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{SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT -1 27 "NUMEERISEN ANALYYSIN DEM
OT " }{TEXT 258 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 27 "Richardso
nin ekstrapolaatio" }}{EXCHG {PARA 4 "" 0 "" {TEXT -1 30 "funktion der
ivaatan laskeminen" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "restart:g:=x-
>sin(x^2)*(x-0.1)/x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "h[0
]:=1.0000;n:=4;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f0:=limit(g(t),t
=0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 
4 "" 0 "" {TEXT -1 21 "tasav\344linen pisteist\366" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "d[i]:=(f[i]-
f(0))/h[i];  p[i,0]:='d[i]';" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "y:=
'y':k:='k':" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "for i from 0 to n do
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "lprint(`h[`||i||`]`,p[i,0]=d[i]
,seq((p[i,k]),k=1..i));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "od:i:='i
':" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "print(` `);" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 58 "p[i,k]:=p[i,k-1]+(p[i,k-1]-p[i-1,k-1])/(h[i-k]/h
[i]-1);   " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "h:=[h[0],seq(
h[0]-0.2*k,k=1..n)];h:=array(0..n,h):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "f:=[seq(g(h[k]),k=0..n)];f:=array(0..n,f):" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 67 "pointplot([[0,0],seq([h[k],f[k]],k=0..n)],symbol=circ
le,color=red);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "for i fro
m 0 to n do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "     d[i]:=(f[i]-f0)
/h[i];  p[i,0]:=d[i];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "     for k
 to i do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "            p[i,k]:=p[
i,k-1]+(p[i,k-1]-p[i-1,k-1])/" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "  \+
         (h[i-k]/h[i]-1);                 " }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "     od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "k:='k':
Digits:=5:lprint(h[i],seq(evalf(p[i,k]),k=0..i));Digits:=10:" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 14 "Rombergin jono" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "N:=10;R:=[seq(2^k,k=0..N)];R
:=array(0..N,R):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "i:='i':
k:='k':f[0]:='f[0]':" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "d[i]:=(f[i]
-f[0])/h[i];  p[i,0]:='d[i]';" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "p[
i,k]:=p[i,k-1]+(p[i,k-1]-p[i-1,k-1])/(R[i]/R[i-k]-1);   " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "h:=[h[0],seq(h[0]/R[k],k=1..n)];h:=
array(0..n,h):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "f:=[seq(g(h[0]/R[
k]),k=0..n)];f:=array(0..n,f):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "p
ointplot([[0,0],seq([h[k],f[k]],k=0..n)],symbol=circle,color=red);" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 27 "for i from 0 to n do       " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
41 "    d[i]:=(f[i]-f0)/h[i];  p[i,0]:=d[i]; " }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "    for k to i do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
44 "      p[i,k]:=p[i,k-1]+(p[i,k-1]-p[i-1,k-1])" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "      /(R[i]/R[i-k]-1);              od:" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 71 "Digits:=5:lprint(evalf(h[i]),seq(evalf(p[i,k
]),k=0..i));Digits:=10: od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{PARA 4 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" 
{TEXT -1 15 "Bulirschin jono" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
102 "N:=20; B[0]:=1:B[1]:=2.:B[2]:=3.:for k from 3 to N do B[k]:=2.*B[
k-2] od: print(B=[seq(B[k],k=0..N)]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "h:=[h[0],seq(h[0]/B[k],k=1..n)];h:=array(0..n,h):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "f:=[seq(g(h[0]/B[k]),k=0..n)];f:=ar
ray(0..n,f):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "pointplot([[0,0],se
q([h[k],f[k]],k=0..n)],symbol=circle,color=red);" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "for i from \+
0 to n do                " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "    d[
i]:=(f[i]-f0)/h[i]; p[i,0]:=d[i];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
18 "    for k to i do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "        p
[i,k]:=p[i,k-1]+(p[i,k-1]-p[i-1,k-1])/(B[i]/B[i-k]-1);" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 7 "    od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "D
igits:=5:lprint(evalf(h[i]),seq(evalf(p[i,k]),k=0..i));Digits:=10: od:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 4 "" 0 "" 
{TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 22 "derivaatan tarkk
a arvo" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "dd:=D(g);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "limit(dd(x),x=0);" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{SECT 1 {PARA 3 "" 0 "" {TEXT -1 29 "Pienimm\344n neli\366summan sovit
us" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "restart:with(linalg):D
igits:=4:N:=6:" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 25 "1. asteen poly
nomisovitus" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "y=a[1]+a[2]*x
;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "F:=matrix([seq([seq(x[i]^j,j=0
..1)],i=1..N)]);y:=vector(N):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 46 
"Normaaliyht\344l\366n kerroinmatriisi ja oikeapuoli:" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 52 "M:=evalm(transpose(F)&*F);b:=evalm(transpose(F)&
*y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 303 "N:=20:x := [1.150,
 3.450, 5.630, 7.650, 10.97, 12.50, 14.79, 16.56, 18.49, 20.63, 22.57,
 23.41, 26.45, 27.92, 29.07, 32.92, 34.43, 35.38, 38.77, 40.66];     y
 := [10.13, 9.520, 10.29, 10.09, 11.66, 12.72, 14.14, 15.60, 16.70, 18
.13, 19.97, 20.39, 22.63, 24.05, 24.94, 28.66, 29.44, 30.08, 33.68, 35
.02];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 118 "with(plots):point
plot([seq([x[j],y[j]],j=1..N)],symbol=circle);pp:=pointplot([seq([x[j]
,y[j]],j=1..N)],symbol=circle):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 46 "F:=matrix([seq([seq(x[i]^j,j=0..1)],i=1..N)]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "M:=evalm(transpose(F)&*F);b:=evalm(
transpose(F)&*y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "augmen
t(M,b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "gausselim(%);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "a:=backsub(%);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "p1:=evalm(transpose(a)&*[1,t]);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "pp1:=plot(p1,t=0..2*N+1,col
or=blue):display(\{pp1,pp\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" 
{TEXT -1 25 "2. asteen polynomisovitus" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 36 "restart:with(linalg):Digits:=4:N:=4:" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "y=a
[1]+a[2]*x+a[3]*x^2;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "F:=matrix([
seq([seq(x[i]^j,j=0..2)],i=1..N)]);y:=vector(N):" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT 257 46 "Normaaliyht\344l\366n kerroinmatriisi ja oikeapuo
li:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "M:=evalm(transpose(F)&*F);b:
=evalm(transpose(F)&*y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
303 "N:=20:x := [1.150, 3.450, 5.630, 7.650, 10.97, 12.50, 14.79, 16.5
6, 18.49, 20.63, 22.57, 23.41, 26.45, 27.92, 29.07, 32.92, 34.43, 35.3
8, 38.77, 40.66];     y := [10.13, 9.520, 10.29, 10.09, 11.66, 12.72, \+
14.14, 15.60, 16.70, 18.13, 19.97, 20.39, 22.63, 24.05, 24.94, 28.66, \+
29.44, 30.08, 33.68, 35.02];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 142 "wi
th(plots):pointplot([seq([x[j],y[j]],j=1..N)],style=point,symbol=circl
e);pp:=pointplot([seq([x[j],y[j]],j=1..N)],style=point,symbol=circle):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "n:=2;F:=matrix([seq([se
q(x[i]^j,j=0..n)],i=1..N)]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 52 "M:=evalm(transpose(F)&*F);b:=evalm(transpose(F)&*y);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "augment(M,b);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 13 "gausselim(%);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "a:=backsub(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 43 "p2:=evalm(transpose(a)&*[seq(t^k,k=0..n)]);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 36 "pp2:=plot(p2,t=0..2*N+1,color=blue):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "with(plots):display(\{pp2,pp
\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 147 "Digits:=10:det(M),
det(inverse(M)),norm(M,2),norm(inverse(M),2),norm(M,2)*norm(inverse(M)
,2);Digits:=20:r:=evalm(b-M&*a);Digits:=10:norm(r)/norm(b);" }}}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 39 "Sovitu
s funktioilla   exp(x) ja exp(-x)" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 36 "restart:with(linalg):Digits:=4:N:=4:" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "y=a
[1]*exp(x)+a[2]*exp(-x);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "F:=matr
ix([seq([exp(x[i]),exp(-x[i])],i=1..N)]); y:=vector(N):" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 260 46 "Normaaliyht\344l\366n kerroinmatriisi ja
