|
D.8.4.5 interpolate
Procedure from library solve.lib (see solve_lib).
- Usage:
- interpolate(p,v,d); p,v=ideals of numbers, d=integer
- Assume:
- Ground field K is the field of rational numbers, p and v are lists
of elements of the ground field K with p[j] != -1,0,1, size(p) = n
(= number of vars) and size(v)=N=(d+1)^n.
- Return:
- poly f, the unique polynomial f of degree n*d with prescribed values
v[i] at the points p(i)=(p[1]^(i-1),..,p[n]^(i-1)), i=1,..,N.
- Note:
- mainly useful when n=1, i.e. f is satisfying f(p^(i-1)) = v[i],
i=1..d+1.
Example:
| LIB "solve.lib";
ring r1 = 0,(x),lp;
// determine f with deg(f) = 4 and
// v = values of f at points 3^0, 3^1, 3^2, 3^3, 3^4
ideal v=16,0,11376,1046880,85949136;
interpolate( 3, v, 4 );
==> 2x4-22x2+36
| See also:
vandermonde.
|