-- Lagrange formula for the interpolating polynomial
-- of degree N passing through N points. 

P(x) = sum(y[k]*L(x)[k],k,1,N)

L(t)[k] = m:=1, r:=1,
     ((r:=r*(t-x[m])/(x[k]-x[m]) when m!=k),,
       m:=m+1) while mēN, r

-- try some points
x={1,4,9,16,25,36,49,64,81,100}[:N]
y={4,8,8,11,12,18,25,44,56,80} [:N]

N=6
plot {x,y}
plot P(X)