 oikeapuoli:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "M:=evalm(transpose(
F)&*F);b:=evalm(transpose(F)&*y);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 91 "N:=12:x:=[0.015, 0.145, 0.263, 0.365, 0.597, 0.650, 0
.779, 0.856, 0.949, 1.06, 1.16, 1.14];" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 76 "y:=[20.1, 18.3, 16.7, 15.6, 13.2, 12.6, 11.5, 10.9, 10.2, 9.34
, 8.77, 8.79];" }}{PARA 11 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 142 "with(plots):pointplot([seq([x[j],y[j]],j=1..N)],styl
e=point,symbol=circle);pp:=pointplot([seq([x[j],y[j]],j=1..N)],style=p
oint,symbol=circle):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "F:=
matrix([seq([exp(x[i]),exp(-x[i])],i=1..N)]);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 52 "M:=evalm(transpose(F)&*F);b:=evalm(transpose(F)&
*y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "augment(M,b);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "gausselim(%);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "a:=backsub(%);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 44 "exps:=evalm(transpose(a)&*[exp(t),exp(-t)]);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "exppl:=plot(exps,t=0..0
.1*(N+1),color=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "with(plots
):display(\{exppl,pp\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 
-1 26 "Linearisointi sovituksessa" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "g:=t->A*exp(B*t); h:=x->A*t^B;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 90 "N:=5:Digits:=5:x:=[1.06, 1.93, 2.92, 4.18, 4.8
5];       y:=[0.78, 1.81, 3.27, 5.88, 7.84];" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 106 "pointplot([seq([x[i],y[i]],i=1..N)],symbol=circ
le);pp:=pointplot([seq([x[i],y[i]],i=1..N)],symbol=circle):" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 258 49 "a)               (ln(g(t)) =  ln(
A) + B t = ln(y)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "ln('A') + 'B'*t = l
n('y');" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "F:=matrix([seq([1.,x[i]
],i=1..N)]);M:=evalm(transpose(F)&*F);b:=evalm(transpose(F)&*[seq(ln(y
[i]),i=1..nops(y))]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "au
gment(M,b);gausselim(%);k:=backsub(%);A:=exp(k[1]);B:=k[2];" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g(t);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 70 "expp:=plot(g(t),t=0..x[N],color=blue): with(pl
ots):display(\{expp,pp\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 43 "b)
   ln(h(t))  =    ln(A) + B ln(t) = ln(y)" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "ln('A') + 'B'*ln(t) = ln('y'
);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 119 "F:=matrix([seq([1.,ln(x[i])]
,i=1..N)]);M:=evalm(transpose(F)&*F);bb:=evalm(transpose(F)&*[seq(ln(y
[i]),i=1..nops(y))]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "au
gment(M,bb);gausselim(%);k:=backsub(%);A:=exp(k[1]);B:=k[2];" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "h(t);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 76 "potp:=plot(h(t),t=0..x[N],color=black): with(p
lots):display(\{potp,expp,pp\});" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 
"" 0 "" {TEXT -1 22 "Kahden muuttujan malli" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 21 "restart:with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 121 "x:=[1.,2.,4.];y:=[1.,3.,6.];z := matrix([[1.5300, 4.
9900, 10.126], [.83000, 6.8940, 15.500], [-.54200, 10.012, 25.898]]);
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 110 "with(plots):pp:=pointplot3d(\{seq(seq([x[i],y[j],z[i
,j]],i=1..3),j=1..3)\},symbol=circle,color=red):display(pp);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "z=a[1]+a[2]*'x'+a[3]*'y'+a[4
]*'x'*'y';" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "x:=vector([se
q(seq(x[i],j=1..3),i=1..3)]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "y:
=vector([seq(seq(y[i],i=1..3),j=1..3)]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 67 "F:=augment(vector(3*3,i->1),x,y,vector(9,[seq(x[i]*y[
i],i=1..9)]));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "b:=vector
(9,[seq(seq(z[i,j],j=1..3),i=1..3)]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 63 "M:=evalm(transpose(F)&*F);Digits:=10:b:=evalm(transpo
se(F)&*b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "a:=linsolve(M
,b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "x:='x':y:='y':z:=ev
alm(transpose(a)&*[1,x,y,x*y]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 58 "zpl:=plot3d(z,x=0..4,y=0..6,color=blue):display(\{zpl,pp\});" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}}}}{MARK "0 0 0" 20 }{VIEWOPTS 1 1 0 3 4 
1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }