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D.8.2.5 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:
 
See also: vandermonde.


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