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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "rec:=\{u(1)=x,u(2)=x
^2-1,u(n+1)=x*u(n)-u(n-1)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$rec
G<%/-%\"uG6#\"\"\"%\"xG/-F(6#\"\"#,&*$F+F/F*!\"\"F*/-F(6#,&%\"nGF*F*F*
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{MPLTEXT 1 0 8 "dim:=10:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
165 "for d to dim do \n  A[d]:=array(1..d,1..d,sparse);\n  for i to d-
1 do A[d][i,i+1]:=1 od;\n  for i to d do A[d][i,i]:=x od;\n  for i fro
m 2 to d do A[d][i,i-1]:=1 od;\nod:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 50 "for d to dim do \n  Delta[d]:=linalg[det](A[d])\nod;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&DeltaG6#\"\"\"%\"xG" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>&%&DeltaG6#\"\"#,&*$%\"xGF'\"\"\"!\"\"F+" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&DeltaG6#\"\"$,&*$%\"xGF'\"\"\"F*!
\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&DeltaG6#\"\"%,(*$%\"xGF'\"
\"\"*$F*\"\"#!\"$F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&DeltaG6#
\"\"&,(*$%\"xGF'\"\"\"*$F*\"\"$!\"%F*F-" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>&%&DeltaG6#\"\"',*!\"\"\"\"\"*$%\"xG\"\"#F'*$F,\"\"%!\"&*$F,F'F
*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&DeltaG6#\"\"(,*%\"xG!\"%*$F)
\"\"$\"#5*$F)\"\"&!\"'*$F)F'\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>&%&DeltaG6#\"\"),,\"\"\"F)*$%\"xG\"\"#!#5*$F+\"\"%\"#:*$F+\"\"'!\"(*$
F+F'F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&DeltaG6#\"\"*,,%\"xG\"\"
&*$F)\"\"$!#?*$F)F*\"#@*$F)\"\"(!\")*$F)F'\"\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%&DeltaG6#\"#5,.!\"\"\"\"\"*$%\"xG\"\"#\"#:*$F,\"\"%!
#N*$F,\"\"'\"#G*$F,\"\")!\"**$F,F'F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 70 "for d from 3 to dim do collect(Delta[d]-x*Delta[d-1]+
Delta[d-2],x) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "U:=rsolve(rec,u
(n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UG,&*(,&*$%\"xG\"\"#\"\"
\"!\"%F+#!\"\"F*),$*$,&F)F+*$F'#F+F*F+F.F*%\"nGF+F2F.!\"#*(F'F-),$*$,&
F)F+F3F.F.F*F5F+F;F.F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "f
or nn to 2 do simplify(subs(n=nn,U),radical,symbolic) od;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#,$*(%\"xG\"\"\",&F%F&*$,&*$F%\"\"#F&!\"%F&#F&F+
F&!\"#,&F%!\"\"F(F&F.\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(,&*$%
\"xG\"\"#\"\"\"!\"\"F)F),&F'F)*$,&F&F)!\"%F)#F)F(F)!\"$,&F'F)F,F*F0\"#
k" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "for nn to 2 do   subs(
n=nn,(x^2-4)^(1/2)=y,(x^2-4)^(-1/2)=1/y,U) od;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*&%\"yG!\"\",&%\"xG\"\"\"F%F)!\"#!\"%*&F%F&,&F(F)F%F&
F*\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"yG!\"\",&%\"xG\"\"\"
F%F)!\"$!\")*&F%F&,&F(F)F%F&F*\"\")" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 95 "for nn to 2 do   expr[nn]:=normal(subs(n=nn,(x^2-4)^(
1/2)=y,(x^2-4)^(-1/2)=1/y,U),expanded) od;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%%exprG6#\"\"\",$*&%\"xGF',(*$F*\"\"%F'*&F*\"\"#%\"yG
F/!\"#*$F0F-F'!\"\"\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%exprG6#
\"\"#*&,&*$%\"xGF'\"#[*$%\"yGF'\"#;\"\"\",**$F+\"\"'F0*&F+\"\"%F.F'!\"
$*&F+F'F.F5\"\"$*$F.F3!\"\"F:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 47 "for nn to 2 do subs(y=sqrt(x^2-4),expr[nn]) od;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,$*&%\"xG\"\"\",(*$F%\"\"%F&*&F%\"\"#,&*$F%F+F&!\"
%F&F&!\"#*$F,F+F&!\"\"\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*$%
\"xG\"\"#\"#k!#k\"\"\"F*,**$F&\"\"'F**&F&\"\"%,&F%F*!\"%F*F*!\"$*&F&F'
F0F'\"\"$*$F0F4!\"\"F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "f
or nn to 2 do normal(subs(y=sqrt(x^2-4),expr[nn]),expanded) od;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,&*$%\"xG\"\"#\"\"\"!\"\"F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 134 "for nn to dim do\n  normal(subs(y=sqrt(x^2-4), \n    normal(s
ubs(n=nn,(x^2-4)^(1/2)=y,(x^2-4)^(-1/2)=1/y,U),expanded)),\n  expanded
)\nod; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"xG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*$%\"xG\"\"#\"\"\"!\"\"F'" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*$%\"xG\"\"$\"\"\"F%!\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*$%\"xG\"\"%\"\"\"*$F%\"\"#!\"$F'F'" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#,(*$%\"xG\"\"&\"\"\"*$F%\"\"$!\"%F%F)" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,*!\"\"\"\"\"*$%\"xG\"\"#\"\"'*$F'\"\"%!\"&*$F'F
)F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*%\"xG!\"%*$F$\"\"$\"#5*$F$\"
\"&!\"'*$F$\"\"(\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,\"\"\"F$*$
%\"xG\"\"#!#5*$F&\"\"%\"#:*$F&\"\"'!\"(*$F&\"\")F$" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#,,%\"xG\"\"&*$F$\"\"$!#?*$F$F%\"#@*$F$\"\"(!\")*$F$\"
\"*\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.!\"\"\"\"\"*$%\"xG\"\"#
\"#:*$F'\"\"%!#N*$F'\"\"'\"#G*$F'\"\")!\"**$F'\"#5F%" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 100 "C:=array(1..dim,1..dim,sparse):\nfor nn \+
to dim do for i to nn do C[nn,i]:=coeff(Delta[nn],x,i) od od:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(C);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%'MATRIXG6#7,7,\"\"\"\"\"!F)F)F)F)F)F)F)F)7,F)F(F)F)
F)F)F)F)F)F)7,!\"#F)F(F)F)F)F)F)F)F)7,F)!\"$F)F(F)F)F)F)F)F)7,\"\"$F)!
\"%F)F(F)F)F)F)F)7,F)\"\"'F)!\"&F)F(F)F)F)F)7,F1F)\"#5F)!\"'F)F(F)F)F)
7,F)!#5F)\"#:F)!\"(F)F(F)F)7,\"\"&F)!#?F)\"#@F)!\")F)F(F)7,F)F:F)!#NF)
\"#GF)!\"*F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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