restart;
dp:=(p,q)->int(p*q,x=-1..1);
nm:=p->sqrt(dp(p,p));
nm(1);
nm(x);
n:=8;
for i from 1 to n
do
    t[i]:=x^(i-1);
    for k from 1 to i-1
    do
        t[i]:=t[i]-dp(x^(i-1),v[k])*v[k];
    od;
    v[i]:=t[i]/nm(t[i]);
od:
for i from 1 to n
do
     print(v[i]);
od:
pl:=[seq(v[j],j=1..n)];
plot(pl,x=-1..1);
plot(v[6],x=-1..1);
v[6];
fsolve(v[6]=0,x);
v[7];
S:=fsolve(v[8]=0,x);
Digits:=20;
evalf(S);