalm(h&*[x,y,z])+k);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 
"implicitplot3d(quadrica1,x=-2..0,y=-1..1,z=-1..1,scaling=CONSTRAINED,
axes=NORMAL,style=PATCHNOGRID,grid=[20,20,20]);" }{TEXT -1 1 " " }}
{PARA 0 "" 0 "" {TEXT -1 85 "ellissoide con assi di simmetria parallel
i agli assi coordinati, centro in (-1,1/2,0)" }}}}{SECT 1 {PARA 4 "" 
0 "" {TEXT -1 4 "Cono" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "pl
ot3d([z*cos(t),z*sin(t),z],z=-2..2,t=-Pi..Pi,scaling=CONSTRAINED,axes=
NORMAL,style=PATCH,orientation=[60,60],grid=[30,30]); " }}{PARA 0 "" 
0 "" {TEXT -1 92 "cono di equazione x^2+y^2=z^2 (in forma parametrica:
 x=z cos(t), y= z sin(t), z,t parametri)" }}{PARA 0 "" 0 "" {TEXT -1 
79 "il piano per P=(1,0,1) normale al vettore n=(1,0,c) ha equazione (
x-1)+c(z-1)=0" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 15 "Sezioni coniche
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 136 "plot3d(\{[z*cos(t),z*si
n(t),z],[1,t,z]\},z=-2..2,t=-Pi..Pi,scaling=CONSTRAINED,axes=NORMAL,st
yle=PATCH,orientation=[60,60],grid=[30,30]); " }}{PARA 0 "" 0 "" 
{TEXT -1 76 "(inter)sezione del cono di equazione x^2+y^2=z^2 con il p
iano x=1 (caso c=0)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 137 "plo
t3d(\{[z*cos(t),z*sin(t),z],[2-z,t,z]\},z=-2..3,t=-Pi..Pi,scaling=CONS
TRAINED,axes=NORMAL,style=PATCH,orientation=[60,60],grid=[30,30]);" }
{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 80 "(inter)sezione del cono \+
di equazione x^2+y^2=z^2 con il piano x+z-2=0 (caso c=1)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 139 "plot3d(\{[z*cos(t),z*sin(t),z],[3-
2*z,t,z]\},z=-2..3,t=-Pi..Pi,scaling=CONSTRAINED,axes=NORMAL,style=PAT
CH,orientation=[60,60],grid=[30,30]);" }{TEXT -1 1 " " }}{PARA 0 "" 0 
"" {TEXT -1 81 "(inter)sezione del cono di equazione x^2+y^2=z^2 con i
l piano x+2z-3=0 (caso c=2)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
135 "plot3d(\{[z*cos(t),z*sin(t),z],[z,t,1]\},z=-2..2,t=-Pi..Pi,scalin
g=CONSTRAINED,axes=NORMAL,style=PATCH,orientation=[60,60],grid=[30,30]
);" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 66 "(inter)sezione del \+
cono di equazione x^2+y^2=z^2 con il piano z=1 " }}}}}}}{MARK "2" 0 }
{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }