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D.7.2.4 interpolate
Procedure from library solve.lib (see solve_lib).
- Usage:
- interpolate(p,v,d); p,v=ideals, d=integer
- Assume:
- ground field K are the rational numbers,
p and v are lists consisting of elements of the ground field K,
size(p)=n and size(v)=N=(d+1)^n where n=nvars(basering)
- Compute:
- polynomial f of degree d with prescribed values at certain points
p1,..,pN derived from p;
more precisely: consider p as point in K^n and v as N elements in K,
let pi=(p[1]^i,..,p[n]^i), i=1,..,N, then the procedure computes the
polynomial f of degree d satisfying f(pi) = v[i]
- Return:
- polynomial f of degree d
- 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
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