Help:=proc(): print(`Leg(n,x) `):end:

 
   #Leg(n,x): inputs a positive integer n and a symbol x
   #outputs the polynomial P(x) of degree n in x such that
   #int(x^i*P(x),x=0..1)=0 for i=0,1,...,n
   Leg:=proc(n,x) local P,eq,var,a,i:
     P:=add(a[i]*x^i,i=0..n):
      var:={seq(a[i],i=0..n)}:
      eq:={a[0]=1,seq(int(x^i*P,x=0..1)=0,i=0..n-1)}:
       P:=subs(solve(eq,var),P):
        
       end: